Handbook of X-ray and Gamma-ray Astrophysics 9789811969591, 9789811969607

Table of contents :
Preface
Contents
About the Editors
Section Editors
Contributors
Part I Introduction to X-ray Astrophysics
1 A Chronological History of X-ray Astronomy Missions
Contents
Introduction
The Early Years of X-Ray Astronomy
Rockets and Balloons in the 1960s and 1970s
Rockets
Balloons
Uhuru and the Others, Opening the Age of the Satellites in the Early 1970s
Uhuru
Apollo 15 and Apollo 16
SAS-3
Heao-1
The Late 1970s and the 1980s: The Program in the USA
Einstein
The Late 1970s and the 1980s: The Program in Europe
Copernicus
ans
Ariel V
Cos-b
ariel VI
exosat
Late 1970s and the 1980s: The Program in Japan
hakucho
Hinotori
tenma
Ginga
The Late 1970s and the 1980s: The Program in Russia and India
filin/salyut-4
skr-02m
xvantimir
aryabhata
bhaskara
The Golden Age of X-Ray Astronomy, From the 1990s to the Present
The Program in the USA
ulysses
bbxrt
Rxte
usa onboard argos
The Program in Europe
rosat
Bepposax
The Program in Japan
asca
suzaku
hitomi
The Program in Russia and India
granat
irs-p3
Conclusions
Cross-References
Appendix 1. List of the Rrockets Launched from 1957 to 1970
Appendix 2. List of the Balloon Missions Launched by the MIT Group
Appendix 3. List of the Balloon Missions Launched by Worldwide Institution
Appendix 4. Balloons Flown by AIT and MPI
Appendix 5. Transatlantic Balloons
References
Part II Optics for X-ray Astrophysics
2 X-ray Optics for Astrophysics: A Historical Review
Contents
Introduction
Early Days of X-Ray Astronomy
The Benefit of X-Ray Optics
Signal to Noise Advantage
Large Dynamic Range and Less Source Confusion
Use of High-Performance Detectors
The Challenges of Fabricating X-Ray Optics
X-Ray Reflection
Optical Configuration
Requirements on Figure and Surface
Trades in Mirror Fabrication Approaches
Overview of Fabrication Techniques
Full Shell Optics
Direct
Replication
Segmented Optics
Chronological List of Mission with X-Ray Optics
Early Days
1970s
1980s
1990s
2000s
2010s
2020s
Future
Conclusion
References
3 Geometries for Grazing Incidence Mirrors
Contents
Introduction
Origin and Adoption of the Wolter I Design
Geometry of Wolter I
Nesting Consideration
Practical Considerations for a Wolter I Telescope
Geometry of Conically Approximated Wolter I
Impact of Figure and Other Fabrication Errors on Angular Resolution
Geometry of Parabolic Optic, Single-Reflection Concentrator
Wolter-Schwarzschild (WS) and Hyperboloid-Hyperboloid Telescopes
X-Ray Optics Flown on Space Missions
Polynomial Designs and Other Recent Innovations
References
4 Lobster Eye X-ray Optics
Contents
Introduction
Lobster Eye X-ray Optics
Introduction
Lobster Eye Telescopes Using Micro Pore Optics
Introduction
MPOs: Production and Design
Design of a Narrow-Field-Optimized Lobster Eye Telescope
Limitations of MPOs
Current Missions
BepiColombo
SVOM
Einstein Probe
SMILE
Lobster Eye Optics in MFO/Schmidt Arrangement
Schmidt Objectives
Substrates for Lobster Eye Lenses in Schmidt/MFO Arrangement
The Application and the Future of Lobster Eye Telescopes in Schmidt Arrangements
Lobster Eye Laboratory Modifications
Hybrid Lobster Eye
Space Experiments with Lobster Eye MFO X-ray Optics
VZLUSAT-1
REX Rocket Experiment
Kirkpatrick-Baez Optics
K-B Systems in Astronomical Applications
K-B as a Segmented Mirror
K-B in Astronomical Telescopes: Recent Status and Future Plans
Conclusion
References
5 Single-Layer and Multilayer Coatings for Astronomical X-ray Mirrors
Contents
Introduction
Theory
X-Ray Reflection and Refraction
Surface Roughness
Materials
Single-Layer Thin Film Materials
Multilayer Thin Film Materials
Coating and Instrument Design
Single-Layer Design
Multilayer Design
Depositing Thin Film Coatings
Characterization of Thin Film Coatings
X-Ray Reflectometry
Other Characterization Techniques
Environmental Stability
Stress in Single and Multilayer Coatings
Stress Measurement Methods
The Stoney Equation
A Method of In Situ Stress Measurement
Contributions of Stress in Single-Layer Films
Effect of Adatom Mobility
Stress Reversal
Methods of Reducing Film Stress
Stress in Multilayer Thin Films
The Effect of Surface Energy on Film Stress
References
6 Silicon Pore Optics
Contents
Introduction
SPO Concept
Potential and Limitations of SPO
SPO Realization
Production of SPO Mirror Plates
Development of Coatings
Cleaning and Activation
Stacking of Mirror Plates
Stacking Robots
Mirror Modules
Ruggedisation
X-Ray Characterization
SPO Stack Characterization
XOU and MM Characterization
Athena
Introduction
Optical Design
Design and Expected Performance for the Athena Optics
Effective Area
Vignetting
Mirror Module Alignment
Mirror Assembly X-Ray Characterization
Summary and Conclusions
References
7 Miniature X-ray Optics for Meter-Class Focal Length Telescopes
Contents
Introduction
Existing X-Ray Optics Technology Leveraged for MiXO
Micropore Optics
Electroformed-Nickel-Replicated Optics
Design, Development, and Challenges in Miniature X-Ray Optics
Wolter Optics Design and Modeling
Ray Tracing
ENR and Metal-Ceramic Hybrid MiXO
Recent X-Ray Tests and Results
Testing MiXO Optics
Performance of ENR MiXO
Mission Concepts Using Miniature X-Ray Optics
Mercury Imaging X-Ray Spectrometer Onboard BepiColombo
Lunar X-Ray Imaging Spectrometer (LuXIS)
SmallSat Exosphere Explorer of Hot Jupiters (SEEJ)
SmallSat Solar X-Ray Activity and Axion X-Ray Imager (SSAXI)
Conclusion
References
8 Diffraction-Limited Optics and Techniques
Contents
Introduction
Focal Length
Diffraction-Limited X-Ray Optics
Reflecting Optics
Transmitting Optics
X-Ray Lens Design and Performance
Zone Plates
Interferometers
An X-Ray Interferometer
A Slatted Mirror
The Fringe Pattern
Simulation of One-Dimensional Imaging
Tolerances, Alignment, and Adjustment
An X-Ray Interferometer with Focusing
Proposed X-Ray Interferometers
Cross-References
References
9 Collimators for X-ray Astronomical Optics
Contents
Introduction
Stray Light and Baffle Design
Classification of the Stray Light
No Reflection
Primary-Only Reflection
Secondary-Only Reflection
Backside Reflection
Advanced Analytical Treatment
Design of the Stray-Light Baffle
XMM-Newton
Suzaku and Hitomi
Suzaku Pre-collimator
Optical Tuning
On-Ground and In-Orbit X-Ray Calibrations
Hitomi Pre-collimator
eROSITA
Future Missions
Conclusion
References
10 Technologies for Advanced X-ray Mirror Fabrication
Contents
Introduction
X-Ray Mirror Fabrication: Fundamentals
Manufacturing Methodologies
X-Ray Mirror Manufacture and Technology
Angular Resolution Versus Effective Area
Production Drivers for Future X-Ray Telescopes
Evaluating Optical Surfaces
Terminology: Basics
Terminology: Optical Surface
Materials
Section Review
Subtractive
Polishing: General
Polishing: Robotic
Ion Beam Figuring
Subtractive: Silicon
Silicon Pore Optics
Monocrystalline Silicon Meta-shell X-Ray Optics
Formative
Electroforming
Slumping
Differential Deposition
Fabricative
Active/Adjustable Optics
Additive
Additive Manufacture
Conclusion
References
11 Diffraction Gratings for X-ray Astronomy
Contents
Introduction: Diffraction Gratings
General Considerations
Physical Principles
Astrophysical Application
Implementation on Focusing X-Ray Telescopes: Slitless Spectrometers, the Rowland Circle, and Variable Line Density Gratings
Examples from Chandra and XMM-Newton
Manufacturing Techniques
Innovative Gratings: Off-Plane Reflection Gratings and the Critical Angle Transmission Grating
Off-Plane Reflection Gratings: High Dispersion and High Efficiency
The Critical Angle Transmission Grating: High Efficiency Combined with Generic Simplicity of a Transmission Grating
Future Diffraction Grating X-Ray Spectrometers
ARCUS
Lynx
References
12 Active X-ray Optics for Astronomy
Contents
Introduction
Corrections with Active Optics
Improving Mirror Figure
Active Mounting and Alignment
Prescription Switching
Characterizing Corrections During Calibration and Flight
Actuator Technologies
External Bonded Actuators
Thin-Film Actuators
Magnetic Smart Material (MSM) Optics
Assessing Correctability
Finite-Element Modeling
Influence Functions
Wavefront Reconstruction
Calculating Theoretical Correctability
Metrology and Model Assessment
Mission-Level Applications of Active X-ray Optics
Gen-X
SMART-X
Lynx
Conclusion
References
13 Facilities for X-ray Optics Calibration
Contents
Introduction
X Versus UV Light
Source Distance
Vacuum
Europe
The PANTER X-Ray Test Facility at MPE (Germany)
The XACT Facility at Palermo (Italy)
The Leicester Long Beamline Test Facility (UK)
The IKI 60 m X-ray Facility (Russia)
United States
X-ray and Cryogenic Facility at MSFC (Huntsville, AL)
The 100-m X-ray Facility at MSFC (Huntsville, AL)
The 100-m X-ray Beamline at NASA GSFC (Greenbelt, MD)
The 47-m X-ray Beamline at PSU (University Park, PA)
Asia
The ISAS 30m X-ray Pencil Beamline (Japan)
The IHEP 100m X-ray Testing Facility (China)
Synchrotron Radiation Facilities
Remarks Concerning Existing X-ray Facilities
Future Facilities
BEaTriX at INAF-OABrera (Italy)
The Vertical X-ray Raster-Scan Facility (Italy)
References
14 Charge Coupled Devices
Contents
Introduction
CCD Sensor Architectures for X-Ray Imaging
Principles of Operation
Architectures
Key X-Ray CCD Sensor Performance Characteristics
Charge Collection
Depletion Depth
Charge Transfer
Read Noise
Dark Current
Scientific Instrument Performance Characteristics
Spectral Resolution
Detection Efficiency
Spatial Resolution
Time Resolution
Instrumental Background and Mitigation
Radiation Damage
TID Effects
TNID Effects
Mitigation
Flight Systems and Performance Over Time
Chandra-ACIS, Suzaku, and OSIRES REX
XMM-Newton and E2V Heritage CCDs
XMM-Newton PN CCD and EROSITA
MAXI and HITOMI
In-Flight Resolution
Instrumental Background
Micrometeorite Damage
Molecular Contamination
Missions in Development
CCD Technology Under Development
Conclusion
References
Part III Detectors for X-ray Astrophysics
15 X-ray Detectors for Astrophysics
Contents
Introduction
The Detection of Photons
Interaction with Matter
Detection of Photons
Scintillation Photons
Electron-Ion Pairs
Electron-Hole Pairs
Quasiparticles
Phonons
X-Ray Detectors
Detector Properties
Compatibility with Space Missions
Overview of Detectors
Scintillators
Proportional Chambers
Microchannel Plates
Silicon-Based Detectors
Si-PIN Diodes
Silicon Strip Detectors
Silicon Drift Detectors
Charge Coupled Devices
Active Pixel Sensors
High-Z Semiconductors
Superconducting Tunnel Junctions
Microcalorimeters
Polarization Sensitive Gas Detectors
Detectors Based on the Compton Effect
Detector Performance and Applications
Conclusion and Outlook
Cross-References
References
16 Proportional Counters and Microchannel Plates
Contents
Introduction
Proportional Counters
Photon Interaction via the Photoelectric Effect
Gas Multiplication and Energy Resolution
Detection Efficiency and Response Function
Time Resolution, Dead Time, and Rate Limitation
Operation in Space: Background and Lifetime
Imaging Proportional Counters
Position Resolution
Imaging Proportional Counters in X-ray Astronomy
Micropattern Gas Detectors and X-ray Polarimetry
Microchannel Plate Detectors
Channel Electron Multipliers
Microchannel Plates
Operation of MCPs in Detectors
Quantum Detection Efficiency
Position-Sensitive Readout, Spatial, and Temporal Resolution
Applications in EUV and X-ray Astronomy
Future Prospects
Cross-References
References
17 Silicon Drift Detectors
Contents
Introduction
Basics of Silicon Detector
The Silicon Substrate Material
Detector Manufacturing, the Planar Process
The P-N Junction
Signal and Leakage Current
Silicon Drift Detectors
X-ray Spectroscopy with Large-Area SDD
Optimization of the Large-Area SDD Design for Low-Energy X-rays
Surface Control: Pitch and Punch-Through
Power Consumption
Quantum Efficiency
Prototype Production and Experimental Results
Surface Control and Leakage Current
Quantum Efficiency Improvement Tests
Anode Pitch Optimization
Radiation Damage
Dopant Inhomogeneity
SDD Characterization for Space Operation
Drift Detector Pixels
Matrices of Drift Detector Pixels
XGIS and Large SDD Pixel Matrixes
Conclusions
References
18 CMOS Active Pixel Sensors
Contents
Introduction
Overview of CMOS Technology
Hybrid Sensors
Silicon-on-Insulator
3D Technologies
Monolithic Sensors
Flight Opportunities
Conclusions
References
19 DEPFET Active Pixel Sensors
Contents
Introduction
Detector Concept
DEPFET Principle
Photon Interaction
Charge Collection
Steering and Readout Electronics
Operation
Performance Characteristics
Energy Resolution
Performance Degradation in Space
Example Case: ATHENA WFI Detector
Calibration
Outlook for DEPFET Options
Linear Gate Layout
Prevention of Energy Misfits
Conclusion
Cross-References
References
20 Transition-Edge Sensors for Cryogenic X-ray Imaging Spectrometers
Contents
Introduction
Theoretical and Experimental Background
Basic Principles
TES Electrical and Thermal Response
Negative Electrothermal Feedback
Fundamental Noise Sources
Non-linearity
Pulse Processing
Detector Design
TES Properties
Thermal Isolation
Absorber Design and Properties
Current State of the Art
Physics of the Superconducting Transition
The Superconducting Transition
Josephson Effects in DC- and AC-Biased TESs
Implication of the Weak-Link Behaviour on the Detector Noise
Detector Calibration Considerations
Response Function
Energy Scale and Sensitivity to Environmental Fluctuations
Drift Correction Algorithms
Multi-Pixel TESs
Applications and Future Technology Needs
Ground-Based Instrumentation
Next-Generation Space Mission Concepts
References
21 Signal Readout for Transition-Edge Sensor X-ray Imaging Spectrometers
Contents
Introduction
Basic Concepts of Signal Readout
Impedance Matching
dc Superconducting Quantum Interference Device (DC-SQUID)
Principles of Multiplexed Readout of X-ray TES Microcalorimeters
Why Is Multiplexed Readout Necessary?
General Considerations
Time-Division Multiplexing (TDM)
Principles of TDM Operation
Circuit Parameters, Multiplexing Factor, and Noise Scaling
Room-Temperature Electronics
Laboratory TDM Systems
Optimizations for Space Flight: Athena X-IFU
MHz Frequency-Domain Multiplexing (FDM)
Room-Temperature Electronics
Lithographic LC Filter
Demonstrations
Demonstration Model of Focal Plane Assembly of Athena X-IFU
Microwave-SQUID Multiplexing (mux)
Flux-Ramp Modulation
mux Readout Noise
mux Crosstalk
mux Optimization for X-ray Applications
Example mux Systems
Summary and Future Prospects
Cross-References
References
22 Introduction to Photoelectric X-ray Polarimeters
Contents
Introduction
Historical Context
The Statistical Demands of Astronomical Polarimetry
Polarization Sensitivity of the Photoelectric Interaction
Photoelectric Polarimetry with MPGD Track Imagers
Photoelectron Track Image Quality
Data Analysis Techniques
MPGD Photoelectric Polarimeter Implementations
References
23 Gas Pixel Detectors for Photoelectric X-ray Astronomical Polarimetry
Contents
Introduction
The Driver to the Design and the Historic Evolution
The Baseline Polarimeter
The Analysis of the Photoelectron Track
The Performances: Efficiency, Space Resolution, Energy Resolution, Spurious Modulation, and Modulation Factor
Advantages of the GPD Design
Issues of the Current GPD Design
An Outlook to the Future
Conclusion
References
24 Time Projection Chamber X-ray Polarimeters
Contents
Introduction
Photoelectron Track Imaging with a Micropattern TPC
Design and Operational Considerations
Component-Level Considerations
Drift Field in the Conversion Region
Multiplication Stage
Induction Gap and Induction Field
Anode Readout Strips
Readout Electronics
Instrument-Level Considerations
Calibration
Rotation
Detector Lifetime
TPC Polarimeter Implementations
The PRAXyS TPC Polarimeter
PRAXyS TPC Polarimeter Components
PRAXyS Active Volume/Drift Region
PRAXyS Gas Electron Multipliers
PRAXyS Induction Gap
PRAXyS Readout Electrodes
PRAXyS Readout Electronics and Signal Processing
PRAXyS TPC Polarimeter Performance
PRAXyS Polarization Sensitivity
PRAXyS Background
PRAXyS Systematic Errors
PRAXyS Mission Capabilities
The Hard X-ray Photoelectric Polarimeter
A Wide Field-of-View Polarimeter for X-ray Transients
Other NITPC Polarimeter Implementations
Conclusion
Cross-References
References
25 Compton Polarimetry
Contents
Introduction
Definitions and Useful Formulae
Polarimeter Design
General Concept of a Compton Scattering Polarimeter
Readout Sensors for Scattering Polarimeters
Single-Phase Scattering Polarimeters
Dual-Phase Scattering Polarimeters
Electronics
Systematic Effects and Calibration
Background Estimation and Mitigation
Operational Issues
Conclusions and Future Perspectives
Cross-References
References
26 In-Orbit Background for X-ray Detectors
Contents
Introduction
The Space Environment for a X-Ray Mission
Orbits and Their Characteristics
The Geomagnetic Field and the Radiation Belts
Trapped Particles
Solar Particles
Cosmic Rays
Neutron Albedo Radiation
Cosmic X-Ray Diffuse Background
Galactic Diffuse Emission
Earth Gamma Ray Albedo Radiation
Radiation Effects on Detectors
Radiation Damage
Scientific Background Effects
Photon Background
Charged Particles
Activation
Background Simulation, Mitigation, and Evaluation Strategies
The Monte Carlo Approach
Mitigation Strategies
Onboard or On-Ground Evaluation
Summary and Conclusions
References
27 Filters for X-ray Detectors on Space Missions
Contents
Introduction
Overview of Filters on Space X-Ray Observatories
Functional Goals
Requirements and Design Drivers
Materials and Technologies
Performance Modeling
X-Ray Transmission
UV/VIS/IR Transmission
Mechanical and Thermal Analysis
Characterization Techniques
X-Ray Transmission Spectroscopy and Imaging
UV/VIS/IR Spectroscopy
X-Ray Photoelectron Spectroscopy
Radio Frequency Shielding Effectiveness
Imaging and Microscopy
Environmental Tests
Mechanical Loads
Calibration
Future Perspectives
References
28 Silicon Strip Detectors
Contents
Introduction
General Properties of Silicon Strip Detector
Energy Resolution of Silicon Strip Detector
Development of Double-Sided Silicon Strip Detector for X-Ray Imaging and Spectroscopy
Performance of Double-Sided Silicon Strip Detector for Focusing Optics X-Ray Solar Imager
Performance of Hard X-Ray Imager Onboard Hitomi Satellite
Overview of DSSD Onboard Hitomi
Readout Noise
Low Energy Threshold
Energy Resolution
Time Resolution and Dead Time
Detection Efficiency
Imaging Performance
In-Orbit Background
Summary of the Performance of the HXI DSSD
Conclusion
References
Part IV X-ray Missions
29 The AstroSat Observatory
Contents
Introduction
AstroSat: Configuration and Auxiliary Instruments
The Attitude and Orbit Control System (AOCS)
Timing Information
Power Source
Thermal Control
The Bus Management Unit
Data Storage and Handling
Communications Systems
Choice of Orbit
Scientific Payload
Ultraviolet Imaging Telescopes (UVIT)
UVIT Filters
UVIT Gratings
UVIT Analysis Software
Large-Area X-Ray Proportional Counters (LAXPC)
LAXPC Data Analysis
Soft X-Ray Focusing Telescope (SXT)
SXT Data Analysis
Cadmium–Zinc–Telluride Imager (CZTI)
CZTI Data Products and Analysis
Scanning Sky Monitor (SSM)
Charged Particle Monitor (CPM)
Conclusions
References
30 The BepiColombo Mercury Imaging X-ray Spectrometer
Contents
Introduction
The Mercury Imaging X-Ray Spectrometer (MIXS)
Optics
MIXS-T Design
MIXS-C Design
Detectors and Electronics
MIXS Performance
Calibration and Data Analysis
The Grain Size Effect
The Phase Angle Effect
Numerical Simulation of Regolith Effects
Future Work Towards a New Semi-analytical Computational Solution
Complementing Planetary Spectroscopy at Ultraviolet, Visible, and Near-Infrared Light
Ground Calibration
Summary of Ground-Based Activities
The Solar Intensity X-Ray and Particle Spectrometer (SIXS)
Technical Specification
X-Ray Detection System
The Particle Detection System
Performance
X-Ray Detection System
Particle Detection System
Science Objectives
MIXS Scientific Requirements
Mercury as an X-Ray Target
The Sun as an X-Ray Source
Particle-Induced Signals
MIXS Science Objectives
Global Coverage
Spatially Resolved Measurements
Particle-Induced X-Ray Fluorescence
Science Operations
SIXS Scientific Requirements
Consortia and Data Rights
Instrument Consortia
Data Rights
Opportunities from MIXS
X-Ray Navigation
Einstein Probe
SVOM
SMILE
Outer Solar System
Auroral Imager
Conclusions and Outlook
References
31 The Chandra X-ray Observatory
Contents
Introduction
Building Chandra
Brief History, Including Initial Design Concept
Restructured Mission
Ground Calibration
Launch
The Chandra X-ray Observatory (Chandra)
The Spacecraft
The Telescope
High Resolution Mirror Assembly (HRMA)
High Energy Transmission Grating (HETG)
Low Energy Transmission Grating (LETG)
The Science Instruments
The Advanced CCD Imaging Spectrometer (ACIS)
The High Resolution Camera (HRC)
The Chandra X-ray Center (CXC)
Science Selection
Mission Planning
Operations
Data Processing
Data Analysis: CIAO
The Chandra Archive
Chandra Source Catalog, CSC
Chandra's Impact on Science and the Public
Chandra's Science Impact
Chandra's Worldwide Impact
Chandra's Future
Evolving Science
Aging Spacecraft
References
32 The HaloSat and PolarLight CubeSat Missions for X-ray Astrophysics
Contents
Introduction
HaloSat
Scientific Goals
Mission and Operations Design
Science Instrument Development and Calibration
Science Results
Data Archive
PolarLight
Detector
Payload
Performance
Operation
On-Orbit Background
Science Results
Conclusions and Discussion
References
33 The Einstein Probe Mission
Contents
Introduction
Background
Scientific Motivations
The Einstein Probe Mission
Science Objectives
New Technologies Employed
Lobster-Eye Micro-pore Optics
CMOS Detectors
Scientific Instruments
Wide-Field X-Ray Telescope
Design of WXT
Performance of WXT
Follow-Up X-Ray Telescope
Design of FXT
Performance of FXT
Satellite and Mission Profile
Satellite System
Onboard Data Processing and Triggering
Science Operation
Communications
Ground Segment and Science Data
References
34 The Enhanced X-ray Timing and Polarimetry Mission: eXTP
Contents
Introduction
Science Case and Scientific Requirements
The Science Payload
Spectroscopy Focusing Array
Large Area Detector
Polarimetry Focusing Array
Wide Field Monitor
Mission Overview
Observation Concept
Appendix
Equation of State of Ultra-Dense Matter: Requirements Flow
Strong Field Gravity: Requirements Flow
Strong Magnetism: Requirements Flow
Cross-References
References
35 HERMES-Pathfinder
Contents
Introduction
HERMES-Pathfinder Payload
Detector System
Electronic Boards
Front-End Electronic (FEE) Boards
Back-End Electronic (BEE) Board
Power Supply Unit (PSU)
Payload Data Handling Unit (PDHU)
Onboard Firmware and Software
Data Handling
HERMES-Pathfinder Service Module
HERMES-Pathfinder Performance
Conclusion
References
36 The Hard X-ray Imager (HXI) on the Advanced Space-based Solar Observatory (ASO-S)
Contents
Introduction
Hard X-Ray Imager
HXI Design
HXI Grids
HXI Detectors
HXI SAS System
HXI Imaging Simulations
Beam Tests
Summary
References
37 The Hard X-ray Modulation Telescope
Contents
Introduction
Overview of the Insight-HXMT Mission
Scientific Instruments
The High Energy X-Ray Telescope
The High Energy Detector (HED)
Automatic Gain Control Detector (HGC)
Anti-coincidence Detector (HVT)
Particle Monitor (HPM)
The Medium Energy X-Ray Telescope
Medium Energy Detector Box
Si-PIN Detector
Readout Electronics and the Application of ASIC Technology
The Low Energy X-Ray Telescope
LE Detector
Readout Electronics
Performance and Response of the Instruments
Response and Performance of the High Energy X-Ray Telescope
Pulse Shape Discrimination
Non-proportionality of NaI and the Energy-Channel (E-C) Relation
Energy Resolution
Detection Efficiency
Response and Performance of the Medium Energy X-Ray Telescope
E-C Relation
Energy Resolution
Quantum Efficiency
Dead Time
Response and Performance of the Low Energy X-Ray Telescope
E-C Relationship
Readout Noise and Energy Resolution
Quantum Efficiency
Time Response
Summary
References
38 MAXI: Monitor of All-Sky X-ray Image
Contents
MAXI Mission
GSC
Gas Counter
Electronics
Background in Orbit
SSC
X-Ray CCD and Its Function
Cooling System
In-Orbit Performance
SSC All-Sky Map
MAXI Data Flow and Nova-Alert System
Data Flow
MAXI/GSC Nova-Alert System
Nova-Search System
Alert System
Scientific Highlights
X-Ray Bursts and Stellar Flares
X-Ray Novae and Short-Lived Transients
Extragalactic Transients and MAXI Catalogs
References
39 NICER: The Neutron Star Interior Composition Explorer
Contents
Introduction
Instrument Description
X-Ray Timing Instrument
X-Ray Concentrators
X-Ray Detector System
Pointing System
Avionics and ISS Interfaces
On-Orbit Operations
Operational Status, Software, and Calibration
Pulsar Navigation Demonstration
Guest Observer Program
The Guest Observer Facility (GOF)
Guest Observer Science
Main Science Results
The Interior Composition of Neutron Stars
Accretion and Jet Evolution in Black Hole Binaries
Future Activities and Conclusion
References
40 Ramaty High Energy Solar Spectroscopic Imager (RHESSI)
Contents
Introduction
Objectives
Design and Capabilities
Spectroscopy
Dynamic Range
Imaging
Rotating Modulation Collimators
Imaging Concept
Image Reconstruction
RHESSI Imaging Example
Scientific Legacy
Discovery of Gamma-Ray Footpoint Structures
Energy Content and Spectrum of Flare Energetic Electrons
Non-thermal Emissions from the Corona and Bulk Energization
Double Coronal X-Ray Sources
Initial Downward Motion of X-Ray Sources
Microflares and the Quiet Sun
Timing of HXR Flare Ribbons
Location of Super-hot X-Ray Sources
The Photosphere as a Compton Mirror
Broadened 511-keV Positron Annihilation Line
Solar Oblateness
Magnetar Timing and Spectroscopy
Terrestrial Gamma-Ray Flashes (TGFs)
Conclusions
References
41 The SMILE Mission
Contents
Introduction
How We Got to SMILE: SMILE Precursor Missions
Scientific Payload
The Soft X-Ray Imager (SXI)
The UltraViolet Imager (UVI)
The Light Ion Analyzer (LIA)
The Magnetometer (MAG)
Spacecraft, Orbit, Mission Design, and Operations
The SMILE Spacecraft
Spacecraft Integration and Testing
Orbit and Mission Design
Operations and Ground Segment
SMILE Science Working Groups, Science Working Team, and Consortium
SMILE Science Working Groups (SWGs)
Science Operations WG
In Situ WG
Data Formats WG
Ground-Based and Additional Science WG
Outreach WG
Modeling WG
SMILE Science Working Team (SWT) and Consortium
Data Policy
SMILE Impact and Legacy
Conclusion
References
42 The Spectrometer Telescope for Imaging X-rays (STIX) on Solar Orbiter
Contents
Introduction
Scientific Objectives
Instrument Design and Description
The Entrance Window
Imaging Concept
Imaging System
Aspect System
Detector/Electronics Module (DEM)
Detectors
X-Ray Attenuator
Onboard Binning
Calibration
The First Scientific Results and Future Potential
The First Results from Cruise Phase
Micro-flare Observations
The First Imaging Results from Different Perspectives
Imaging Spectroscopy with STIX
A Stereoscopic Potential: Measuring X-ray Directivity
STIX Data Access
References
43 Space-Based Multi-band Astronomical Variable Objects Monitor (SVOM)
Contents
Introduction
The SVOM Mission Profile
Scientific Instruments
Gamma-Ray Monitor
ECLAIRs
Microchannel X-Ray Telescope
Visible Telescope
Ground Wide Angle Cameras (GWAC)
Ground Follow-Up Telescopes (GFTs)
Observing Programs
Conclusion
References
44 The Neil Gehrels Swift Observatory
Contents
Introduction
Swift Instruments
Burst Alert Telescope
Technical Description
BAT Operations
Instrument Performance
X-Ray Telescope (XRT)
Technical Description
XRT Operations
Instrument Performance
UV/Optical Telescope
Technical Description
UVOT Operations
UVOT Instrument Performance
Ground System, Operations, and Data Processing
Ground System
Operations
Data Processing
BAT Pipeline and Survey
XRT Pipeline
UVOT Pipeline
Science Highlights
Conclusion
References
45 IXPE: The Imaging X-ray Polarimetry Explorer
Contents
Review of Scientific Objectives
Requirements and Criteria
Payload Description
The Mirror Module Assemblies
Design, Fabrication, and Assembly
Thermal Requirements
Environmental Testing
X-Ray Calibration
Coilable Boom, Tip/Tilt/Rotate System, and X-Ray Shields
The Instrument
The Detector Units
The Gas Pixel Detectors
The Calibration Set and the Filter and Calibration Wheel
The Detector Service Unit
The Telescope Calibration
Effective Area and Half-Power Diameter
Measurement of the Modulation Factor
Measurement of the Spurious Modulation
Data Analysis
Event Reconstruction
Calibration and Removal of Spurious Effects
Event Weighting
Detector Response and High-Level Science Analysis
The IXPE Spacecraft
IXPE Operation, Expected Performance, and Science
Operation
Review of Performance
Specific Examples of IXPE Science
Microquasars
Pulsar Wind Nebulae
Magnetars
Supermassive Black Holes
Conclusion
Cross-References
References
46 XMM-Newton
Contents
Introduction
The Spacecraft
X-Ray Mirrors
European Photon Imaging Camera (EPIC)
The Instrument
Scientific Performance
The Reflection Grating Spectrometers (RGSs)
The Instrument
Scientific Performance
Optical Monitor (OM)
The Instrument
Scientific Performance
Organization of the XMM-Newton Ground Segment
Observing with XMM-Newton
Scientific Data and Analysis
Scientific Strategy and Impact
Authors Contribution
References
Part V Optics and Detectors for Gamma-Ray Astrophysics
47 Telescope Concepts in Gamma-Ray Astronomy
Contents
Introduction
Historical Perspective
First Observations
Missions 1960–1990
The ``MeV Sensitivity'' Gap
Interactions of Light with Matter
Instrument Capabilities and Requirements
Earth's Atmosphere and Space Environment
Atmospheric Effects
In-Space Observations
Orbit Considerations
Instrumental Background
Variations of the Background
Background as a Function of Energy
Background Suppression
Anticoincidence Shields
Pulse Shape Discrimination
Tailored Data Selections
Astrophysical Sources of Gamma Rays: Not One Fits All
Instrument Designs
General Considerations: A Gamma-Ray Collimator
Temporal and Spatial Modulation Apertures, Geometry Optics: Coded Mask Telescopes
Quantum Optics in the MeV: Compton Telescopes
Quantum Optics for Higher Energies: Pair Tracking Telescopes
Scattering Information: Gamma-Ray Polarimeters
Other Apertures: Combinations and Wave Optics
Coded Mask Compton Telescopes
Reflective Optics for Gamma-Rays
Diffractive Optics
Interplanetary Network
Gamma-Ray Detectors
Understanding Gamma-Ray Measurements
Simulations
Calibrations
MeV: Radioactive Sources
GeV: Particle Accelerators
Gamma-Ray Polarimetry
Outlook and Conclusion
Cross-References
References
48 Coded Mask Instruments for Gamma-Ray Astronomy
Contents
Introduction
Basics Principles of Coded Mask Imaging
Definitions and Main Properties
Coding and Decoding: The Case of Optimum Systems
Historical Developments and Mask Patterns
Patterns Based on Cyclic Different Sets
Other Optimum Patterns
Real Systems and Random Patterns
Image Reconstruction and Analysis
Reconstruction Methods
Deconvolution by Correlation in the Extended FOV
Detector Binning and Resolution: Fine, Delta, and Weighted Decoding
Image Analysis
Significance of Detection
System Point Spread Function
Flux and Location Errors
Non-uniform Background and Detector Response
Overall Analysis Procedure, Iterative Cleaning, and Mosaics
Coded Mask System Performances
Sensitivity and Imaging Efficiency
Angular Resolution
Point Source Localization Accuracy
Sensitivity Versus Localization Accuracy
Coded Mask Instruments for High-Energy Astronomy
First Experiments on Rockets and Balloons
Coded Mask Instruments on Satellites
SIGMA on GRANAT: The First Gamma-Ray Coded Mask Instrument on a Satellite
IBIS on INTEGRAL: The Most Performant Gamma-Ray Coded Mask Instrument
IBIS Data Analysis and Imaging Performance
ECLAIRs on SVOM: The Next Coded Mask Instrument in Space
Summary and Conclusions
References
49 Laue and Fresnel Lenses
Contents
Introduction
Laue Lenses
Laue Lenses Basic Principles: Bragg's Law
Crystal Diffraction
Ideal and Mosaic Crystals
Diffraction Efficiency
Extinction Effects
Focusing Elements
Classical Perfect Crystals
Classical Mosaic Crystals
Crystals with Curved Lattice Planes
Laue Lens Optimization
Crystal Selection
Narrow- and Broadband Laue Lenses
Tunable Laue Lens
Multiple Layer Laue Lenses
Flux Concentration and Imaging Properties of Laue Lenses
Technological Challenges
I. Production of Proper Crystals and Substrate
II a. Crystal Mounting Methods and Accuracy
II b. Laue Lens Alignment
Examples of Laue Lens Projects
The CLAIRE Balloon Project (2001)
The MAX Project (2006)
GRI: The Gamma-Ray Imager (2007)
ASTENA: An Advanced Surveyor of Transient Events and Nuclear Astrophysics (2019)
Fresnel Lenses
Construction
The Focal Length Problem
Effective Area
Chromatic Aberration
Detector Issues for Focused Gamma Rays
Conclusions
Cross-References
References
50 Compton Telescopes for Gamma-Ray Astrophysics
Contents
Introduction
Physics of Compton Scattering
Basic Operating Principles of Compton Telescopes
The Classic Double-Scattering Compton Telescope
Modern Compton Telescopes
Electron-Tracking
Dedicated Polarimeter
Event Reconstruction
Event Identification and Track Recognition
Recoil Electron Track Reconstruction
Compton Sequencing
Two-Site Event Reconstruction
Compton Telescope Performance Parameters
Point Spread Function
Angular Resolution Measure
Scatter Plane Distribution
Uncertainties in the Angular Resolution
Doppler Broadening as a Lower Limit to the Angular Resolution
Sensitivity
Imaging Capabilities
Polarization Capabilities
Limitations and Challenges
Background Radiation
Notable Compton Telescope Designs
Semiconductor-Based Compton Imagers
Soft Gamma-Ray Detector on Hitomi
The Compton Spectrometer and Imager
Gaseous and Liquid Time-Projection Chambers
Liquid Xenon Gamma-Ray Imaging Telescope
Dedicated Polarimeters
POLAR
Compton and Pair Telescopes
Medium Energy Gamma-Ray Astronomy Telescope
Applications in Other Fields
Conclusions
Cross-References
References
51 Grid-Based Imaging of X-rays and Gamma Rays with High Angular Resolution
Contents
Introduction
Multi-Grid Collimators
Generalities
Multi-Grid Example Application: HXIS on SMM
Bi-grid Systems: Fourier Imagers
Generalities
Bi-grid Example Application: Yohkoh/HXT's and ASO-S/HXI's Fixed Subcollimators with Sine/Cosine Components
Bi-grid Example Application: Solar Orbiter/STIX's Fixed Subcollimators Using Moiré Patterns and Coarse Detectors
Bi-grid Example Application: RHESSI's Rotating Modulation Collimators (RMCs)
RHESSI Design
The RHESSI Imaging Concept
Single-Grid Imaging Systems
Generalities
Rotating Modulator (RM)
Multi-Pitch Rotating Modulator (MPRM)
Comparison with Coded-Aperture Imaging
General Grid System Design
Initial (``Optical'') design
Diffraction
Grid Manufacture
Alignment, Aspect, and Calibration
Bi-grid Collimators
Systems with 2D Detectors
Conclusions
References
52 Pair Production Detectors for Gamma-Ray Astrophysics
Contents
Introduction
Counter Detectors
First-Generation Imaging Detectors
Pioneering Balloon Instruments
Satellite Instruments
Second-Generation Imaging Detectors
Advanced Balloon Instruments
Second-Generation Imaging Satellite Instruments
Third Generation: Solid-State Imaging Detectors
Continuing Developments and the Future
Conclusion
Cross-References
References
53 Readout Electronics for Gamma-Ray Astronomy
Contents
Introduction
Fundamental Concepts
Signal and Noise
Chain Components
Analog vs. Digital Pulse Processing
Integrated vs. Discrete Implementations
Readout Circuits
Voltage Mode
Charge Mode
Current Mode: Negative Feedback
Current Mode: Positive Feedback
Conclusions
References
54 Orbits and Background of Gamma-Ray Space Instruments
Contents
Introduction
Orbits of Gamma-Ray Space Missions
Low-Earth Orbits
High-Earth, Highly Elliptical, and L1/L2 Orbits
Stratospheric Balloon Experiments
Background Components
Extragalactic Gamma-Ray Emission
Galactic Gamma-Ray Emission
Galactic Cosmic Rays and Anomalous Cosmic Rays
Protons and Alpha Particles
Electrons and Positrons
Solar Energetic Particles
Secondary Particles in Low-Earth Orbits and the Stratosphere
Secondary Protons
Secondary Electrons and Positrons
Secondary Gamma Rays (and X-Rays)
Secondary Neutrons
Particles Trapped in the Inner Van Allen Radiation Belt
Delayed Background from Activation of Satellite Materials
Conclusions
Cross-References
References
55 The Use of Germanium Detectors in Space
Contents
Introduction
The Germanium as a Solid-State Detector for High Energy
Radiation Detection
Energy Measurement
The Germanium Detector (GeD) Configurations
Charge Carriers Inside the GeD: Speed-Trapping-Collection
Implementation of Germanium Detector in View of Space Usage
Thermal Constraints
Irradiation by Heavy Particles, Detector Degradation, and Recovery
Background Issue
Energy Calibration
Germanium Detectors for Astrophysics
HEAO-3/HGRS: The First Space HPGeD
Gamma-Ray Imaging Spectrometer (GRIS)
Introduction
Technical Description
Isotopically Enriched Germanium
Transient Gamma-Ray Spectrometer (TGRS) Onboard WIND : Hermetically Sealed Detectors
Introduction
Technical Description
RHESSI : Segmented GeDs
INTEGRAL/SPI: maintaining Ged more than 20 years in space
COSI: In Development
Use of Germanium Detectors in Planetary Science
Benefits of Germanium Detectors for Planetary Composition Measurements
Challenges for Using Germanium Detectors with Planetary Missions
Summary of Planetary Germanium Detectors
Instrumental Perspectives and conclusion
Electronics and Digital Processing
Cryogenics
Germanium Detectors
A 3D Germanium Focal Plane for a Hard X-Ray Telescope
Conclusion
References
56 Silicon Detectors for Gamma-Ray Astronomy
Contents
Introduction
Principles of Silicon Detectors
Photon Interactions in Silicon
Silicon Semiconductors Detectors
Characterizing Silicon Devices
Noise in Silicon Detectors
Radiation Damage
Silicon Detector Technologies
PIN Diode Detectors
Strip Detectors
Pixel Detectors
Hybrid Pixel Detectors
Gamma-Ray Telescopes
Fermi Large-Area Telescope
Fermi-LAT Tracker Testing and Calibration
Fermi-LAT Tracker On-Orbit Performance
AGILE
The AGILE Silicon Tracker
The AGILE Silicon Tracker Tests and Performance
The Silicon Tracker Calibration
Suzaku/HXD
Hitomi
Hard X-Ray Imager
Soft Gamma-Ray Detector
Technology Development for Future Gamma-Ray Missions
Conclusions
Cross-References
References
57 Cd(Zn)Te Detectors for Hard X-ray and Gamma-ray Astronomy
Contents
Introduction
Motivations for New Semiconductor Compounds for High Energy Astrophysics
Basic Principles of Detection and Associated Challenges for Cn(Zn)Te Devices
Material and Technologies
Crystal Production
Electrodes Fabrication
Electrode Segmentation
Interconnects
Detectors
Quantum Efficiency
Spectroscopy
Energy Conversion and Spectral Analysis
Charge Collection
Energy Resolution
Detector Design for Spectral Performance Enhancement
Imaging
Charge Sharing
Segmentation Geometries
3D Position-Sensitive Sensors
Polarimetry
Trade-Offs for the Design of a Detector
CdTe Versus CZT
Detector Geometry
Readout Strategy
Space Systems and Instruments
Detection Planes for Indirect (or Multiplexing) Imaging Systems
Focal Plane for Focusing Optics
Compton Camera
Radiation Damage
Future Challenges
Crystal Growth
Detector Developments for Future Hard X-Ray Missions
Detector Developments for Future Soft Gamma-Ray Missions
Conclusion
References
58 Scintillation Detectors in Gamma-Ray Astronomy
Contents
Introduction
Basic Principles of Scintillating Detectors
Inorganic Scintillators
Scintillation Mechanism in Inorganic Scintillators
Organic Scintillators
Scintillation Mechanism in Organic Scintillators
Gas Scintillators
Neutron Detectors
Radiation Hardness, Internal Background and Induced Radioactivity of Scintillators
Radiation-Induced Degradation of Scintillators
Creation of Defects Under Ionizing Radiation
General Damage Properties in Scintillating Materials Under Gamma Radiation
Phosphorescence
Radio-Luminescence due to Produced Radioisotopes in Heavy and Light Scintillation Crystalline Materials
Summary of Background Produced Effects in the Scintillator
Photosensors
Photo-Multipliers (PMT)
Silicon Devices
Photodiodes
Photodiodes with Internal Amplification (Avalanche PD, SiPM)
Scintillator-Photodetector Optical Coupling
Basic Concept for Scintillator Detectors Signal Electronics System
Scintillator Detectors Used in Space Observatories for Gamma-Ray Astronomy
Background Noise in Gamma-Ray Telescopes
Scintillator Detectors in Early Gamma-Ray Observatories
Scintillator Detectors Used as Active Anti-Coincidence Detectors
The Phoswich Technique
Position Sensitive Techniques
Scintillators in Pair-Production Based Telescopes: Calorimeters and Hodoscopes
Scintillators in Compton Techniques
Scintillators in Polarimetry Techniques
Gas Scintillators
Scintillating Detectors for Gamma-Ray Astronomy at Ground-Based Observatories
Conclusions and Outlook for Scintillators in Gamma-Ray Astronomy
References
59 Photodetectors for Gamma-Ray Astronomy
Contents
Introduction
Photomultiplier Tubes
Photocathodes
Photoelectron Collection Efficiency
Electron Multiplication
Single-Photoelectron Response
Timing Characteristics
Dark Current and Dark Counts
Afterpulses
Energy Resolution
Position-Sensitive Multi-Anode PMTs
Environmental Considerations
PMTs in Imaging Atmospheric Cherenkov Telescopes
PMTs in Spaceborne Scintillation Detectors
Photodiodes
Silicon Photomultipliers
Ground-Based Gamma-Ray Detectors Adopting SiPMs
The SCT Camera
The ASTRI-Horm Camera
Space-Based Gamma-Ray Detectors Adopting SiPMs
Current Missions
GRID
GECAM
CAMELOT
SIRI and SIRI-II
Future Missions
EIRSAT
BurstCube
Glowbug and MoonBEAM
AMEGO-X and APT
Silicon Drift Detector as scintillator photodetector
Silicon Drift Detector Fundamentals for Scintillation Detection
SDD-Based Detectors for Gamma-Ray Astronomy Applications
Conclusions
References
60 Time Projection Chambers for Gamma-Ray Astronomy
Contents
Introduction
Charged Particles Production and Transport in a Medium
Ionization
Drift, Diffusion
Negative Ion Technique
Energy Measurements
Magnetic Field
Absolute Time Measurement
Electron-Tracking Compton Camera with Gaseous Time-Projection Chamber
How to Realize Complete Bijection Imaging for MeV Gamma Rays
Background Rejection in ETCC
Estimation of Sensitivity of ETCC in MeV Gamma Astronomy
How to Obtain a Good PSF
Development of ETCC
SMILE-2+ Balloon Experiment
Analysis for Background Reduction
Future Prospects
TPCs as Pair Telescopes
Polarimetry with Pair Conversions and Multiple Scattering
Past Experimental Achievements and Future Prospects
HARPO
AdEPT
Liquid or Solid TPCs
Effective Area
Angular Resolution
Sensitivity: Gas Choice
Dense Phase TPCs
LXeGRIT
Liquid TPCs as High-Resolution Homogeneous Calorimeters
Summary/Conclusions
Cross-References
List of Variables
References
61 Gamma-Ray Polarimetry
Contents
Introduction
Science Drivers of Gamma-Ray Polarimetry
Scattering Polarimetry
Basic Concepts
Experimental Approaches
Wide-Field Instruments
3D Instruments
Collimated and Coded-Mask Instruments
Focal Plane Instruments
Pair Production Polarimetry
Differential Cross-Section
Polarization Asymmetry
Multiple Scattering
Polarimetry with Triplet Conversions
Past Experimental Achievements
Future Prospects
Effective Area and Sensitivity
Summary and Outlook
Cross-References
References
62 CubeSats for Gamma-Ray Astronomy
Contents
Introduction
CubeSats as Platforms for In-Orbit Demonstration (IOD) of New Technologies
The Science Case for High-Energy Astrophysics CubeSats
GRBs and Multi-Messenger Astronomy
Solar Flares
Terrestrial Gamma-Ray Flashes
Persistent Sources
Instrumental Background
Polarimetry
Nuclear Lines
Cosmic Diffuse Background
Currently Operating Gamma-Ray CubeSats
GRBAlpha/VZLUSAT-2
GRID
LIGHT-1
MinXSS
Gamma-Ray CubeSat Missions Under Development
BurstCube
EIRSAT-1
Gamma-Ray Module (GMOD)
HERMES-Pathfinder
MAMBO
IMPRESS
LECX
Other Proposed Gamma-Ray CubeSat Concepts
CubeSats for Bright Transients
CubeSats for Gamma-Ray Polarimetry
CubeSats for Gamma-Ray Line Studies
CubeSats for General MeV Astrophysics
Conclusions
References
63 Gamma-Ray Detector and Mission Design Simulations
Contents
Introduction: Why We Do Simulations and How We Use Them
Common Aspects of Simulations
Astronomical Inputs, Sources, Fluxes, Backgrounds
Detector Geometries
Physics Input
Extensive Air Showers
Particle Interactions in the Detector Volume
Detector Readout
Event Reconstruction
High-Level Data Analysis
Performance Metrics
Sensitivity Estimates
Simulation Tools for Different Types of Instruments
Simulating Energy Deposition in the Instrument
Air Shower Simulations
Ray Tracing
Simulating Particles in Matter With Geant4
Simulating Detector Electronics
Event Reconstruction
Trade Studies and Instrument Design
Figures of Merit and Sensitivity Metrics
Examples of Trade Studies
Using Simulations for Science
IRFs: Instrument Response Characterization
IRFs for Variable Observing Conditions
Fast Simulations to Characterize Signal Significance
Simulating Events Using IRFs
Simulating Maps Using IRFs and Exposure Tables
Simulation Verification and Limitations
Summary
Cross-References
References
Part VI Space-Based Gamma-Ray Observatories
64 The COMPTEL Experiment and Its In-Flight Performance
Contents
Introduction
COMPTEL Basics
Instrument Design
Response Function
Launch and Deployment
The Orbit
Observatory Operations
In-Orbit Experiences
Background
Activation
Prompt Background
Results
The Cosmic Diffuse Gamma Background
Point-source Investigations
Steady-State Source Sensitivity
Transient Observations
Neutron Measurements
Conclusion
References
65 The INTEGRAL Mission
Contents
Introduction: The INTEGRAL mission
INTEGRAL Operations
The IBIS Telescope
The SPI Telescope
SPI Pioneering: Recurrent Annealings
SPI as a Polarimeter
The INTEGRAL Monitors
The Joint European X-Ray Monitor: JEM-X
The Optical Monitoring Camera: OMC
INTEGRAL Radiation Environment Monitor
INTEGRAL Data Analysis
The Coded Mask Imaging Process
Data Analysis and Archiving at ISDC
INTEGRAL In-Flight Calibration
Imaging and Timing Calibrations
Imaging Calibration
Timing Calibration
Energy Calibration
IBIS
SPI
INTEGRAL Main Scientific Outcomes
Nuclear Astrophysics, Pair Annihilation, and Galactic Diffuse Emission
Death of Stars and Nucleosynthesis
56Ni and 56Co
44Ti
26Al
Galactic Diffuse Emission
Positron/Electron Annihilation on the Galactic Scale
Accretion/Ejection Processes Close to Galactic Compact Objects
Multi-messenger and Time Domain Astronomy
Gravitational-Wave Events
Ultrahigh-Energy Neutrino Events
Fast Radio Bursts
INTEGRAL View of the Extragalactic Sky
Conclusions
References
66 The AGILE Mission and Its Scientific Results
Contents
The AGILE Mission
The AGILE Payload
AGILE Scientific Performance
The AGILE Silicon Tracker
The AGILE Mini-calorimeter
Super-AGILE: The AGILE X-Ray Detector
The AGILE Anticoincidence System
AGILE Observation Modes
Pointing Mode
Spinning Mode
The AGILE Ground Segment
AGILE Data Processing
ADC Standard Analysis and Consolidated Archive
The AGILE-LV3 Tool for Easy Online Scientific Analysis
Fast Reaction to High-Energy Transients
AGILE Scientific Results
Flares from the Crab Nebula
Flares From Cygnus X-3
The Origin of Cosmic Rays in Supernova Remnants
Fast Flares from Active Galactic Nuclei
High-Energy Emission from Gamma-Ray Bursts
Search for Gravitational Wave Event Counterparts
Search for High-Energy Neutrino Counterparts
Terrestrial Gamma-Ray Flashes
Highlighting the Mechanism of Fast Radio Bursts
Solar Flares
Conclusions
References
67 Fermi Gamma-Ray Space Telescope
Contents
Introduction
Scientific Instruments
Gamma-Ray Burst Monitor
Large Area Telescope
Instrument Operations
GBM Operations
LAT Operations
Fermi Observatory
Fermi Operations
Fermi as an Astrophysical Facility
Science Highlights
GBM Highlights
Gamma-Ray Bursts Associated with Gravitational Waves
Joint Observations of GRBs by GBM and LAT
Magnetars
Crab Variations Observed by GBM and LAT
Accreting Pulsars and X-ray Binaries
Solar Flares
Terrestrial Gamma-Ray Flashes
LAT Highlights
Fermi Bubbles
Novae
Dark Matter
Pulsars
AGN
Cosmic-Ray Sources
Conclusion
Cross-References
References
68 The Fermi Large Area Telescope
Contents
Introduction
A Space-Based MeV–GeV Gamma-Ray Observatory
The Tracker (TKR)
The Calorimeter (CAL)
The Anticoincidence Detector (ACD)
Data Acquisition and Event Analysis
Operation
Calibration
Performance
Conclusion
Cross-References
References
69 The ASTROGAM Concept
Contents
Introduction
The ASTROGAM Instrument
ASTROGAM's Capability to Answer Key Scientific Questions
A Short History of the ASTROGAM Concept
Conclusions
References
Part VII Ground-Based Gamma-Ray Observatories
70 Introduction to Ground-Based Gamma-Ray Astrophysics
Contents
Introduction
Cosmic Rays at the Earth
Cosmic Rays: An Observational Summary
Cosmic-Ray Transport Picture
Transition from Galactic and Extragalactic Source Dominance
Astrophysical Source Classes That Can Contribute Significantly to the Cosmic Rays
The Origin of Cosmic Rays
Gamma-Ray Production Mechanisms
Population of Gamma-Ray Sources
Particle Accelerators as Astrophysical Probes
Characterization of the Galactic and extragalactic media
Testing Relativistic Effects
Summary
References
71 How to Detect Gamma Rays from Ground: An Introduction to the Detection Concepts
Contents
Introduction
Electromagnetic Air Showers
The Earth's Atmosphere
Longitudinal and Lateral Development of Electromagnetic Showers
Cherenkov Light
Differences Between Electromagnetic and Cosmic-Ray Showers
Air Shower Simulations
Air Shower Particle Detectors
Event Reconstruction with Air Shower Particle Detectors
Cosmic-Ray Rejection with Air Shower Particle Detectors
Sampling Cherenkov Arrays
Event Reconstruction and Cosmic-Ray Rejection with Sampling Cherenkov Arrays
Imaging Atmospheric Cherenkov Telescopes
Event Reconstruction and Cosmic-Ray Rejection with IACTs
Complementarity Between Ground-Based Techniques
Other Detection Concepts
Conclusion
References
72 The Development of Ground-Based Gamma-Ray Astronomy: A Historical Overview of the Pioneering Experiments
Contents
Introduction
The Very Beginning
Developments in 1930s
Contribution of Cherenkov Emission from EAS into LoNS
Discovery of Cherenkov Emission in the Atmosphere
First Generation Atmospheric Cherenkov Telescopes
Chudakov's Telescopes in Crimea
Other First Generation Telescopes
A Short Summary on the First Generation Telescopes
Image Shape of EAS
Air Shower Photos Taken in Cherenkov Light
Monte Carlo Simulations of EAS and the “Stereo” Observations
The Second Generation Telescopes
The 10 m Whipple Telescope
GT-48 in Crimea
High Energy Gamma Ray Astronomy (HEGRA)
The Japanese 7-Telescope Array
The CAT Telescope
CANGAROO
Wide FoV Telescopes TACTIC and SHALON
The CLUE Telescope
The Durham Mark 6 Telescope
Solar Power Plants as Gamma-Ray Telescopes
The Solar Power Plants, the Threshold Energy and the MAGIC Telescope
The Third Generation Telescopes
H.E.S.S.
VERITAS
MAGIC
The Fourth Generation Instruments
Cherenkov Telescope Array – The Major Instrument
TAIGA
LHAASO
Conclusions
References
73 Detecting Gamma Rays with High Resolution and Moderate Field of View: The Air Cherenkov Technique
Contents
Introduction
Air Shower Properties and Imaging
Telescope Optics
Mechanical Structure
Mirror Technology
Telescope Control, Event Reconstruction, and Data Products
Photosensors
Camera Trigger and DAQ
Camera Trigger
Stereo Trigger
DAQ Electronics
Analysis Techniques
Signal Extraction
Image Cleaning
Gamma–Hadron Separation
Determination of Gamma-Ray Energy and Incident Direction
Typical Performance and Scientific Plots
Current Telescopes and Future Evolution of the Technique
References
74 Detecting Gamma-Rays with Moderate Resolution and Large Field of View: Particle Detector Arrays and Water Cherenkov Technique
Contents
Introduction
Ground-Based Detection
Air Shower Physics
Simplified Treatment
Adding Complexity to the Air Shower Model
Example Experiments
HAWC
LHAASO
Detector Performance
Sensitivity to a γ-Ray Point Source
The Energy Threshold
Relative Trigger Efficiency R
The Angular Resolution
Background Discrimination from the Ground
Future Prospects
Conclusions
References
75 The High-Altitude Water Cherenkov Detector Array: HAWC
Contents
Introduction
Science Goals of the HAWC Observatory
Observatory Site and Design
Observatory Site
Water Cherenkov Detectors (WCDs)
Water
Electronics
Methods of Data Reconstruction and Analysis
Overview of Important Scientific Results
Synergies with Imaging Atmospheric Cherenkov Telescopes
Conclusion and Outlook
References
76 Current Particle Detector Arrays in Gamma-Ray Astronomy
Contents
Introduction
Progress of the Particle Detector Array in China
Tibet ASγ
ARGO-YBJ
Identification of the First TeV Gamma-Ray Super-Bubble
Long-Term Monitoring at VHE Band and Multiwave Band Study of AGN
LHAASO
KM2A
WCDA
Major Achievement of LHAASO in Gamma-Ray Astronomy
Conclusion
References
77 The Major Gamma-Ray Imaging Cherenkov Telescopes (MAGIC)
Contents
Introduction
The MAGIC History
The MAGIC Collaboration
Envisioned Scientific Goals
First Light and Start of MAGIC-I Operation
First Scientific Results
Going to Stereo
The MAGIC Technology
The Light Structure
The Mirrors
The Camera
Receivers and the Trigger Systems
The Readout
The Data Center
From Mono to Stereo
MAGIC Upgrades
The MAGIC Performance
Sensitivity
Angular and Energy Resolution
Systematic Uncertainties
Special Observation Conditions
The MAGIC Scientific Achievements
Pulsars
Binary Systems
Gamma-Ray Bursts
Monitoring of Bright AGNs
ToO Program
Extragalactic Background Light
Fundamental Physics
The Future of MAGIC
CTA North Being Built
MAGIC Data Legacy
Alternative and Complementary Uses of MAGIC
Conclusion
References
78 The Very Energetic Radiation Imaging Telescope Array System (VERITAS)
Contents
Introduction
Telescopes
Reflectors
Cameras
Electronics and Data Acquisition
Diagnostic and Monitoring Systems
Telescope Positions
Performance
Components for Ancillary Science
The Scientific Program of VERITAS
Extragalactic Source Studies
The VERITAS Blazar Sample
Jets of Radio Galaxies
Understanding Gamma-Ray Emission in Blazars
Variability of Gamma-Ray Flux in Blazars
Blazars as Probes of Cosmology
The Starburst Galaxy M82
Galactic Astrophysics
Supernova Remnants
Pulsar Wind Nebulae and the Search for PeVatrons
The Cygnus Survey and the Galactic Diffuse Emission
The Crab Pulsar
Gamma-Ray Binaries
Multimessenger Partnership
Using VERITAS Data to Explore Fundamental Physics
Legacy and Prospects for the Future
References
79 H.E.S.S.: The High Energy Stereoscopic System
Contents
Introduction
The H.E.S.S. Telescopes in Namibia
H.E.S.S. Site
Telescope Optical Systems
Telescope Structures and Drive Systems
Mirror Systems
Mirror Alignment
Point Spread Function and Pointing Accuracy
Cameras
CT1-4: The HESS1U Cameras
CT5
Central Facilities
Central Trigger System
Data Acquisition System
Internal and External Network Connection
Power Connection
Auxiliary Facilities
ATOM and All-Sky Camera
AERONET
Data Analysis
Introduction
Data Transfer
Data Calibration in H.E.S.S.
Toward DL3: γ-Hadron Separation and IRFs
Background Estimation
High-Level Analysis
Scientific Highlights Achieved with H.E.S.S.
Galactic Science
Extragalactic Science
Dark or Exotic Matter Searches
Conclusion
Cross-References
References
80 The Cherenkov Telescope Array
Contents
Introduction
CTA Concept and History
CTA Concept
CTA History
Telescope Arrays
Simulation and Layout Optimisation
Telescopes
Large-Sized Telescope (LST)
Medium-Sized Telescope (MST)
Small-Sized Telescope (SST)
Triggering
Monitoring and Calibration
Sites
The Alpha Configuration
CTA Observatory
Architecture and Data Flow
Observatory Organization and Access to the Observatory
CTA Science Performance and Key Science
Instrument Performance
Key Science Projects
Science Performance: Selected Topics
Surveying the Galactic Plane
Understanding Active Galactic Nuclei
Measurement of the EBL Intensity
Search for Dark Matter Annihilation
Conclusions
Cross-References
References
81 Future Developments in Ground-Based Gamma-Ray Astronomy
Contents
Introduction
Overview of Techniques
Extensive Air Showers
Particle Detector Arrays
Air Cherenkov Technique
TAIGA – Gamma-Ray and Cosmic-Ray Astrophysics in Siberia
The Tunka Site
Experimental Concept
TAIGA-HiSCORE
Station and Array Design
Data Acquisition and Slow Control Electronics
Data Reconstruction
Monte Carlo Simulations and Array Performance
TAIGA-IACT
The IACT Technique and TAIGA
TAIGA-IACT Design
Event Reconstruction
TAIGA-Muon
Hybrid Imaging-Timing Concept
TAIGA Sensitivity
Outlook
Southern Hemisphere EAS Array Proposals
Southern Wide-Field Gamma-Ray Observatory, SWGO
The Observatory Concept
The Array Configuration Evaluation
The Detector Design Options
An Andean Large-Area Particle Detector for γ-Rays – the ALPACA Experiment
ALPAQUITA
The Cosmic Multiperspective Event Tracker (CoMET) Project
ALTO Stations
CLiC Stations
RPC-Based Proposals
The STACEX Concept
Future Imaging Atmospheric Cherenkov Experiments
The CTA Context
ASTRI
The ASTRI Mini-Array
MACE
Conclusions
Cross-References
References
Part VIII Solar System Planets
82 Comets, Mars and Venus
Contents
Introduction
Comets
Charge Exchange
X-Ray Observation of Comets
Preparing a Comet Observation
Data Analysis
X–Ray Spectra
X-Ray Images
Alternatives to Charge Exchange
Mars
Mars and Comets: Similarities and Differences
Scattered Solar X–Rays
First Observation with Chandra
Subsequent Observation with XMM-Newton
Importance of Mars X-Ray Observations
Venus
Venus and Mars: Similarities and Differences
Observing Venus in X-Rays
Results
Conclusions
References
83 X-ray Emissions from the Jovian System
Contents
Introduction
Jupiter's Equatorial Emissions
Jupiter's X-Ray Aurorae
Jupiter's Hard X-Ray Aurorae
Dawn Storms and Injections in the UV and Hard X-Ray Aurorae
Jupiter's Polar Soft X-Ray Aurorae
Pulsed X-Ray Ion Auroral Flares/Pulses
Swirl/Flickering Polar Soft X-Ray Aurora
Jupiter's Dark Polar Region
Direct Imaging of Jupiter's Surrounding Space Plasma
X-Rays from the Io Plasma Torus
X-Rays from the Radiation Belts
X-Ray Observations of the Galilean Satellites: Io, Europa, Ganymede, and Callisto
Future Observations
Forthcoming and Proposed In Situ X-Ray Instruments
Conclusion and Summary
References
84 The Earth, the Moon, Mercury, Saturn and Its Rings, and Asteroids
Contents
Introduction
Earth's X-Ray Emissions
The Moon
Mercury
Saturn
Rings of Saturn
Asteroids
Conclusions
Cross-References
References
85 Earth's Exospheric X-ray Emissions
Contents
Introduction
A Brief Description of Earth's Magnetosphere
Exospheric Hydrogen Density
Legacy from X-Ray Astronomy
Realizing the Astronomical Observing Problem Caused by Exospheric SWCX
Techniques to Observe Exospheric SWCX
Initial Modelling of Exospheric SWCX
Technical Issues for Observing Exospheric SWCX
Characteristics of Exospheric SWCX Emission
Time Variability of Exospheric SWCX
Spectral Characteristics of Exospheric SWCX
Spatial Distribution of Exospheric SWCX
Missions Exploiting Geocoronal Charge Exchange X-Ray Emission
Cross-References
References
86 SMILE: A Novel Way to Explore Solar-Terrestrial Interactions
Contents
Introduction
The Earth's Magnetosphere
In Situ Measurements Versus Global View
A Novel Method to Image the Magnetosphere
The Novel Approach with SMILE
SMILE Scientific Motivations
The Character of Reconnection
The Geomagnetic Substorm Cycle
CME-Driven Geomagnetic Storms
Modeling in Preparation for SMILE
SMILE Impact and Conclusions
References
87 X-ray Emissions from the Ice Giants and Kuiper Belt
Contents
Introduction to the Ice Giants and Kuiper Belt
Dominant Sources of Planetary X-rays
X-ray Observations of Uranus
X-ray Observations of Neptune
X-ray Observations of Pluto
Conclusions and the Future of the Field
References
Part IX The Sun, Stars, and Exoplanets
88 The Solar X-ray Corona
Contents
Introduction
Quiet Sun, Coronal Bright Points, and Coronal Holes
Active Regions
Solar Flares and Coronal Mass Ejections
Surprising Flares: Rocket Experiments and Skylab
The Power of Spectroscopy: The Solar Maximum Mission
The Digital Era: From Yohkoh to Hinode and Onward
Coronal Mass Ejections
Conclusions
Cross-References
References
89 Stellar Coronae
Contents
Introduction: The Solar-Stellar Analogy and Its Limits
Stellar Coronal Plasma
The Solar Prototype
Coronal X-ray Spectra
Diagnostics from Low-Resolution X-Ray Spectra
Coronal Structure
Temperature Structure and Emission Measure Distribution
Coronal Morphology and Spatial Structure
Density Diagnostics
Geometrical and Doppler Shift Diagnostics of Coronal Structure
Chemical Abundances in Stellar Coronae
Evolutionary Aspects
The Main Sequence
Coronal Activity and Angular Momentum
Coronal Activity Through Time
Open Problems on the X-Ray Activity-Rotation-Age Relation
Evolved Stars
The Dividing Line: The Haves and the Have Nots
X-Rays from Supergiants and Cepheid Variables
Stellar Coronae in Limiting Regimes
A-Type Stars: Toward Coronal Darkness
Very Low-Mass Stars and Brown Dwarfs
The Puzzle of Magnetic Behavior over the Fully Convective Limit
To the Brown Dwarf Limit and Beyond
Close Binary Stars
RS Canum Venaticorum Binaries
BY Draconis and W UMa Binaries
Algol-Type Binaries
Multiwavelength Connections
Variability
Flares
A Short History of Stellar X-Ray Flare Observations
Elements of Flare Physics: Thermodynamical Evolution
Elements of Flare Physics: Frequency Distribution of X-Ray Flare Energy
Elements of Flare Physics: Coronal Mass Ejections
Elements of Flare Physics: Correlated Emission in Different Wavebands
X-Ray Magnetic Cycles
Conclusion
Cross-References
References
90 X-ray Emission of Massive Stars and Their Winds
Contents
Introduction
X-Ray Emission from Single Massive Stars
OB Stars
Evolved Massive Stars
Magnetic Massive Stars
Massive Binaries
γ Cas Stars
Accreting Compact Companion Scenarios
Hot Subdwarf Companion Scenario
Magnetic Star/Disk Interaction
Conclusions and Future Prospects
Cross-References
References
91 Magnetically Confined Wind Shock
Contents
Introduction
Historical Perspective
Magnetic Confinement
Alfv́en Radius
Rotation and Kepler Radius
MHD Simulations
Rotation-Confinement Diagram and Stellar Spindown
X-Ray Luminosity from Magnetically Confined Wind Shocks
UV Wind Line Variation Observed by HST
Hα Line Emission from Dynamical Magnetospheres
Centrifugal Breakout and Hα Emission from Centrifugal Magnetospheres
CBO Challenges to Rigid-Field Models
Future Outlook
Cross-References
References
92 Pre-main Sequence: Accretion and Outflows
Contents
Introduction
T Tauri Stars
The Power of X-Rays for Studying T Tauri Stars
Accretion
The Accretion Stream and Its Footpoints
X-Ray Signatures of the Accretion Shock
Physics of Accretion in 1D
The Shock Front
Structure of the Post-Shock Region
Why We Need to Go Beyond 1D Models
The Multi-D Structure of the Accretion Shock
Variability and Accretion Outbursts
Toward a Coherent Picture of the Accretion Shock
X-Rays from Protostellar Jets
X-Ray Observations of Jets
X-Rays from Jet Knots
X-Rays from the Jet Base
Origin of the X-Ray Emission at the Jet Base
Comparison with Other Jet Tracers
Toward a Coherent Model for X-Ray Emission from Protostellar Jets
Conclusions and Outlook
Cross-References
References
93 Star-Forming Regions
Contents
Introduction
The Early Einstein Discoveries, the Emergence of Intriguing Questions, and Some Initial Answers
ROSAT and the Nearby Star-Forming Sites
ASCA: Looking for X-Rays from Class I and Class 0 YSOs
The Transformational Impact of Chandra and XMM-Newton
Systematic Studies of the Star Cluster Formation Process
Long-Look, Large-Area, and Multiwavelength Simultaneous Surveys
NGC 1893: Exploring Star Formation in the Outer Galaxy
DROXO and Follow-On: The Enigmatic Variability of YSO Fe 6.4keV Line
XEST and the Origin of YSO Mass-LX and Accretion-LX Relations
COUP: LX vs. Rotation and Age, Insights on the Dynamo, and the Origin of Saturation
CSI-2264: Unveiling Circumstellar Disks with Simultaneous Multiwavelength Variability Studies
X-Rays from Class 0 YSOs
The YSO Flares: Nature and Effects on Circumstellar Disks
Circumstellar Disk Evolution and High-Energy Radiation
YSO X-Ray Emission Effects on Small and Large Scales
A Glance into the Future
References
94 Nearby Young Stars and Young Moving Groups
Contents
Introduction
Young Stars and Stellar Groups Within 100pc
Nearby Young Moving Groups
Identifying NYMG Members: X-Rays, UV, and Gaia
Well-Studied NYMGs and Their Members
The Cha Association, age 5 Myr
The TW Hya Association, age 8Myr
The β Pic Moving Group, age 24Myr
The Tuc-Hor and Columba Associations, age 40–50Myr
The AB Dor Moving Group, age 120Myr
High-Energy Stellar Astrophysics: Exploiting Nearby, Young Stars
Early Evolution of Magnetic Activity
X-Ray Emission from Young, Intermediate-Mass Stars
Pre-MS Accretion and Coronae at High (X-Ray) Spectral Resolution
X-Ray Signatures of Accretion: TW Hya as Archetype
Accretion Signatures in X-Ray Spectra of Other NYMG Members
Physical Conditions Within Pre-MS Coronae
High-Energy Irradiation of Planet-Forming Environments
Photoevaporation and Chemical Evolution of Protoplanetary Disks
Young-Planet Atmospheres: X-Ray Irradiation Processes
Future Prospects: Impacts of Forthcoming X-Ray Missions and Facilities
The eROSITA All-sky Survey
High-Resolution Spectroscopy: Athena, Lynx, Arcus, and XRISM
Summary
Cross-References
References
95 Extrasolar Planets and Star-Planet Interaction
Contents
Introduction
Extrasolar Planets
X-Ray Emission
X-Ray Absorption
Atmospheric Evaporation
Star-Planet Interaction
Tidal Star-Planet Interaction
Magnetic Star-Planet Interaction
X-Ray Observations of Tidal and Magnetic SPI
Conclusion
References
96 The X-ray Emission from Planetary Nebulae
Contents
Introduction
Sources of X-Ray Emission in PNe
Early X-Ray Observations of PNe
PNe in the Era of Chandra and XMM-Newton
What Has Been Learned from the X-Ray Observations of PNe
Diffuse X-Ray Emission
PN Evolution
Refining Models of PN Formation
The Physics at the Interphase Between the PN and Its Hot Bubble
The Connection Between PNe and WR Wind-Blown Bubbles
Differential Extinction
X-Ray Emission from Born-Again PNe
Point Sources of X-Ray Emission
Photospheric X-Ray Emission from CSPNe
Binary CSPNe
Shock-In Winds
The Future of X-Ray Observations of PNe
References
Part X Supernovae, Supernova Remnants, and Diffuse Emission
97 Stellar Evolution, SN Explosion, and Nucleosynthesis
Contents
Introduction
Massive Star Evolution and Core-Collapse Supernovae
Core Evolution Toward the Iron-Core Formation
Core-Collapse Supernova (CCSN) Explosion Mechanism
Core-Collapse Supernova Progenitors
White Dwarfs in a Binary and Thermonuclear Supernovae
Thermonuclear Supernovae: Progenitors and Explosion Mechanisms
Binary Evolution of a White Dwarf Toward Thermonuclear Runaway
Explosive Nucleosynthesis
Emissions from Supernovae
Characteristic Behaviors
Power Sources
SN Progenitors and Explosions as Seen in Observations
High-Energy Emissions from Supernovae
Conclusion
References
98 Radioactive Decay
Contents
Introduction: Basics of Radioactivity
Discovery
Characteristics
Radioactivity in Astrophysics
General Considerations
Different Processes
New Astronomy
Astrophysical Studies Using Radioactivity
Tracing Past Activity
Tracing Flows of Nucleosynthesis Ejecta
Diagnostics of Explosions
Summary and Conclusions
References
99 Supernova Remnants: Types and Evolution
Contents
Introduction
Evolution of Supernova Remnants
Free Expansion Phase
Adiabatic Expansion Phase
Snowplow Phase
Dissipation Phase
Types of Supernova Remnants
Shell-Type SNRs
Plerion-Type SNRs
Mixed-Morphology SNRs
Conclusions
References
100 Thermal Processes in Supernova Remnants
Contents
Shock Heating
Rankine–Hugoniot Equations
Collisionless Processes
Postshock Processes
Temperature Equilibration
Ionization
Cooling and Recombination
Thermal X-Ray Emission and Spectral Diagnostics
Short Summary
References
101 Nonthermal Processes and Particle Acceleration in Supernova Remnants
Contents
Introduction
SNRs as the Origin of Galactic Cosmic Rays
The Cosmic-Ray Spectrum
The Cosmic-Ray Composition and Leptonic Versus Hadronic Cosmic Rays
The Galactic Cosmic-Ray Energy Budget
Radiation from Leptonic and Hadronic Cosmic Rays
Synchrotron Radiation
Inverse Compton Scattering
Nonthermal Bremsstrahlung
Pion Production and Decay
The Mechanism of Diffusive Shock Acceleration
Collisionless Shocks
Diffusive Shock Acceleration Theory and Its Extensions
Acceleration Timescales and Maximum Energies
The Effects of Radiative Losses and Cosmic-Ray Escape on the Maximum Energy
Nonlinear Cosmic-Ray Acceleration
The Injection Problem
X-Ray and Gamma-Ray Evidence for Cosmic-Ray Acceleration
Radio and X-Ray Synchrotron
GeV-TeV Gamma Rays
Measurements of the Cosmic-Ray Acceleration Efficiency
Evidence or Lack of Evidence for PeVatrons
Evidence for Low-Energy Cosmic Rays
Cosmic-Ray Escape from Acceleration Sites
Polarimetry and Magnetic-Field Turbulence and Topology
Concluding Remarks
References
102 Pulsar Wind Nebulae
Contents
Introduction
Physical Description of a PWN
PWN Evolution
Observational Signatures and Notable PWNe
Radio
Infrared, Optical, and Ultraviolet
X-Ray
Gamma-Ray
Young PWN: The Crab Nebula
``Stage 2'': Vela X
Pulsar Halos
``Middle-Aged'': Geminga
Ultrahigh-Energy Gamma-Ray Emission
Recent Progress and Open Questions
PWNe as PeVatrons
``Non-pulsar'' Wind Nebulae
Particle Transport (Diffusion and Advection)
Conclusion
References
103 Diffuse Hot Plasma in the Interstellar Medium and Galactic Outflows
Contents
The Hot Phase of the ISM
Sources of the Hot ISM
Stellar-Wind Bubbles and Bow Shocks
Supernova Remnants
HII Regions and Superbubbles
X-Ray Spur in the LMC
Galactic Center
Sgr A
X-Ray Reflection Nebulae
Galactic Ridge Emission
Hot Interstellar Medium
Nonthermal X-Ray Filaments and the Galactic Center Magnetic Field
The Galactic Outflow
Signs of a Galactic Outflow
The Chimneys and the Base of the Galactic Outflow
The eROSITA Bubbles
Summary
References
104 Interstellar Absorption and Dust Scattering
Contents
Introduction
The Cold ISM
Interstellar Dust
The Extinction Curve
The Dust Size Distribution
Attenuation of X-Rays by the Interstellar Medium
Dust Scattering from the ISM
The X-Ray Fine Structure
Correcting X-ray Observations for ISM Attenuation
Laboratory Measurements of Solid Particles
Implementation to Astrophysical Models
Interaction of X-rays with Dust Grains
Scattering and Absorption of X-rays: The State of Art
Future Outlook
References
Part XI Compact Objects
105 Low-Mass X-ray Binaries
Contents
Introduction
The Nature of the Compact Primary in LMXBs
Donors and Accretion Phenomenology in LMXBs
Canonical Roche Lobe Overflow with Main Sequence or Giant Stars
Ultracompact X-Ray Binaries
Eclipsing LMXBs
Wind-Fed Accretion in LMXBs: Symbiotic X-Ray Binaries
Magnetically Channeled Accretion in LMXBs: X-Ray Pulsars
Variability and Transient Outbursts in LMXBs
Long-Term X-Ray Behavior: Transient and Persistent LMXBs
Extended Outbursts: Quasi-persistent LMXBs
Outburst Statistics of Transient LMXBs
The Role of the Orbital Period in the Long-Term X-Ray Behavior
Short-Term X-Ray Behavior and Subclasses of NS LMXBs
Classification Based on X-Ray Luminosity: Two Extreme Ends
Very-Faint X-Ray Binaries
Accretion Around the Eddington Luminosity in LMXBs
Distribution and Demographics of LMXBs in the Galaxy
Galactic Center and Bulge
Galactic Plane and Outer Parts
Globular Clusters
Orbital Period Distribution
Conclusion
Cross-References
References
106 High-Mass X-ray Binaries
Contents
Introduction
Accretion in HMXBs
Disk-Fed Accretion
Wind Accretion
Interactions Between the Accretion Flow and the Magnetosphere
Classes of High-Mass X-Ray Binaries
Supergiant X-Ray Binaries
Persistent ``Classical'' HMXBs
Supergiant Fast X-Ray Transients
Be X-Ray Binaries
Wolf-Rayet X-Ray Binaries
Ultraluminous X-Ray Sources
Gamma-Ray Binaries
Black Hole Versus Neutron Star X-Ray Binaries
Mass Measurements of Compact Objects in HMXBs
On the Ratio of NS to BH HMXBs
Emission Properties
NS HMXB X-Ray Spectra
Cyclotron Resonance Scattering Features
Spectral States of Be XBs
Spectral States of BH Systems
Variability
Periodic Variability
X-Ray Pulsations
Orbital Periods and Variability
Superorbital Modulations
Aperiodic Variability
Short-Timescale Variability
Long-Timescale Variability
HMXB Populations in the Milky Way and Magellanic Clouds
HMXB Luminosity Function
Spatial Distribution and Ages
Comparing the Milky Way and Magellanic HMXB Populations
Cross-References
References
107 Accreting White Dwarfs
Contents
Introduction
What Is a White Dwarf?
Electron Degeneracy
The Equation of State of Electron-Degenerate Matter
The Chandrasekhar Mass
White Dwarf Formation
White Dwarf Characteristics
Rotation Rates
Magnetic Field
Temperature and Cooling
Composition
Observed Masses and Radii
Accreting White Dwarfs
Roche Lobe Overflow and Accretion
Outflows and Jets
Binary Components and the Diversity in Accreting White Dwarfs
Cataclysmic Variables
Classical Novae
Supersoft Sources
Dwarf Novae and Novalikes
U Gem Stars
SU UMa Stars
Z Cam stars
ER UMa Stars
Permanent Superhumpers
Non-magnetic Novalikes
AM CVn Binaries
Other Non-magnetic CVs
Symbiotic Stars
Be Star-White Dwarf Systems
Magnetic CVs
Polars and Intermediate Polars
Accreting White Dwarfs in the Broader Astrophysical Context
The Origin and Evolution of Accreting White Dwarfs
Observed Orbital Period Distribution
The Period Spike
The Period Gap
Exceeding the Chandrasekhar Mass
White Dwarfs in Globular Clusters
Discovering Accreting White Dwarfs
Accreting White Dwarfs Found in Optical Surveys
Accreting White Dwarfs Found in the SDSS Survey
Accreting White Dwarfs Found in the Gaia Survey
Accreting White Dwarfs Found in Other Optical Surveys
Accreting White Dwarfs Found in X-Ray Surveys
Future Surveys That Will Detect Accreting White Dwarfs
Conclusions
References
108 Formation and Evolution of Accreting Compact Objects
Contents
Introduction
The Accreting Compact Object Zoo
Modes of Mass Transfer
Stability of Mass Transfer Through Roche Lobe Filling
Dynamical Timescale Mass Transfer
Thermal Timescale Mass Transfer
Nuclear or Orbital Angular Momentum Loss Timescale Mass Transfer
Formation Channels
Common-Envelope Evolution
The Energy Budget of Common-Envelope Evolution
Common-Envelope Evolution from Hydro-dynamical Simulations
Dynamically Stable Non-conservative Mass Transfer
Low-/Intermediate-Mass Stars
High-Mass Stars
Combination of Dynamically Stable Non-conservative Mass Transfer and Common-Envelope Evolution
Evolution Through Two Episodes of Common-Envelope Evolution
Dynamically Stable Non-conservative Mass Transfer Followed by Common-Envelope Evolution
Common-Envelope Evolution Followed by Dynamically Stable Non-conservative Mass Transfer
Evolution Through Two Episodes of Dynamically Stable Non-conservative Mass Transfer
Further Considerations on the Formation of Ultra-Compact X-Ray Binaries
Additional Channels Through Dynamical Interactions in High-Density Environments
Secular Evolution
Cataclysmic Variables and Low-Mass X-Ray Binaries
Low-Mass Unevolved M-/K-Type Main-Sequence Star Donors
Subgiant or A-/F-/G-Type Main-Sequence Star Donors
Comparison with Observations
AMCVns and Ultra-Compact X-Ray Binaries
Helium White Dwarf or Helium Star Donors
Comparison with Observations
Symbiotic Stars and Symbiotic X-Ray Binaries
Atmospheric Roche Lobe Overflow
Gravitationally Focused Wind Accretion
Supergiant and Wolf–Rayet High-Mass X-Ray Binaries
Conclusion
Cross-References
References
109 Black Holes: Accretion Processes in X-ray Binaries
Contents
Introduction
Physics of Accretion onto BHs
Formation of Accretion Disk
Viscous Process
Fundamental Principles
Accretion Disk Models
Shakura–Sunyaev Disks
Advective-Dominated Accretion Flows
Slim Disks
Disk-Corona and Jets
Radiation Cooling
Links to Observations in XRBs
Spectral Components and Identifications
Accretion Disk
Corona
Reflection
Spectral States
Timing Perspectives on Accretion
Noise and Propagation
QPOs
Conclusion
References
110 Black Holes: Timing and Spectral Properties and Evolution
Contents
Introduction
Galactic Black Holes: An Observational View
Iron Lines
Absorption Lines and Winds
Radio- and Near-Infrared Emission and Jets
Quasi-periodic Oscillations
Low-Frequency QPOs
High-Frequency QPOs
Lags and Reverberation
Soft γ-Rays and Polarization
Outliers in Hardness Intensity Diagram Evolution
Modeling and Interpretation
Thermal Disc Modeling
Origin of Winds
Hard State Accretion Geometry
Corona Origin/Jet Connection
Origin of Gamma-Ray Tail
Origin of QPOs
Future of Black Hole Research in X-ray and Gamma-Ray Domain
Cross-References
References
111 Isolated Neutron Stars
Contents
Introduction
Rotation-Powered Pulsars
Magnetars
Magnetar History in a Nutshell
Persistent Emission
Transient Emission
Low-Magnetic Field Magnetars
Magnetar-Like Activity from High-B Rotation-Powered Pulsars
Central Compact Objects
Fun Facts About CCOs
1E161348–5055: A Hidden Magnetar
X-Ray Dim Isolated Neutron Stars
Overview of the Observational Properties
Rotating Radio Transients
Conclusion
References
112 Low-Magnetic-Field Neutron Stars in X-ray Binaries
Contents
Introduction
The Zoo of Low-Magnetic-Field Neutron Stars
Transient and Persistent Sources
Classical LMXBs: Z-Sources and Atolls
Fast X-ray Variability
X-ray Spectral Properties
The Continuum Spectrum: An Historical Overview
Soft and Hard Spectral States
Soft Spectral States
Hard Spectral States
The Reflection Component
Bursting Sources
Observational Properties of Bursts
Photospheric Radius Expansion Bursts
Burst Oscillations
Probing the Surrounding Accretion Environment
High-Inclinations Sources
Accreting Millisecond Pulsars
Accretion Torques
Spin Frequency Distribution
X-ray Spectra
Pulse Profiles
X-ray Quiescence
Binary Evolution
Transitional Millisecond Pulsars
Faint and Very Faint Sources
Multiwavelength Observations of NS LMXBs
Facts (and Peculiarities) of NS LMXBs Jets
Conclusions and Future Perspectives
References
113 Accreting Strongly Magnetized Neutron Stars: X-ray Pulsars
Contents
Introduction
Magnetic Field: The Reason for the XRP Uniqueness
Observational Appearance of X-ray Pulsars
Coherent Pulsations: The Definitive Feature of XRPs
How Bright Are They?
Aperiodic Variability or Flickering XRPs
Energy Spectrum
Polarization Properties of XRPs
Optical Companions in XRPs
Physics and Geometry of Accretion in XRPs
Mass Transfer in the Binary System
Accretion Flow Interacting with the NS Magnetosphere
Magnetospheric Boundary
Influence of the Magnetospheric Rotation
Spin-Ups and Spin-Downs of NS in XRPs
Different Physical Conditions in Accretion Discs Around XRPs
Stochastic Fluctuations of the Mass Accretion Rate
Geometry and Physics of the Emitting Region at the NS Surface
Spectra Formation
Challenges and Complications
Broadband Energy Spectra
Cyclotron Lines: The Fingerprints of a Strong Magnetic Field
Open Issues
Key Points to Have in Mind
Cross-References
References
114 Fundamental Physics with Neutron Stars
Contents
Introduction
Formation of Neutron Stars
First Observation of a Neutron Star
Theoretical Arguments for the Existence of Neutron Stars
Rotating Neutron Stars
Magnetic Fields of Neutron Stars
Gamma Ray Blasts from the Past
Many Observational Faces of Neutron Stars
Laboratories of Gravitation
Space-Time Deformations
Rotating Stars
Radiation from the Star's Surface
Pulse Profile Modeling
Gravitational Waves
Interpretation of Gravitational Waveforms
Laboratories of Nuclear Physics
Dense Matter Inside Compact Objects
Degeneracy Pressure
Thermal-Like Emission from Isolated Neutron Stars
Thermonuclear X-ray Bursts
Laboratories of Electrodynamics
Spindown Power of Magnetized Balls
Charges in the Magnetosphere
Force-Free and Magnetohydrodynamic Solutions
Evolving Magnetic Topology
Mysterious Pulsar Radio Emission
Pulsar Wind Nebulae
Laboratories of Plasma Physics
Standard Quantum Electrodynamic Interactions
Pair Cascades
Vacuum Birefringence
Superfluid and Superconducting Interiors
Gliches and Quakes
Giant Bursts and Fast Radio Bursts from Magnetars
Extreme Particles: Cosmic Rays, Neutrinos, and More
Summary
Cross-References
References
115 X-ray Emission Mechanisms in Accreting White Dwarfs
Contents
Introduction
Novae
X-Ray Light Curves of Novae
X-Ray Spectra of Novae
Higher Energies
Dwarf Novae
Combination Novae
Nova-Like Variables
Persistent Super-Soft Sources
BeWD Systems
Symbiotic Stars
Oddballs
Magnetic Cataclysmic Variables
X-Ray Spectra of mCVs
Cyclotron Cooling in Polars
Reflection
The Soft Component of mCVs
Masses of White Dwarfs in mCVs
X-Ray Light Curves of mCVs
X-Ray Light Curves of Polars
X-Ray Light Curves of Intermediate Polars
AEAqr and the Propeller Systems
AMCVn Systems
HMCnc and V407Vul: Direct Impact Accretion
Conclusions
References
Part XII Galaxies
116 Introduction to the Section on Galaxies
Contents
Introduction
References
117 X-ray Binaries in External Galaxies
Contents
Introduction
High- and Low-Mass X-Ray Binaries
X-Ray Scaling Relations and Luminosity Functions
Disentangling HMXB and LMXB Populations in External Galaxies
X-Ray Scaling Relations
Time Dependence of HMXB Population
Metallicity and Age Effects
Sub-galactic Scales
X-Ray Luminosity Functions
X-Ray Emission as a SFR Proxy for Normal Galaxies
Expectations from SRG/eROSITA All-Sky Survey
Spatial Distribution of X-Ray Binaries in Galaxies
Primordial and Dynamically Formed LMXBs
LMXB Formation Channels
Clues from Luminosity Functions
Clues from the Spatial Distributions
Ultraluminous X-Ray Sources
Association with Star Formation
Main Conclusions from Optical Studies
Inferences from the Shape of the HMXB Luminosity Function
Possible Nature and Implications for Accretion Physics
Population Synthesis Results
Relevant Results from Binary Evolution
Summary of Population Synthesis Models and Their Results
How Frequent Are X-Ray Binaries?
Connection to LIGO-Virgo Sources
Cosmic Evolution of X-Ray Binaries and Their Contribution to CXB
Contribution of X-Ray Binaries to Cosmic X-Ray Background
X-Ray Investigations of Cosmologically Distant Galaxies
Drivers of the Redshift Evolution of X-Ray Binary Populations
Recent Constraints on X-Ray Evolution of Galaxies
Contribution to (Pre)Heating of IGM
Conclusion
References
118 The Hot Interstellar Medium
Contents
Introduction
The Hot ISM of Star-Forming Galaxies
Shock Heating and Diffuse X-Ray Emission
Theory and Observations of Superwinds
Chemical and Physical Evolution of the Hot ISM
Starbursts in Galaxy Mergers
An Ideal Laboratory: NGC6240
Observational Properties of the Hot ISM in Early-Type Galaxies
From Discovery with the Einstein Observatory to Chandra and XMM-Newton
Global Properties of the Hot ISM: Scaling Laws
The Mass of ETGs
1D Radial Profiles of the X-Ray Surface Brightness and Temperature Distributions
Radial Distributions of Fe Abundance
Entropy Profiles
2D Spatial Distributions of X-Ray Surface Brightness and Gas Temperature
Origin and Evolution of the Hot ISM in Early-Type Galaxies
Origin of the Hot ISM
Relative Importance and Evolution of the Mass Sources
Heating of the Mass Sources
Injection Temperatures and Observed Temperatures
Cooling and Evolution of the Hot ISM
The Mass Deposition Problem
AGN Heating
The Various Forms and Effects of the SMBH Accretion Output
Modeling of the Hot ISM: The Simplest Model
The Complex Lifetime of Hot Gas in ETGs
The Global Picture
Two More Actors: Environment and AGN Feedback
Future Prospects
References
119 X-ray Halos Around Massive Galaxies: Data and Theory
Contents
Introducing X-Ray Halos Around Massive Galaxies
Motivation
Overview of Past X-Ray Observations
Massive Elliptical Galaxies
Massive Disk Galaxies
Simulating X-Ray Halos Around Massive Spiral Galaxies
Confronting the Observed and Simulated Properties of the CGM
X-Ray Scaling Relations
Metallicity of the CGM
Missing Baryon Problem
Searching for the Missing Baryons with X-Ray Emission Measurements
Searching for the Missing Baryons with X-Ray Absorption Studies
Sunyaev–Zel'dovich Effect
The Importance of AGN Feedback on the Observed Properties of the CGM
Missing Feedback Problem
Future Outlook
References
120 The Interaction of the Active Nucleus with the Host Galaxy Interstellar Medium
Contents
Introduction and Chapter Outline
Theoretical and Multiwavelength Observational Background
Galaxy Evolution and Feedback
Multiwavelength Imaging of Radio-Quiet AGN Interactions with Host Galaxies
The “Unified Scheme” of AGNs
Early X-Ray Observations of Extended AGN Emission Through Chandra
The Spectral Components of CT AGN Emission
Chandra Imaging: The Soft Component
Prevalence of Extended X-Rays
Chandra High-Resolution Imaging Techniques
Broad-Band (0.3–2.5 keV) Soft X-Ray Morphology
Narrow-Band X-Ray Emission Line Imaging
Spectra: Photoionization and Shock Excitation
Seyfert and LINER Emission Coexisting in AGNs
Chandra Imaging: Discovery of Extended Hard Continuum and Fe Kα (Neutral)
The Effect of Fast Shocks: The Fe XXV Kα Line Emission
Cross-Cone Emission: Leaky Torus or Jet-Stimulated Outflows?
X-Ray Irradiation of Molecular Clouds in the Central 100 Pc: Imaging the Torus and AGN Feedback
Mapping the Past History of AGNS
AGN Feedback on the Host Galaxy ISM
Summary: Revised View of AGNs and Their Interaction with the Host Galaxy
References
121 Probing the Circumgalactic Medium with X-ray Absorption Lines
Contents
Introduction
Further Insights from Theory
Semi-analytic Models
Why Study the CGM in Absorption?
Technical Advances Enabling Absorption Line Spectroscopy of the CGM
The X-Ray Absorbing Gas in the Milky Way
Temperature Measurements
Evidence for Multiple Temperature Components
Column Density Measurements
Pathlength, Density, and Mass Measurements
Evidence for Non-thermal Line Broadening
All Sky Distribution of Ovii Absorbers
Uncertainties in Going from Observed Parameters to Derived Physical Conditions
What Do We Detect: The CGM or the ISM in the Galactic Disk?
The MW CGM Contains Sub-virial, Virial, and Super-virial Temperature Gas with Non-solar Abundance Ratios
Does the Milky Way CGM Account for Its Missing Baryons?
The CGM of External Galaxies
The Sightline to PKS0405–123
Open Questions
Future Directions
Conclusion
References
Part XIII Active Galactic Nuclei in X- and Gamma-rays
122 Active Galactic Nuclei and Their Demography Through Cosmic Time
Contents
Active Galactic Nuclei as Multiwavelength and Multi-messenger Emitters
The AGN ``Zoo''
AGN as High-Energy and Multi-messenger Sources
Circumnuclear Matter on Different Physical Scales
Within the Sublimation Radius
The Torus
Beyond the Torus up to the Host Galaxy
AGN Demography and Evolution in the X-Ray and γ-Ray Bands
X-Ray Band
γ-Ray Band
References
123 The Super-Massive Black Hole Close Environment in Active Galactic Nuclei
Contents
Introduction
The Compact Source of X-Rays
Reprocessing of X-Ray Radiation in the Gaseous Environment Close to the SMBH
Basics of X-Ray Photons Interaction with Matter
X-Ray Reflection
The Fluorescent Iron Line
Complex X-Ray Partial Covering Absorption
Reprocessing in the Wind
Strong-Field Gravity Signatures in X-Rays
The Soft X-Ray Excess
Observational Signatures
The Soft X-Ray Excess Modelling
X-Ray and Optical/UV Variability
Aperiodic Variability
X-Ray Reverberation Mapping
Quasi-Periodic Oscillations
Quasi-Periodic Eruptions
Optical/UV Variability
Accretion Properties in AGN Populations: The Disc–Corona Coupling
Future Prospects
X-Ray Polarimetry
X-Ray Microcalorimeters: XRISM and Athena
References
124 Black Hole-Galaxy Co-evolution and the Role of Feedback
Contents
AGN Fueling
Interacting Galaxies
Isolated Galaxies
AGN Feedback
Warm Absorbers
Ultra-fast Outflows
Scaling Relations for X-ray Winds
Winds on Galactic Scales
Warm Ionized Galactic Winds
Cold Neutral and Molecular Winds
Extended X-ray Emission and Cavities: ISM
Feedback Models
Extragalactic Surveys and Statistical Populations of AGN
AGN Selection Through X-ray Surveys and Characterization of Host Galaxies
Connections Between BH Accretion and Star Formation
Black Hole Fueling and Galaxy Morphologies and Mergers
Clustering and Dark Matter Halos
Obscured and Elusive AGN
Prospects for the Future and New Facilities
References
125 The Dawn of Black Holes
Contents
Introduction
The Earliest Black Holes
Light Seed Black Holes
Medium-Weight Seed Black Holes
Heavy Seed Black Holes
Primordial Black Holes and Exotic Candidates
From Seeds to SMBHs
SMBH Assembly in a Cosmological Context
Seeding Galaxies with the Earliest BHs
Eddington-Limited Growth
SMBH Growth Boosted by Heavy Seeds
The Relative Role of Seed BH Populations
Super-Eddington-Driven Growth
The Role of BH Mergers
The Role of Feedback
Observational Results on High-Redshift QSOs
X-Ray Observations of High-Redshift QSOs
The X-Ray View of Accretion Physics in High-z QSOs
Quasars as Cosmological Probes
How to Build a Quasar Hubble Diagram: The Technique
How to Build a Quasar Hubble Diagram: Required Measurements and Sample Selection
Cosmological Constraints from the Quasar Hubble Diagram
The Unexplored Black Hole Universe
The Missing QSO Population
Conclusions and Future Prospects
References
Part XIV Galaxy Clusters
126 X-ray Cluster Cosmology
Contents
Introduction: Role of X-Rays in Cluster Cosmology
Role of Massive Halos in Cosmology
The Homogeneous Model
Linear Growth of Matter Perturbations
The Smoothed Linear Density Field
Departures From Linear Growth
The Halo Mass Function and Abundance of Clusters
Galaxy Cluster Abundances in X-Ray Surveys
X-Ray Mass Estimate: Hydrostatic and Proxies
The X-Ray Luminosity Function
The X-Ray Temperature Function
The Baryon Mass Function
X-Ray Observable-Space Distribution: The logN-logS
X-Ray Observable-Space Distribution: General Observables
Recent Cluster Abundance Studies
Clusters as Tracers of Large-Scale Structure
Two-Point Clustering of Halos and the Bias Parameter
Constraints from X-Ray Clusters Two-Point Clustering Analyses
Sample Variance Considerations
Variance in Cluster Number Counts
Extensions of the Sample Variance Formalism
Clusters as Standard Candles
The Gas Fraction Tests
Distance Measurements with Combined X-Ray and SZ Observations
Recent Results on the Hubble Constant Measurements
Sources of Systematic Uncertainties
Distance Measurements from Spectra of X-Ray Resonant Lines
Cluster Internal Mass Distributions
Pink Elephants
Extreme-Value Statistics
Rareness of Events
Extreme Pairwise Velocities
Clusters as Gravitational Theory Probes
Selection Function
Conclusions and Forward Look
Resources
References
127 Scaling Relations of Clusters and Groups and Their Evolution
Contents
Introduction
Theoretical Background
The X-Ray Emission from Clusters of Galaxies
Self-Similarity
The Mgas–M Relation
The TX–M Relation
The LX–M Relation
The YX–M Relation
The LX–TX Relation
The Entropy of the ICM
Heating and Cooling the ICM
Analysis Methods and Considerations
Observational Biases
Selection Effects and Selection Functions
X-Ray vs Optically and SZ-Selected Samples
Correlated Errors
Linear Regression and Fitting Packages
Multivariate Analysis
X-Ray Telescope Calibration
Emission-Weighted and Spectroscopic-Like Temperatures
Observational Results and Deviations from Self-Similarity
The Slopes of Scaling Relations
The Evolution of Scaling Relations
Scatter and Covariance
Mass Proxies
Interpretation of Scaling Relations
Comparison with Simulations
Summary and Future Outlook
eROSITA
ATHENA
References
128 Thermodynamic Profiles of Galaxy Clusters and Groups
Contents
Introduction
Cluster Scaling Properties
Dark Matter Haloes
Intracluster Msedium
X-Ray Observations
Introduction
Measurement of Physical Quantities
Density
Temperature
Pressure
Combined X-Ray/SZE Studies
Observations
Density
Temperature
Entropy
Pressure
Scatter in Scaled Profiles
Evolution
Cosmological Simulations of Groups and Clusters
Non-radiative Cluster Simulations
Simulations with Radiative Cooling and Preheating
Simulations with Stellar and AGN Feedback
Future Outlook
References
129 Cluster Outskirts and Their Connection to the Cosmic Web
Contents
Introduction
Definition of Cluster Outskirts
Observations
Methods for Measuring Thermodynamic Properties
Observed Thermodynamic Profiles in the Outskirts
Biases Due to Gas Clumping and Non-thermal Pressure Support
Cold Fronts in the Cluster Outskirts
Merger Shocks in the Cluster Outskirts
Metals in the Cluster Outskirts
Connections to the Cosmic Web
Theory and Simulations
Self-Similarity in Cluster Outskirts
Thermodynamical Profiles of ICM in Cluster Outskirts
Non-thermal Gas Motions in Cluster Outskirts
Gas Density Inhomogeneities or Gas Clumping in Cluster Outskirts
Shocks and Electron-Ion Non-equilibration
Future Simulations and Modeling Efforts
Upcoming and Future X-Ray Measurements
Cross-References
References
130 Absorption Studies of the Most Diffuse Gas in the Large-Scale Structure
Contents
Introduction
Theory
History: A Hot Intergalactic Medium
The Large Scale Structure and the Warm-Hot Intergalactic Medium
The Circumgalactic Medium
X-Ray Techniques
Ionization Balance of the LSS Gas in the Local Universe
The WHIM Absorption Observables
Absorption Line Curves of Growth
WHIM Gas Diagnostics
WHIM Physical Conditions
WHIM Kinematics
WHIM Chemical Conditions
Feasibility of LSS Gas Absorption Observations
Observations
Currently Available Instruments
Intervening X-Ray Absorption Lines
Sightline to H1821+642
Sightline to Mrk421
Sightline to PKS2155–304
Sightline to 3C273
Sightlines to H2356–309 and Mrk501
Sightline to 1ES1553+113
WHIM and the CGM
WHIM and the Missing Baryons
Future
Dispersive Spectrometers
Nondispersive Spectrometers
Detectability and Study of LSS Absorbers with Future Missions
References
131 AGN Feedback in Groups and Clusters of Galaxies
Contents
Introduction
Observational Signatures of AGN Feedback
Historical Perspective
The Case of AGN Feedback in Groups and Clusters of Galaxies
How Does AGN Feedback Work (From an Observational Perspective)
Accretion Processes and Modes
Energetics and Timescales
Heating by Shocks, Mixing, Turbulence, and/or Sound Waves
Radio Jets and Massive Molecular Outflows
The Evolution of AGN Feedback in Groups and Clusters of Galaxies
Models of AGN Feedback
Feeding the AGN
Energy Release by Supermassive Black Holes
Heating Efficiency by Radiation
Heating Efficiency by Mechanical Energy
Variants of the Mechanical Feedback Models
Buoyantly Rising Bubbles
Winds, Outflows of Thermal Plasma, and Mixing
Strong Shocks
Sound Waves
Heating by Cosmic Ray Streaming
Broader Outlook
Cooling of the Gas
Simulating AGN Feedback in General: Basic Models and Important Parameters
Modeling AGN Feedback in Cosmological Simulations
Modeling AGN Feedback in Idealized Simulations
Understanding AGN Feedback in Simulations
Modeling SMBH Accretion in Simulations
Conclusion
References
132 Chemical Enrichment in Groups and Clusters
Contents
Introduction
Abundances and Metallicity
Stars and Supernovae as Sources of Metals
Asymptotic Giant Branch Stars
Core-Collapse Supernovae
Type Ia Supernovae
Measuring/Simulating the ICM Chemical Properties: Techniques and Current Limitations
Deriving Abundances from X-Ray Spectroscopy
Current Observing Limitations
Simulations
Numerical Uncertainties and Limitations
How and When Did the ICM Become Chemically Enriched?
Spatial Uniformity of the Metal Distribution
Mechanisms for Metal Transport
Galaxy Clusters and Groups: Similar or Different Enrichment?
Chemical Composition of the ICM
Metal Budget in Clusters
Redshift Evolution of the Chemical Enrichment
Understanding Stellar Physics from Metals in the ICM
Future Prospects
References
133 The Merger Dynamics of the X-ray-Emitting Plasma in Clusters of Galaxies
Contents
Introduction
X-Ray Features Produced by Cluster Mergers
Cold Fronts
``Merger-Remnant'' Cold Fronts
``Sloshing'' Cold Fronts
Shock Fronts
Ram-Pressure-Stripped Tails
The Measurement of Merger-Driven Gas Motions
The Impact of ICM Plasma Physics on Merger-Driven Features
Magnetic Fields
Thermal Conduction
Viscosity
Electron–Ion Equilibration at Cluster Shocks
Merging Clusters and Cosmic Rays: Observable Signatures in the Radio and X-Ray Bands
Conclusions
Cross-References
References
134 Plasma Physics of the Intracluster Medium
Contents
Introduction
Plasma Physics of the Thermal ICM
Scale Hierarchy
Plasma Magnetization and Anisotropic Transport
Adiabatic Invariance and Temperature Anisotropy
Kinetic Micro-instabilities and Their Impact on Transport
Example: Suppressed Viscosity in the Coma Cluster
Anisotropic Viscosity and Turbulent Amplification of Cluster Magnetic Fields
Observational Constraints on ICM/IGM Magnetic Fields
Plasma Theory Basics for Seed-Field Generation: Biermann and Weibel
Plasma Theory Basics for Turbulent Dynamo
Enter Plasma Physics
Energetic Particle Transport and Acceleration in the ICM
Some CR Transport Basics in the ICM Context
Evolution of the ICM CR Distributions
Some Models for Dpp
CR Acceleration in ICM Shocks: ``DSA''
Future Perspectives
References
Part XV Transient Events
135 Gamma-Ray Bursts
Contents
Introduction
Observations
Prompt Emission
Afterglow and Associated Supernova/Kilonova
Host Galaxy
Theory
Central Engine and Jet
Energy Sources
Jet Acceleration
Jet Propagation
Prompt Emission
Internal Dissipation
Shocked Material
Synchrotron Emission
High-Energy Photon and Neutrino Emission
Multiwavelength Afterglows
External Reverse Shock
External Forward Shock
Post-standard Afterglow Models
Supernova and Kilonova
Supernova
Kilonova/Mergernova
Statistics and Cosmological Applications
Luminosity Function
High-Redshift Universe
Luminosity Correlations of GRBs
Cosmological Constraints
References
136 Accretion Disk Evolution in Tidal Disruption Events
Contents
Introduction
Steady State of a Local Ring Region
Dynamical Evolution
Piecewise Steady-State One-Zone Model
Results and Comparison with Observations
Conclusion and Future Directions
References
137 Fast Radio Bursts
Contents
Introduction
General Properties and Propagation Effects
Dispersion
Scattering Effect
Scintillation
Plasma Lensing
Absorption
Faraday Rotation
Global Statistical Properties and Population Study
Energy, Pulse Width, and Waiting Time Distribution
Host Galaxy Properties
Luminosity Function and Redshift Evolution
FRB Classification
Periodicity
Physical Mechanism of FRBs
Radiation Mechanism
Antenna Mechanism
Synchrotron Maser Emission from Magnetized Shocks
Source Models
FRB Counterpart
Applications in Cosmology
DM Contribution of Host Galaxy and Source Environment
Fluctuations in IGM
Conclusion
References
Part XVI Miscellanea
138 Probing Black-Hole Accretion Through Time Variability
Contents
Introduction
X-Ray Variability in BH XRBs
Time Scales of Variability
Aperiodic X-Ray Variability
Quasi-periodic Oscillations
Low-Frequency Quasi-periodic Oscillations
High-Frequency Quasi-periodic Oscillations
X-ray Variability as a Tracer of the Accretion State
A Variable Disc or a Variable Hard X-Ray Source?
X-Ray Cross-Spectral-Timing Studies of BH XRBs
Coherence
X-Ray Time Lags
Hard X-Ray Lags of the Aperiodic Variability
X-Ray Reverberation Lags
Lags Associated with QPOs
A Brief Comparison Between BH XRBs and AGN Variability
Constraining the Variability Process
A Word About Models of X-Ray Variability
A Word About QPOs Theoretical Models
Conclusion
Cross-References
References
139 Surveys of the Cosmic X-ray Background
Contents
Introduction
The Cosmic X-Ray Background and Early Global Studies
Imaging Surveys of the CXRB: A Very Brief Review
The Currently Resolved CXRB Fraction
Sources Detected in CXRB Surveys
CXRB Source Counterparts, Redshifts, and Classifications
Main Extragalactic Source Types
Insights on the AGN Population from CXRB Surveys
AGN Demographics
AGN Physics
AGN Ecology
Some Future Prospects and Other Relevant Reviews
Some Future Prospects for CXRB Surveys
Other Relevant Reviews
References
140 Tests of General Relativity Using Black Hole X-ray Data
Contents
Introduction
Black Holes
Black Holes in General Relativity
Astrophysical Black Holes
Stellar-Mass Black Holes
Supermassive Black Holes
Black Holes Beyond General Relativity
Accretion Disks
Infinitesimally Thin Disks
Finitely Thin and Thick Disks
Observational Tests
Thermal Spectrum
Reflection Spectrum
Other Tests
X-Ray Reverberation Mapping
Quasiperiodic Oscillations
X-Ray Polarization
Conclusion
Cross-References
References
141 Tests of Lorentz Invariance
Contents
Introduction
Vacuum Dispersion
Modified Photon Dispersion Relation
Present Constraints from Time-of-Flight Measurements
Gamma-Ray Bursts
Active Galactic Nuclei
Pulsars
Vacuum Birefringence
General Formulae
Present Constraints from Polarization Measurements
Photon Decay and Photon Splitting
Photon Decay
Photon Splitting
Present Constraints from Spectral Cutoff
Comparison with Different Methods
Summary and Outlook
References
142 X- and Gamma-Ray Astrophysics in the Era of Multi-messenger Astronomy
Contents
Introduction
X-ray and Gamma-Ray Multi-messenger Sources
Gamma-Ray Bursts
Joint GW and EM Observations of GRBs
Joint Neutrino and EM Observations of GRBs
Blazars
Joint Neutrino and EM Observations of Blazars
Other Multi-messenger Source Candidates
Core-Collapse SNe: Long GRBs and Shock Breakouts
Bursting Magnetars and Soft Gamma Repeaters
Multi-messenger Observations
High-Frequency Gravitational Wave Detectors
Neutrino Detectors
X-ray and Gamma-Ray Facilities
Einstein Probe
SVOM
eXTP
Athena
THESEUS
Conclusions
Cross-References
References
Part XVII Spectral-Imaging Analysis
143 Modeling and Simulating X-ray Spectra
Contents
Introduction
X-ray Spectra and Spectral Modelling
Data Structure and Formats
Data Reduction
Pattern/Grade Selection
Cuts Based on the Background
Pile-up and Optical Loading
Selecting Events of Interests
Software for Spectral Analysis
Spectral Analysis
How to Fit and How to Test a Spectral Model
Spectral Energy Resolution and Binning
Background Treatment
Testing Model Components
Parameters Correlations and Confidence Levels
Additional Technical Recommendations for Spectral Analysis
Performance Estimates for Proposals and Surveys
References
144 Statistical Aspects of X-ray Spectral Analysis
Contents
The Story of Detected X-ray Photon Counts
Combining Independent Data
Understanding Chi2 and CStat
Detector Details, Binning, and Grouping
Background Spectra
Frequentist Data Analysis
Fitting by Minimization
Frequentist Error Analysis
Model Checking
Model Comparison
Limitations So Far
Bayesian Inference
Terminology
Parameter Estimation
Choosing Priors
Computation in Multiple Dimensions
Markov Chain Monte Carlo
Nested Sampling
Using Posteriors
Model Checking
Model Comparison
Parameter Distributions of a Sample
Further Information
Conclusion
References
145 Analysis Methods for Gamma-Ray Astronomy
Contents
Introduction
Fermi-LAT Data and Spectral Analysis
Data Structure and Organization
Raw Fermi-LAT Data
Access to Analysis-Ready Data
Structure of the Fermi-LAT Spacecraft and Event Files
Structure and Content of Photon Files
Structure and Content of Spacecraft Files
Fermi-LAT Data Analysis
Data Analysis Software
Data Quality Cuts
Imaging Analysis
Aperture Photometry Analysis
Likelihood Analysis
Unbinned and Binned Likelihood Analysis
Source Detection
Concluding Remarks
Analysis Methods for Ground-Based Gamma-Ray Instruments
Data Levels and Formats
Low-Level Data Processing
Calibration
Image Cleaning
Hillas Parameters
Event Reconstruction
Event Reconstruction with Hillas Parameters
Event Reconstruction with Image Templates
Event Reconstruction with Deep Learning Techniques
Gamma/Hadron Separation
Event Selection with Hillas Parameters
Event Selection with Other Approaches
Background Modelling
First Success: The On/Off Method
Estimating the Background from the Observation Itself
Background Model from Archival Observations
Generation of Instrument Response Functions
High-Level Data Analysis
Aperture Photometry
3D Likelihood Analysis
Open Software Tools for IACT Data Analysis
Similarities and Differences for Ground-Level Particle Detector Arrays
Multi-wavelength Spectral Modelling
Conclusion
Cross-References
References
Part XVIII Timing Analysis
146 Basics of Fourier Analysis for High-Energy Astronomy
Contents
Fourier 101
Fourier Series
Continuous Fourier Transform
Discrete Fourier Transform
Windowing and Sampling
Windowing Effects
Sampling Effects: Aliasing
Window Carpentry
Observational Windows
Fast Fourier Transform
The Power Density Spectrum and Its Representation
PDS Normalization
PDS Representation
PDS Decomposition
Bartlett's Method and Data Gaps
Auto- and Cross-Correlation
Cross-Spectra, Phase Lag Spectra, and Coherence
Bispectrum and Bicoherence
Lomb-Scargle Technique for Non-uniform Sampling
Time-Frequency Analysis
Short-Time Fourier Transform
Wavelets
Other Techniques
References
147 Time Domain Methods for X-ray and Gamma-ray Astronomy
Contents
Variability in High Energy Astronomy
Methodological Foundations for High Energy Light Curves
Detecting Variability in Light Curves
Anderson-Darling Test
Test for Overdispersion
Other Nonparametric Tests
Sequential Likelihood-Based Tests
Treatment of Background Events
Characterization of Variability
Autocorrelation Function
Structure Function
Wavelet Analysis
Multiple Change Point Model
Integer Autoregressive Models
Astrophysical Modeling
Multidimensional Variability Detection
Software Packages
Final Remarks
References
148 Fourier Methods
Contents
Introduction
Fourier Basics
Terminology and Notation
The Periodogram
The Welch/Bartlett Periodogram
Models for Commonly Encountered Signals
Coherent Signals
Stochastic Processes
Quasi-Periodic Signals
Fast Transients
Periodogram Statistics
The Likelihood for Periodograms
Simulating Stochastic Time Series
Dynamical Periodograms
Periodicity Detection
Signal Detection in Constant Noise
Upper Limits on the Pulsed Amplitude
Methods Not Based on the FFT
The Rayleigh Test and Z2n Searches
The H-Test
Periodicity Searches in Variable Light Curves: Red Noise
Searching for QPOs with Model Comparison Techniques
Spectral Timing
The Cross Spectrum
Coherence
Time Lags
Total rms
Covariance
Variability-Energy Spectra
Common Pitfalls
Detector Effects: Dead Time and Friends
Non-stationarity
Unevenly Sampled Data: The Lomb–Scargle Periodogram
Conclusions
References
149 X-ray Polarimetry-Timing
Contents
Introduction
Theoretical Expectations
Pulsations
Propagating Accretion Rate Fluctuations
X-ray Reverberation Mapping
Quasi Periodic Oscillations
Blazars
Observational Techniques
Direct Measurement
Stokes Parameters
Pulsations
Phase-Folding of QPOs
Cross-Spectrum Between Modulation Angle Bins
Modulation Angle Dependent Cross-Spectra
Null Hypothesis Tests for Polarization Variability
Technical Challenges
Conclusions
References
Part XIX Polarimetry
150 General History of X-ray Polarimetry in Astrophysics
Contents
Introduction
The Very Early Stage
Ariel-5 and OSO-8
The Stellar X-Ray Polarimeter
The Quest for Photoelectric Polarimeter
The First Gas Pixel Detectors
The Time Projection Chamber
Toward a Mission
Not Only IXPE
Conclusions
References
151 Bayesian Analysis of the Data from PoGO+
Contents
Introduction
The PoGO+ Mission: Principles, Methods, and Results
Operating Principle and Analysis Framework
Compton Polarimetry
Minimum Detectable Polarization
Stokes Parameters
Bayesian Analysis
X-Ray Polarimetry in the Bayesian Framework
The PoGO+ Payload and Flight
Instrument Design
Flight Systems
Preflight Calibration
Flight Performance and Observations
Data Reduction and Analysis
Data Products During Flight
On-Ground Data Preprocessing
Polarization Analysis
Preliminary Analysis
Posterior Density Distribution and Parameter Estimation
Results
The Crab
Cygnus X-1
Conclusion
Cross-References
References
152 Gamma-Ray Polarimetry of Transient Sources with POLAR
Contents
Introduction
Introduction to POLAR
Detection Principle
The POLAR Detector
Polarization Sensitivity of POLAR
The Importance of Calibration
Measuring Zero Polarization
On-Ground Calibration
In-Orbit Validation
χ2 Analysis
Data Processing
GRB Analysis
Simulated Response
Systematic Errors from Spectral and Localization
χ2 Fitting
Shortcomings of This Method
Bayesian Time-Integrated Analysis
Forward-Folding Polarization Data
Background Modeling
Adding Data from Other Instruments
Time-Integrated Results
Time-Resolved Analysis
Energy-Resolved Analysis
References
153 Analysis of the Data from Photoelectric Gas Polarimeters
Contents
Introduction: Photoelectric Polarimeters
Reconstruction of Photoelectron Track
A Simple Analysis with the Modulation Curve
The Minimum Detectable Polarization
Stokes Parameters
Properties of Stokes Parameters
Spectro-Polarimetry with Stokes Parameters and Forward-Folding
Polarization and Its Statistical Uncertainty
Conclusions
References
154 Neural Network Analysis of X-ray Polarimeter Data
Contents
Introduction
How This Chapter Is Organized
Imaging X-Ray Polarimetry
Track Reconstruction
Emission Angle Reconstruction
Absorption Point Reconstruction
Energy Reconstruction
Events Converting Outside of the Gas Volume
Polarization Estimation
Stokes Parameters
Methods
Minimum Detectable Polarization (MDP)
Deep Neural Networks
Machine Learning with Deep Neural Networks
Training
Validation and Model Selection
Convolutional Neural Networks
Multitask Learning
Uncertainty Quantification
Deep Ensembles
Neural Networks for Track Reconstruction
Dataset
Geometric Bias
Hexagonal to Square Conversion
Deep Ensemble Setup
Removing Tail Tracks
Training and Ensemble Selection
Performance
Neural Networks for Polarization Estimation
Modulation Factor
Weighted Maximum Likelihood Estimator
Deep Ensembles
Performance
Weights
Comparison
Conclusion and Future Directions
References
155 Soft Gamma-Ray Polarimetry with COSI Using Maximum Likelihood Analysis
Contents
Introduction
Compton Telescopes and Polarization Measurements
Operation of Compton Telescopes
Compton Polarimetry
Designing a Compton Polarimeter
The Compton Spectrometer and Imager
Instrument
Polarization Calibration
2016 Balloon Flight and GRB 160530A
Maximum Likelihood Method
Framework for Polarization Measurements for Next-Generation Compton Telescopes
Transient Sources
Persistent Sources
Conclusions
References
156 Stokes Parameter Analysis of XL-Calibur Data
Contents
Introduction
XL-Calibur
Stokes Parameters
Application to XL-Calibur
Background and Observation Strategy
Spectropolarimetric Analysis by Forward Folding
A z-Dependent Forward-Folding Method for XL-Calibur
Conclusion
Cross-References
References
Index

Citation preview

Cosimo Bambi Andrea Santangelo Editors

Handbook of X-ray and Gamma-ray Astrophysics

Handbook of X-ray and Gamma-ray Astrophysics

Cosimo Bambi • Andrea Santangelo Editors

Handbook of X-ray and Gamma-ray Astrophysics

With 2227 Figures and 224 Tables

Editors Cosimo Bambi Department of Physics Fudan University Shanghai, China

Andrea Santangelo Institute for Astronomy and Astrophysics University of Tuebingen Tuebingen, Baden-Württemberg, Germany

ISBN 978-981-19-6959-1 ISBN 978-981-19-6960-7 (eBook) https://doi.org/10.1007/978-981-19-6960-7 © Springer Nature Singapore Pte Ltd. 2024 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Singapore Pte Ltd. The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721, Singapore Paper in this product is recyclable.

Preface

X-ray and gamma-ray astrophysics concerns the study of the Universe, and thus also of the celestial sources in it, in the energy bands characteristic of X-rays and gamma rays. The X-ray and gamma-ray Universe is a violent, somewhat extreme Universe, often characterized by physical conditions that cannot be reproduced in terrestrial laboratories. Together with the study of astrophysical sources in the UV band, neutrinos, cosmic rays, and gravitational waves, X-ray and gamma-ray astrophysics is a fundamental part of high-energy astrophysics, and of multimessenger astrophysics. X-rays and gamma rays of cosmic origin are blocked by the upper layers of the Earth’s atmosphere. Therefore, X-ray and gamma-ray astrophysics (up to the GeV energies) had to wait for the development of space activities, which began at the end of World War II – from rockets and balloons to satellites – to become an essential discipline of astronomy. At higher energies, those of TeV, the limited fluxes of photons make space research unfeasible. Very high energy gamma astronomy uses ground-based observatories that detect the electromagnetic showers that highenergy gamma rays produce in the Earth’s atmosphere. Since the discovery of the first extrasolar X-ray source in 1962 (Scorpius X-1) by a team led by Riccardo Giacconi, who received the Nobel Prize in Physics in 2002 for his pioneering contributions to the development of X-ray astrophysics, an entire new Universe has been unveiled to the human eyes. Extreme objects like Galactic compact objects and, among others, white dwarfs, neutron stars, and black holes, as well as extragalactic sources such as active galactic nuclei, clusters of galaxies, and gamma-ray bursts, have been discovered as cosmic laboratories for extreme physics. However, studies of X-ray and gamma-ray astrophysics are now rather general and regard a large variety of objects, from planets to potential sources of dark matter. A large number of X-ray and gamma-ray satellites have revolutionized the field, thanks to their improved spectral-timing performance. The launch of IXPE in December 2021 has broken the last uncharted frontier since opened a new window on the study of the polarization of the X-ray radiation from celestial sources. At the same time, TeV observatories have unveiled the very high energy gamma Universe. The future of the discipline is bright. New missions are being developed and some will be launched soon. Large new TeV observatories are being deployed. With

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the emergence of multi-messenger astronomy, we felt it was time of providing the community with a comprehensive handbook for X-ray and gamma-ray astrophysics. The handbook provides an updated coverage of X-ray and gamma-ray astrophysics. All chapters are written by leading experts in the field. The handbook is organized into four subjects: (i) X-ray experimental techniques and observatories (Volumes 1 and 2), (ii) gamma-ray experimental techniques and observatories (Volumes 3 and 4), (iii) science (Volumes 5, 6, and 7), and (iv) analysis techniques in X-ray and gamma-ray astrophysics (Volume 8). Each subject is divided into different “Parts” or “Sections”. Subject I on X-ray experimental techniques and observatories covers optics for X-ray astrophysics (Section Editors: Jessica Gaskin, Rene Hudec, Daniele Spiga), detectors for X-ray astrophysics (Section Editors: JanWillem den Herder, Marco Feroci, Norbert Meidinger), and X-ray missions (Section Editors: Arvind Parmar, Andrea Santangelo, Shuang-Nan Zhang). Subject II on gamma-ray experimental techniques and observatories covers optics and detectors for gamma-ray astrophysics (Section Editors: Lorraine Hanlon, Vincent Tatischeff, David Thompson), space-based gamma-ray observatories (Section Editors: Denis Bastieri, Pablo Saz-Parkinson, Hiroyasu Tajima), and ground-based gamma-ray observatories (Section Editors: Daniel Mazin, Miguel Mostafa, Gerd Pühlhofer). Subject III on science covers Solar System planets (Section Editor: Graziella Branduardi-Raymont), the Sun, stars, and exoplanets (Section Editors: Giuseppina Micela, Beate Stelzer), supernovae, supernova remnants, and diffuse emissions (Section Editors: Aya Bamba, Keiichi Maeda, Manami Sasaki), compact objects (Section Editors: Victor Doroshenko, Andrea Santangelo), galaxies (Section Editors: Giuseppina Fabbiano and Marat Gilfanov), active galactic nuclei in X- and gamma rays (Section Editors: Alessandra De Rosa, Cristian Vignali), galaxy clusters (Section Editors: Etienne Pointecouteau, Elena Rasia, Aurora Simionescu), transient events (Section Editor: Bin-Bin Zhang), and miscellanea (Section Editor: Cosimo Bambi). Subject IV covers spectral-imaging analysis (Section Editors: Victor Doroshenko, Andrea Santangelo, Sergey Tsygankov), timing analysis (Section Editors: Tomaso Belloni, Dipankar Bhattacharya), and polarimetry (Section Editors: Hua Feng, Henric Krawczynski). We hope that the Handbook of X-ray and Gamma-ray Astrophysics can become a valuable reference work for graduate students and research scholars in the high energy astrophysics community for the next two decades. With the living edition, we will keep the handbook always updated. We are extremely grateful to all section editors and authors for their contributions in this project as well as for their future efforts to update their chapters. Shanghai, China Tuebingen, Germany February 2024

Cosimo Bambi Andrea Santangelo

Contents

Volume 1 Part I Introduction to X-ray Astrophysics . . . . . . . . . . . . . . . . . . . . . . . .

1

1

A Chronological History of X-ray Astronomy Missions . . . . . . . . . Andrea Santangelo, Rosalia Madonia, and Santina Piraino

3

Part II Optics for X-ray Astrophysics . . . . . . . . . . . . . . . . . . . . . . . . . . . . Jessica Gaskin, Rene Hudec, and Daniele Spiga

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X-ray Optics for Astrophysics: A Historical Review . . . . . . . . . . . . Finn E. Christensen and Brian D. Ramsey

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3

Geometries for Grazing Incidence Mirrors . . . . . . . . . . . . . . . . . . . . Michael J. Pivovaroff and Takashi Okajima

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Lobster Eye X-ray Optics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Rene Hudec and Charly Feldman

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5

Single-Layer and Multilayer Coatings for Astronomical X-ray Mirrors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Kristin K. Madsen, David Broadway, and Desiree Della Monica Ferreira

6

Silicon Pore Optics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Nicolas M. Barrière, Marcos Bavdaz, Maximilien J. Collon, Ivo Ferreira, David Girou, Boris Landgraf, and Giuseppe Vacanti

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Miniature X-ray Optics for Meter-Class Focal Length Telescopes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Jaesub Hong, Suzanne Romaine, Vinay L. Kashyap, and Kiranmayee Kilaru

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Diffraction-Limited Optics and Techniques . . . . . . . . . . . . . . . . . . . Richard Willingale

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Collimators for X-ray Astronomical Optics . . . . . . . . . . . . . . . . . . . Hideyuki Mori and Peter Friedrich

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Technologies for Advanced X-ray Mirror Fabrication . . . . . . . . . . Carolyn Atkins

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Diffraction Gratings for X-ray Astronomy . . . . . . . . . . . . . . . . . . . . Frits Paerels, Jelle Kaastra, and Randall Smith

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Active X-ray Optics for Astronomy . . . . . . . . . . . . . . . . . . . . . . . . . . Jacqueline M. Davis, Casey T. DeRoo, and Melville P. Ulmer

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Facilities for X-ray Optics Calibration . . . . . . . . . . . . . . . . . . . . . . . . Bianca Salmaso, Alberto Moretti, and Jessica Gaskin

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Charge Coupled Devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . M. W. Bautz, Andrew D. Holland, and D. H. Lumb

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Volume 2 Part III Detectors for X-ray Astrophysics . . . . . . . . . . . . . . . . . . . . . . . . . Jan-Willem den Herder, Marco Feroci, and Norbert Meidinger

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X-ray Detectors for Astrophysics . . . . . . . . . . . . . . . . . . . . . . . . . . . . J. W. den Herder, Marco Feroci, and Norbert Meidinger

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Proportional Counters and Microchannel Plates . . . . . . . . . . . . . . . Sebastian Diebold

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Silicon Drift Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Andrea Vacchi

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CMOS Active Pixel Sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Konstantin D. Stefanov and Andrew D. Holland

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DEPFET Active Pixel Sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Norbert Meidinger and Johannes Müller-Seidlitz

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Transition-Edge Sensors for Cryogenic X-ray Imaging Spectrometers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Luciano Gottardi and Stephen Smith

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Signal Readout for Transition-Edge Sensor X-ray Imaging Spectrometers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . H. Akamatsu, W. B. Doriese, J. A. B. Mates, and B. D. Jackson

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Introduction to Photoelectric X-ray Polarimeters . . . . . . . . . . . . . . Kevin Black, Enrico Costa, Paolo Soffitta, and Anna Zajczyk

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Gas Pixel Detectors for Photoelectric X-ray Astronomical Polarimetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Paolo Soffitta and Enrico Costa

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Time-Projection Chamber X-ray Polarimeters . . . . . . . . . . . . . . . . Kevin Black and Anna Zajczyk

841

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Compton Polarimetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ettore Del Monte, Sergio Fabiani, and Mark Pearce

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In-Orbit Background for X-ray Detectors . . . . . . . . . . . . . . . . . . . . . Riccardo Campana

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Filters for X-ray Detectors on Space Missions . . . . . . . . . . . . . . . . . Marco Barbera, Ugo Lo Cicero, and Luisa Sciortino

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Silicon Strip Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . H. Tajima and K. Hagino

991

Part IV X-ray Missions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1017 Arvind Parmar, Andrea Santangelo, and Shuang-Nan Zhang 29

The AstroSat Observatory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1019 Kulinder Pal Singh

30

The BepiColombo Mercury Imaging X-ray Spectrometer . . . . . . . 1059 Adrian Martindale, Michael J. McKee, Emma J. Bunce, Simon T. Lindsay, Graeme P. Hall, Tuomo V. Tikkanen, Juhani Huovelin, Arto Lehtolainen, Max Mattero, Karri Muinonen, James F. Pearson, Charly Feldman, Gillian Butcher, Martin Hilchenbach, Johannes Treis, and Petra Majewski

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The Chandra X-ray Observatory . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1115 Belinda J. Wilkes and Harvey Tananbaum

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The HaloSat and PolarLight CubeSat Missions for X-ray Astrophysics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1149 Hua Feng and Philip Kaaret

33

The Einstein Probe Mission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1171 Weimin Yuan, Chen Zhang, Yong Chen, and Zhixing Ling

34

The Enhanced X-ray Timing and Polarimetry Mission: eXTP . . . 1201 Andrea Santangelo, Shuang-Nan Zhang, Marco Feroci, Margarita Hernanz, Fangjun Lu, and Yupeng Xu

35

HERMES-Pathfinder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1231 Fabrizio Fiore, Alejandro Guzman, Riccardo Campana, and Yuri Evangelista

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The Hard X-ray Imager (HXI) on the Advanced Space-based Solar Observatory (ASO-S) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1249 Yang Su, Zhe Zhang, Weiqun Gan, Jian Wu, and Xiankai Jiang

37

The Hard X-ray Modulation Telescope . . . . . . . . . . . . . . . . . . . . . . . 1263 Fangjun Lu, Yupeng Xu, Congzhan Liu, Xuelei Cao, Yong Chen, Fan Zhang, and Yunxiang Xiao

38

MAXI: Monitor of All-Sky X-ray Image . . . . . . . . . . . . . . . . . . . . . . 1295 Tatehiro Mihara, Hiroshi Tsunemi, and Hitoshi Negoro

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NICER: The Neutron Star Interior Composition Explorer . . . . . . 1321 Keith Gendreau, Zaven Arzoumanian, Elizabeth Ferrara, and Craig B. Markwardt

40

Ramaty High Energy Solar Spectroscopic Imager (RHESSI) . . . . 1343 Brian Dennis, Albert Y. Shih, Gordon J. Hurford, and Pascal Saint-Hilaire

41

The SMILE Mission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1369 G. Branduardi-Raymont and C. Wang

42

The Spectrometer Telescope for Imaging X-rays (STIX) on Solar Orbiter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1391 Laura A. Hayes, Sophie Musset, Daniel Müller, and Säm Krucker

43

Space-Based Multi-band Astronomical Variable Objects Monitor (SVOM) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1409 Jianyan Wei and Bertrand Cordier

44

The Neil Gehrels Swift Observatory . . . . . . . . . . . . . . . . . . . . . . . . . . 1423 Lorella Angelini, S. Bradley Cenko, Jamie A. Kennea, Michael H. Siegel, and Scott D. Barthelmy

45

IXPE: The Imaging X-ray Polarimetry Explorer . . . . . . . . . . . . . . . 1455 Martin C. Weisskopf, Paolo Soffitta, Brian D. Ramsey, and Luca Baldini

46

XMM-Newton . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1501 Norbert Schartel, Rosario González-Riestra, Peter Kretschmar, Marcus Kirsch, Pedro Rodríguez-Pascual, Simon Rosen, Maria Santos-Lleó, Michael Smith, Martin Stuhlinger, and Eva Verdugo-Rodrigo

Volume 3 Part V Optics and Detectors for Gamma-Ray Astrophysics . . . . . . . . . 1539 Lorraine Hanlon, Vincent Tatischeff, and David Thompson 47

Telescope Concepts in Gamma-Ray Astronomy . . . . . . . . . . . . . . . . 1541 Thomas Siegert, Deirdre Horan, and Gottfried Kanbach

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Coded Mask Instruments for Gamma-Ray Astronomy . . . . . . . . . 1613 Andrea Goldwurm and Aleksandra Gros

49

Laue and Fresnel Lenses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1671 Enrico Virgilli, Hubert Halloin, and Gerry Skinner

50

Compton Telescopes for Gamma-Ray Astrophysics . . . . . . . . . . . . 1711 Carolyn Kierans, Tadayuki Takahashi, and Gottfried Kanbach

51

Grid-Based Imaging of X-rays and Gamma Rays with High Angular Resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1783 Pascal Saint-Hilaire, Albert Y. Shih, Gordon J. Hurford, and Brian Dennis

52

Pair Production Detectors for Gamma-Ray Astrophysics . . . . . . . 1817 David J. Thompson and Alexander A. Moiseev

53

Readout Electronics for Gamma-Ray Astronomy . . . . . . . . . . . . . . 1851 Marco Carminati and Carlo Fiorini

54

Orbits and Background of Gamma-Ray Space Instruments . . . . . 1875 Vincent Tatischeff, Pietro Ubertini, Tsunefumi Mizuno, and Lorenzo Natalucci

55

The Use of Germanium Detectors in Space . . . . . . . . . . . . . . . . . . . . 1925 J.-P. Roques, B. J. Teegarden, D. J. Lawrence, and E. Jourdain

56

Silicon Detectors for Gamma-Ray Astronomy . . . . . . . . . . . . . . . . . 1969 R. Caputo, Y. Fukazawa, R. P. Johnson, Francesco Longo, M. Prest, H. Tajima, and E. Vallazza

57

Cd(Zn)Te Detectors for Hard X-ray and Gamma-ray Astronomy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1999 Aline Meuris, Kazuhiro Nakazawa, Irfan Kuvvetli, and Ezio Caroli

58

Scintillation Detectors in Gamma-Ray Astronomy . . . . . . . . . . . . . 2035 A. F. Iyudin, C. Labanti, and O. J. Roberts

59

Photodetectors for Gamma-Ray Astronomy . . . . . . . . . . . . . . . . . . . 2077 Elisabetta Bissaldi, Carlo Fiorini, and Alexey Uliyanov

60

Time Projection Chambers for Gamma-Ray Astronomy . . . . . . . . 2123 Denis Bernard, Stanley D. Hunter, and Toru Tanimori

61

Gamma-Ray Polarimetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2173 Denis Bernard, Tanmoy Chattopadhyay, Fabian Kislat, and Nicolas Produit

62

CubeSats for Gamma-Ray Astronomy . . . . . . . . . . . . . . . . . . . . . . . . 2215 Peter Bloser, David Murphy, Fabrizio Fiore, and Jeremy Perkins

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Gamma-Ray Detector and Mission Design Simulations . . . . . . . . . 2247 Eric A. Charles, Henrike Fleischhack, and Clio Sleator

Volume 4 Part VI Space-Based Gamma-Ray Observatories . . . . . . . . . . . . . . . . . 2279 Denis Bastieri, Pablo Saz-Parkinson, and Hiroyasu Tajima 64

The COMPTEL Experiment and Its In-Flight Performance . . . . . 2281 James M. Ryan and Werner Collmar

65

The INTEGRAL Mission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2307 E. Kuulkers, P. Laurent, Peter Kretschmar, A. Bazzano, S. Brandt, M. Cadolle-Bel, F. Cangemi, A. Coleiro, M. Ehle, C. Ferrigno, E. Jourdain, J. M. Mas-Hesse, M. Molina, J.-P. Roques, and Pietro Ubertini

66

The AGILE Mission and Its Scientific Results . . . . . . . . . . . . . . . . . 2353 Marco Tavani, Carlotta Pittori, and Francesco Longo

67

Fermi Gamma-Ray Space Telescope . . . . . . . . . . . . . . . . . . . . . . . . . 2383 David J. Thompson and Colleen A. Wilson-Hodge

68

The Fermi Large Area Telescope . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2415 Riccardo Rando

69

The ASTROGAM Concept . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2445 Alessandro De Angelis

Part VII Ground-Based Gamma-Ray Observatories . . . . . . . . . . . . . . . 2457 Daniel Mazin, Miguel Mostafa, and Gerd Pühlhofer 70

Introduction to Ground-Based Gamma-Ray Astrophysics . . . . . . . 2459 Alberto Carramiñana, Emma de Oña Wilhelmi, and Andrew M. Taylor

71

How to Detect Gamma Rays from Ground: An Introduction to the Detection Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2483 Manel Errando and Takayuki Saito

72

The Development of Ground-Based Gamma-Ray Astronomy: A Historical Overview of the Pioneering Experiments . . . . . . . . . . 2521 Razmik Mirzoyan

73

Detecting Gamma Rays with High Resolution and Moderate Field of View: The Air Cherenkov Technique . . . . . . . . . . . . . . . . . . 2547 Juan Cortina and Carlos Delgado

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Detecting Gamma-Rays with Moderate Resolution and Large Field of View: Particle Detector Arrays and Water Cherenkov Technique . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2575 Michael A. DuVernois and Giuseppe Di Sciascio

75

The High-Altitude Water Cherenkov Detector Array: HAWC . . . 2607 Jordan Goodman and Petra Huentemeyer

76

Current Particle Detector Arrays in Gamma-Ray Astronomy . . . 2633 Songzhan Chen and Zhen Cao

77

The Major Gamma-Ray Imaging Cherenkov Telescopes (MAGIC) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2667 O. Blanch and J. Sitarek

78

The Very Energetic Radiation Imaging Telescope Array System (VERITAS) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2703 David Hanna and Reshmi Mukherjee

79

H.E.S.S.: The High Energy Stereoscopic System . . . . . . . . . . . . . . . 2745 Gerd Pühlhofer, Fabian Leuschner, and Heiko Salzmann

80

The Cherenkov Telescope Array . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2787 Werner Hofmann and Roberta Zanin

81

Future Developments in Ground-Based Gamma-Ray Astronomy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2835 Ulisses Barres de Almeida and Martin Tluczykont

Volume 5 Part VIII Solar System Planets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2895 Graziella Branduardi-Raymont 82

Comets, Mars and Venus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2897 Konrad Dennerl

83

X-ray Emissions from the Jovian System . . . . . . . . . . . . . . . . . . . . . . 2921 W. R. Dunn

84

The Earth, the Moon, Mercury, Saturn and Its Rings, and Asteroids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2977 Anil Bhardwaj

85

Earth’s Exospheric X-ray Emissions . . . . . . . . . . . . . . . . . . . . . . . . . 3001 Jennifer Alyson Carter

86

SMILE: A Novel Way to Explore Solar-Terrestrial Interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3029 G. Branduardi-Raymont and C. Wang

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X-ray Emissions from the Ice Giants and Kuiper Belt . . . . . . . . . . 3049 W. R. Dunn

Part IX The Sun, Stars, and Exoplanets . . . . . . . . . . . . . . . . . . . . . . . . . . 3073 Giuseppina Micela and Beate Stelzer 88

The Solar X-ray Corona . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3075 Paola Testa and Fabio Reale

89

Stellar Coronae . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3113 Jeremy J. Drake and Beate Stelzer

90

X-ray Emission of Massive Stars and Their Winds . . . . . . . . . . . . . 3185 Gregor Rauw

91

Magnetically Confined Wind Shock . . . . . . . . . . . . . . . . . . . . . . . . . . 3217 Asif ud-Doula and Stan Owocki

92

Pre-main Sequence: Accretion and Outflows . . . . . . . . . . . . . . . . . . 3237 P. Christian Schneider, H. Moritz Günther, and Sabina Ustamujic

93

Star-Forming Regions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3271 Salvatore Sciortino

94

Nearby Young Stars and Young Moving Groups . . . . . . . . . . . . . . . 3313 Joel H. Kastner and David A. Principe

95

Extrasolar Planets and Star-Planet Interaction . . . . . . . . . . . . . . . . 3347 Katja Poppenhaeger

96

The X-ray Emission from Planetary Nebulae . . . . . . . . . . . . . . . . . . 3365 Martín A. Guerrero

Part X Supernovae, Supernova Remnants, and Diffuse Emission . . . 3387 Aya Bamba, Keiichi Maeda, and Manami Sasaki 97

Stellar Evolution, SN Explosion, and Nucleosynthesis . . . . . . . . . . . 3389 Keiichi Maeda

98

Radioactive Decay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3431 Roland Diehl

99

Supernova Remnants: Types and Evolution . . . . . . . . . . . . . . . . . . . 3467 Aya Bamba and Brian J. Williams

100

Thermal Processes in Supernova Remnants . . . . . . . . . . . . . . . . . . . 3479 Hiroya Yamaguchi and Yuken Ohshiro

101

Nonthermal Processes and Particle Acceleration in Supernova Remnants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3497 Jacco Vink and Aya Bamba

Contents

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102

Pulsar Wind Nebulae . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3531 A. M. W. Mitchell and J. Gelfand

103

Diffuse Hot Plasma in the Interstellar Medium and Galactic Outflows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3583 Manami Sasaki, Gabriele Ponti, and Jonathan Mackey

104

Interstellar Absorption and Dust Scattering . . . . . . . . . . . . . . . . . . . 3615 E. Costantini and L. Corrales

Volume 6 Part XI Compact Objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3655 Victor Doroshenko and Andrea Santangelo 105

Low-Mass X-ray Binaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3657 Arash Bahramian and Nathalie Degenaar

106

High-Mass X-ray Binaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3719 Francesca Fornasini, Vallia Antoniou, and Guillaume Dubus

107

Accreting White Dwarfs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3775 Natalie A. Webb

108

Formation and Evolution of Accreting Compact Objects . . . . . . . . 3821 Diogo Belloni and Matthias R. Schreiber

109

Black Holes: Accretion Processes in X-ray Binaries . . . . . . . . . . . . 3911 Qingcui Bu and Shuang-Nan Zhang

110

Black Holes: Timing and Spectral Properties and Evolution . . . . . 3939 Emrah Kalemci, Erin Kara, and John A. Tomsick

111

Isolated Neutron Stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3983 Alice Borghese and Paolo Esposito

112

Low-Magnetic-Field Neutron Stars in X-ray Binaries . . . . . . . . . . . 4031 Tiziana Di Salvo, Alessandro Papitto, Alessio Marino, Rosario Iaria, and Luciano Burderi

113

Accreting Strongly Magnetized Neutron Stars: X-ray Pulsars . . . 4105 Alexander Mushtukov and Sergey Tsygankov

114

Fundamental Physics with Neutron Stars . . . . . . . . . . . . . . . . . . . . . 4177 Joonas Nättilä and Jari J. E. Kajava

115

X-ray Emission Mechanisms in Accreting White Dwarfs . . . . . . . . 4231 K. L. Page and A. W. Shaw

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Contents

Part XII Galaxies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4275 Giuseppina Fabbiano and Marat Gilfanov 116

Introduction to the Section on Galaxies . . . . . . . . . . . . . . . . . . . . . . . 4277 Giuseppina Fabbiano and Marat Gilfanov

117

X-ray Binaries in External Galaxies . . . . . . . . . . . . . . . . . . . . . . . . . . 4283 Marat Gilfanov, Giuseppina Fabbiano, Bret Lehmer, and Andreas Zezas

118

The Hot Interstellar Medium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4321 Emanuele Nardini, Dong-Woo Kim, and Silvia Pellegrini

119

X-ray Halos Around Massive Galaxies: Data and Theory . . . . . . . 4369 Ákos Bogdán and Mark Vogelsberger

120

The Interaction of the Active Nucleus with the Host Galaxy Interstellar Medium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4399 Giuseppina Fabbiano and M. Elvis

121

Probing the Circumgalactic Medium with X-ray Absorption Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4445 Smita Mathur

Volume 7 Part XIII Active Galactic Nuclei in X- and Gamma-rays . . . . . . . . . . . . . 4481 Alessandra De Rosa and Cristian Vignali 122

Active Galactic Nuclei and Their Demography Through Cosmic Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4483 Stefano Bianchi, Vincenzo Mainieri, and Paolo Padovani

123

The Super-Massive Black Hole Close Environment in Active Galactic Nuclei . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4515 William Alston, Margherita Giustini, and Pierre-Olivier Petrucci

124

Black Hole-Galaxy Co-evolution and the Role of Feedback . . . . . . 4567 Pedro R. Capelo, Chiara Feruglio, Ryan C. Hickox, and Francesco Tombesi

125

The Dawn of Black Holes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4617 Elisabeta Lusso, Rosa Valiante, and Fabio Vito

Part XIV Galaxy Clusters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4679 Etienne Pointecouteau, Elena Rasia, and Aurora Simionescu 126

X-ray Cluster Cosmology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4681 Nicolas Clerc and Alexis Finoguenov

Contents

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127

Scaling Relations of Clusters and Groups and Their Evolution . . . 4733 Lorenzo Lovisari and Ben J. Maughan

128

Thermodynamic Profiles of Galaxy Clusters and Groups . . . . . . . . 4783 S. T. Kay and G. W. Pratt

129

Cluster Outskirts and Their Connection to the Cosmic Web . . . . . 4813 Stephen Walker and Erwin Lau

130

Absorption Studies of the Most Diffuse Gas in the Large-Scale Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4851 Taotao Fang, Smita Mathur, and Fabrizio Nicastro

131

AGN Feedback in Groups and Clusters of Galaxies . . . . . . . . . . . . 4895 Julie Hlavacek-Larrondo, Yuan Li, and Eugene Churazov

132

Chemical Enrichment in Groups and Clusters . . . . . . . . . . . . . . . . . 4961 François Mernier and Veronica Biffi

133

The Merger Dynamics of the X-ray-Emitting Plasma in Clusters of Galaxies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5005 John ZuHone and Yuanyuan Su

134

Plasma Physics of the Intracluster Medium . . . . . . . . . . . . . . . . . . . 5049 Matthew W. Kunz, Thomas W. Jones, and Irina Zhuravleva

Part XV Transient Events . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5091 Bin-Bin Zhang 135

Gamma-Ray Bursts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5093 Yun-Wei Yu, He Gao, Fa-Yin Wang, and Bin-Bin Zhang

136

Accretion Disk Evolution in Tidal Disruption Events . . . . . . . . . . . 5127 Wenbin Lu

137

Fast Radio Bursts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5151 Di Xiao, Fa-Yin Wang, and Zigao Dai

Part XVI Miscellanea . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5189 Cosimo Bambi 138

Probing Black-Hole Accretion Through Time Variability . . . . . . . 5191 Barbara De Marco, Sara E. Motta, and Tomaso M. Belloni

139

Surveys of the Cosmic X-ray Background . . . . . . . . . . . . . . . . . . . . . 5233 W. N. Brandt and G. Yang

140

Tests of General Relativity Using Black Hole X-ray Data . . . . . . . . 5269 Dimitry Ayzenberg and Cosimo Bambi

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Contents

141

Tests of Lorentz Invariance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5305 Jun-Jie Wei and Xue-Feng Wu

142

X- and Gamma-Ray Astrophysics in the Era of Multi-messenger Astronomy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5335 G. Stratta and Andrea Santangelo

Volume 8 Part XVII Spectral-Imaging Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5367 Victor Doroshenko, Andrea Santangelo, and Sergey Tsygankov 143

Modeling and Simulating X-ray Spectra . . . . . . . . . . . . . . . . . . . . . . 5369 Lorenzo Ducci and Christian Malacaria

144

Statistical Aspects of X-ray Spectral Analysis . . . . . . . . . . . . . . . . . . 5403 Johannes Buchner and Peter Boorman

145

Analysis Methods for Gamma-Ray Astronomy . . . . . . . . . . . . . . . . 5453 Denys Malyshev and Lars Mohrmann

Part XVIII Timing Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5507 Tomaso M. Belloni and Dipankar Bhattacharya 146

Basics of Fourier Analysis for High-Energy Astronomy . . . . . . . . . 5509 Tomaso M. Belloni and Dipankar Bhattacharya

147

Time Domain Methods for X-ray and Gamma-ray Astronomy . . . 5543 Eric D. Feigelson, Vinay L. Kashyap, and Aneta Siemiginowska

148

Fourier Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5569 Matteo Bachetti and Daniela Huppenkothen

149

X-ray Polarimetry-Timing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5617 Adam Ingram

Part XIX Polarimetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5661 Hua Feng and Henric Krawczynski 150

General History of X-ray Polarimetry in Astrophysics . . . . . . . . . . 5663 Enrico Costa

151

Bayesian Analysis of the Data from PoGO+ . . . . . . . . . . . . . . . . . . . 5683 Mózsi Kiss and Mark Pearce

152

Gamma-Ray Polarimetry of Transient Sources with POLAR . . . . 5717 Merlin Kole and Jianchao Sun

Contents

xix

153

Analysis of the Data from Photoelectric Gas Polarimeters . . . . . . . 5757 Fabio Muleri

154

Neural Network Analysis of X-ray Polarimeter Data . . . . . . . . . . . 5781 A. L. Peirson

155

Soft Gamma-Ray Polarimetry with COSI Using Maximum Likelihood Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5829 John A. Tomsick, Alexander Lowell, Hadar Lazar, Clio Sleator, and Andreas Zoglauer

156

Stokes Parameter Analysis of XL-Calibur Data . . . . . . . . . . . . . . . . 5853 Fabian Kislat and Sean Spooner

Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5871

About the Editors

Cosimo Bambi is currently Xie Xide Junior Chair Professor at the Department of Physics at Fudan University. He received the Laurea degree from Florence University in 2003 and the PhD degree from Ferrara University in 2007. He worked as a postdoctoral research scholar at Wayne State University (2007–2008), at IPMU at The University of Tokyo (2008–2011), and in the group of Gia Dvali at LMU Munich (2011–2012). He joined Fudan University at the end of 2012 as Associate Professor under the Thousand Young Talents Program of the State Council of the People’s Republic of China. He was promoted to Full Professor at the end of 2013 and named Xie Xide Junior Chair Professor of Physics in 2016. In 2015, he was awarded a Humboldt Fellowship to collaborate with the group of Kostas Kokkotas at Eberhard Karls Universität Tübingen. Professor Bambi has received a number of awards, including the Magnolia Gold Award in 2022 and the Magnolia Silver Award in 2018 from the Municipality of Shanghai, the International Excellent Young Scientists Award from the National Natural Science Foundation of China in 2022, and the Xu Guangqi Prize from the Embassy of Italy in Beijing in 2018. Professor Bambi has worked on a number of topics in the fields of high-energy astrophysics, particle cosmology, and gravity. His main research interests focus on theoretical and observational studies of black holes. He has published about 200 papers on high impact factor refereed journals as first or corresponding author and has over 10,000 citations. He has authored/edited several academic books xxi

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About the Editors

with Springer: Introduction to Particle Cosmology: The Standard Model of Cosmology and Its Open Problems (Springer-Verlag Heidelberg Berlin, 2016), Astrophysics of Black Holes: From Fundamental Aspects to Latest Developments (Springer-Verlag Heidelberg Berlin, 2016), Black Holes: A Laboratory for Testing Strong Gravity (Springer Singapore, 2017), Introduction to General Relativity (Springer Singapore, 2018), Tutorial Guide to X-ray and Gamma-ray Astronomy: Data Reduction and Analysis (Springer Singapore, 2020), Handbook of Gravitational Wave Astronomy (Springer Singapore, 2022), Regular Black Holes: Towards a New Paradigm of Gravitational Collapse (Springer Singapore, 2023), and HighResolution X-ray Spectroscopy: Instrumentation, Data Analysis, and Science (Springer Singapore, 2023). The book Introduction to General Relativity was published in Chinese by Fudan University Press in 2020, in Spanish by Editorial Reverté in 2021, and in Persian by Jahan-Adib in 2022. Professor Bambi has also written a popular science book, Niente é impossibili: Viaggiare nel tempo, attraversare i buchi neri e altre sfide scientifiche (in Italian), published by Il Saggiatore in 2020 and translated in Chinese and published by Fudan University Press in 2024. Professor Andrea Santangelo studied Physics at the University of Palermo in Italy and later specialized in Astrophysics at the Institute of Cosmic Physics of the Italian National Research Council, with Prof. Livio Scarsi, and at Columbia University, New York, with Prof. Robert Novick. After many years as staff scientist at the Italian CNR and INAF, Andrea Santangelo is since 2004 Professor of High Energy Astrophysics and Director of the High Energy Section of the Institute of Astronomy and Astrophysics of the Eberhard Karls Universität Tübingen in Germany. He has served several terms as Director of the Institute and as Chairman of the physics department. In 2009, he was granted a RIKEN Grant as Senior Scientist, while in 2010 he was co-recipient, as member of the HESS collaboration, of the “Bruno Rossi” Prize for the scientific achievements of the HESS Telescope, and in 2007 he was co-recipient, as member of the HESS collaboration, of the European “Descartes” Prize for the scientific

About the Editors

xxiii

achievements of the HESS Telescope. In 2016, he was granted a CAS President’s International Fellowship as Visiting Full Professor at IHEP (CAS), and since then he has kept a close collaboration with IHEP. He is among the very few scientists who has been granted a second CAS President’s International Fellowship in 2021. Prof. Santangelo’s research interests are in the field of multi-messenger astronomy with focus on High Energy Astrophysics, from a fraction of keV, in the X-rays, to 10^21 eV in the Ultra High Energy Comic rays. He has participated, with leading roles, in many X-ray missions such as BeppoSAX, INTEGRAL, XMM-Newton, eROSITA, and more recently to eXTP, THESEUS, and ATHENA. He is also leading research for the TeV observatories HESS and CTA, and in the past, the EUSO program for the search of Ultra High Energy Cosmic Rays from space. Among the sources populating the High Energy Sky, Prof. Santangelo likes very much X-ray binaries, elusive dark matter sources, and TeV emitters. Andrea Santangelo has published about 500 articles in refereed journals in the fields of Experimental High Energy Astrophysics, Experimental TeV Astrophysics, Space Instrumentation, SpaceBased search for UHECRs, Galactic Compact objects: from accretion to population studies, Dark Matter indirect search, Ultra High Energy Cosmic Rays, Instruments Calibration, and Instrument Background studies.

Section Editors

Aya Bamba Department of Physics Graduate School of Science The University of Tokyo Tokyo, Japan Research Center for the Early Universe School of Science The University of Tokyo Tokyo, Japan Trans-Scale Quantum Science Institute The University of Tokyo Tokyo, Japan Cosimo Bambi Department of Physics Fudan University Shanghai, China

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Section Editors

Denis Bastieri Department of Physics and Astronomy “G. Galilei” Padua University Padua, Italy National Institute for Nuclear Physics (INFN) Section Padua Padua, Italy Center for Astrophysics Guangzhou University Guangzhou, China Tomaso M. Belloni Brera Astronomical Observatory National Institute for Astrophysics (INAF) Merate, Italy

Dipankar Bhattacharya Department of Physics Ashoka University Haryana, India

Tomaso M. Belloni: deceased.

Section Editors

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G. Branduardi-Raymont Mullard Space Science Laboratory Department of Space and Climate Physics University College London London, UK

Alessandra De Rosa National Institute for Astrophysics (INAF) Institute of Space Astrophysics and Planetology (IAPS) Rome, Italy

Jan-Willem den Herder Foundation for Dutch Scientific Research Institutes (NWO) Netherlands Institute for Space Research (SRON) Leiden, The Netherlands University of Amsterdam Amsterdam, The Netherlands Victor Doroshenko Institute of Astronomy and Astrophysics University of Tuebingen Tübingen, Germany

G. Branduardi-Raymont: deceased.

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Section Editors

G. Fabbiano Center for Astrophysics Harvard & Smithsonian Cambridge, MA, USA

Hua Feng Department of Astronomy Tsinghua University Beijing, China

Marco Feroci National Institute for Astrophysics (INAF) Institute of Space Astrophysics and Planetology (IAPS) Rome, Italy National Institute for Nuclear Physics (INFN) Section Roma Tor Vergata Rome, Italy

Section Editors

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Jessica Gaskin NASA Marshall Space Flight Center Huntsville, AL, USA

Marat Gilfanov Max Planck Institute for Astrophysics Garching, Germany

Lorraine Hanlon Centre for Space Research & School of Physics University College Dublin Dublin, Ireland

Rene Hudec Faculty of Electrical Engineering Czech Technical University in Prague Prague, Czech Republic Astronomical Institute Czech Academy of Sciences Ondrejov, Czech Republic

xxx

Section Editors

Henric Krawczynski Washington University in St. Louis St. Louis, MO, USA

Keiichi Maeda Department of Astronomy Kyoto University Kyoto, Japan

Daniel Mazin The University of Tokyo Tokyo, Japan

Norbert Meidinger Max Planck Institute for Extraterrestrial Physics Garching, Germany

Section Editors

xxxi

Giuseppina Micela Palermo Astronomical Observatory Palermo, National Institute for Astrophysics (INAF) Italy

Miguel Mostafá Temple University Philadelphia, PA, USA

Arvind Parmar European Space Agency Noordwijk, The Netherlands

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Section Editors

Etienne Pointecouteau National Center for Scientific Research (CNRS) IRAP, Toulouse, France University of Toulouse Toulouse, France

Gerd Pühlhofer Institute of Astronomy and Astrophysics University of Tuebingen Tübingen, Germany

Elena Rasia Trieste Astronomical Observatory National Institute for Astrophysics (INAF) Trieste, Italy

Andrea Santangelo Institute of Astronomy and Astrophysics University of Tuebingen Tübingen, Baden-Württemberg, Germany

Section Editors

xxxiii

Manami Sasaki Dr. Karl Remeis Sternwarte Erlangen Centre for Astroparticle Physics University of Erlangen-Nuernberg Bamberg, Germany

Pablo M. Saz Parkinson Santa Cruz Institute for Particle Physics University of California Santa Cruz Santa Cruz, CA, USA

Aurora Simionescu Institutes Organization of the Dutch Research Council (NWO) Netherlands Institute for Space Research (SRON) Leiden, Netherlands

Daniele Spiga Brera Astronomical Observatory National Institute for Astrophysics (INAF) Milan, Italy

xxxiv

Section Editors

Beate Stelzer Institute of Astronomy and Astrophysics University of Tuebingen Tübingen, Germany

H. Tajima Solar-Terresterial Enviornment Laboratory Nagoya University Nagoya, Japan

Vincent Tatischeff Paris-Saclay University & National Center for Scientific Research (CNRS)/IN2P3 IJCLab Orsay, France

David J. Thompson NASA Goddard Space Flight Center Greenbelt, MD, USA

Section Editors

xxxv

Sergey Tsygankov Department of Physics and Astronomy University of Turku Turku, Finland

Cristian Vignali Department of Physics and Astronomy “Augusto Righi” University of Bologna Bologna, Italy

Bin-Bin Zhang Nanjing University Nanjing, China

Shuang-Nan Zhang Key Laboratory for Particle Astrophysics Institute of High Energy Physics CAS, Beijing, China University of Chinese Academy of Sciences Chinese Academy of Sciences Beijing, China

Contributors

H. Akamatsu SRON Netherlands Institute for Space Research, The Netherlands

Leiden,

Ulisses Barres de Almeida Brazilian Center for Physics Research (CBPF), Rio de Janeiro, Brazil William Alston Centre for Astrophysics Research, University of Hertfordshire, Hatfield, Hertfordshire, UK Lorella Angelini Astrophysics Science Division, NASA Goddard Space Flight Center, Greenbelt, MD, USA Vallia Antoniou Department of Physics and Astronomy, Texas Tech University, Lubbock, TX, USA Center for Astrophysics, Harvard & Smithsonian, Cambridge, MA, USA Zaven Arzoumanian NASA/GSFC, Greenbelt, MD, USA Carolyn Atkins STFC UK Astronomy Technology Centre, Edinburgh, UK Dimitry Ayzenberg Theoretical Astrophysics, Eberhard-Karls Universität Tübingen, Tübingen, Germany Matteo Bachetti INAF-Osservatorio Astronomico di Cagliari, Selargius, CA, Italy Arash Bahramian International Centre for Radio Astronomy Research – Curtin University, Perth, WA, Australia Luca Baldini Universita’ di Pisa e INFN-Pisa, Pisa, Italy Aya Bamba Research Center for the Early Universe, School of Science, The University of Tokyo, Bunkyo-ku, Tokyo, Japan Cosimo Bambi Center for Field Theory and Particle Physics and Department of Physics, Fudan University, Shanghai, China Marco Barbera Dipartimento di Fisica e Chimica “E. Segrè”, Università degli Studi di Palermo, Palermo, Italy xxxvii

xxxviii

Contributors

Nicolas M. Barrière cosine, Sassenheim, The Netherlands Scott D. Barthelmy Astrophysics Science Division, NASA Goddard Space Flight Center, Greenbelt, MD, USA M. W. Bautz MIT Center for Space Research, Cambridge, MA, USA Marcos Bavdaz European Space Agency, ESTEC, Noordwijk, The Netherlands A. Bazzano IAPS/INAF, Rome, Italy Diogo Belloni Departamento de Física, Universidad Técnica Federico Santa María, Valparaíso, Chile Tomaso M. Belloni Osservatorio Astronomico di Brera, INAF, Merate, Italy Denis Bernard LLR, Ecole polytechnique, CNRS/IN2P3 and Institut Polytechnique de Paris, Palaiseau, France Anil Bhardwaj Physical Research Laboratory, Ahmedabad, India Dipankar Bhattacharya Inter-University Centre for Astronomy and Astrophysics, Ganeshkhind, Pune, India Ashoka University, Sonipat, Haryana, India Stefano Bianchi Dipartimento di Matematica e Fisica, Università degli Studi Roma Tre, Roma, Italy Veronica Biffi INAF – Osservatorio Astronomico di Trieste, Trieste, Italy Elisabetta Bissaldi Dipartimento Interateneo di Fisica, Politecnico di Bari, Bari, Italy Sezione di Bari, Istituto Nazionale di Fisica Nucleare, Bari, Italy Kevin Black Rock Creek Scientific and NASA Goddard Space Flight Center, Greenbelt, MD, USA O. Blanch Inistitut de Física d’Altes Energies (IFAE) – The Barcelona Institute of Science and Technology (BIST), Barcelona, Spain Peter Bloser Los Alamos National Laboratory, Los Alamos, NM, USA Ákos Bogdán Center for Astrophysics | Harvard & Smithsonian, Cambridge, MA, USA Peter Boorman Astronomical Institute, Academy of Sciences, Boˇcní, Prague, Czech Republic Alice Borghese Institute of Space Sciences (ICE, CSIC), Barcelona, Spain Departamento de Astrofisica, Universidad de La Laguna, Tenerife, Spain

Tomaso M. Belloni: deceased.

Contributors

xxxix

S. Brandt DTU Space–National Space Institute, Technical University of Denmark, Lyngby, Denmark W. N. Brandt Department of Astronomy & Astrophysics, The Pennsylvania State University, University Park, PA, USA Institute for Gravitation and the Cosmos, The Pennsylvania State University, University Park, PA, USA Department of Physics, The Pennsylvania State University, University Park, PA, USA G. Branduardi-Raymont Mullard Space Science Laboratory, Department of Space and Climate Physics, University College London, Holmbury St Mary, Dorking, Surrey, UK David Broadway NASA Marshall Space Flight Center (MSFC), Huntsville, AL, USA Qingcui Bu Institut für Astronomie und Astrophysik, Kepler Center for Astro and Particle Physics, Eberhard Karls Universität, Tübingen, Germany Johannes Buchner Max Planck Institute for Extraterrestrial Physics, Gießenbachstrasse, Garching, Germany Emma J. Bunce School of Physics and Astronomy, University of Leicester, Leicester, UK Luciano Burderi Dipartimento di Fisica, Universitá degli Studi di Cagliari, Monserrato, Italy Gillian Butcher School of Physics and Astronomy, University of Leicester, Leicester, UK M. Cadolle-Bel Allane Mobility Group, Pullach, Germany Riccardo Campana INAF-OAS, Bologna, Italy F. Cangemi CNRS/LPNHE, Paris, France Xuelei Cao Key Laboratory of Particle Astrophysics, Institute of High Energy Physics, Chinese Academy of Sciences, Beijing, China Zhen Cao Key Laboratory of Particle Astrophysics, Institute of High Energy Physics, Chinese Academy of Sciences, Beijing, China Pedro R. Capelo Center for Theoretical Astrophysics and Cosmology, Institute for Computational Science, University of Zurich, Zürich, Switzerland R. Caputo NASA Goddard Space Flight Center, Greenbelt, MD, USA Marco Carminati DEIB, Politecnico di Milano, Milano, Italy

G. Branduardi-Raymont: deceased.

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Contributors

Ezio Caroli INAF/OAS of Bologna, Bologna, Italy Alberto Carramiñana Instituto Nacional de Astrofísica, Óptica y Electrónica, Tonantzintla, Puebla, Mexico Jennifer Alyson Carter University of Leicester, Leicester, UK S. Bradley Cenko Astrophysics Science Division, NASA Goddard Space Flight Center, Greenbelt, MD, USA Eric A. Charles Kavli Institute for Particle Astrophysics and Cosmology, SLAC National Accelerator Laboratory, Menlo Park, CA, USA Tanmoy Chattopadhyay Kavli Institute of Particle Astrophysics and Cosmology, Stanford University, Stanford, CA, USA Songzhan Chen Key Laboratory of Particle Astrophysics, Institute of High Energy Physics, Chinese Academy of Sciences, Beijing, China Yong Chen Key Laboratory of Particle Astrophysics, Institute of High Energy Physics, Chinese Academy of Sciences, Beijing, China Finn E. Christensen DTU Space, Technical University of Denmark, Lyngby, Denmark Eugene Churazov Max Planck Institute for Astrophysics, Garching, Germany Space Research Institute (IKI), Moscow,Russia Nicolas Clerc IRAP, Université de Toulouse, CNRS, UPS, CNES, Toulouse, France A. Coleiro AstroParticule et Cosmologie, Université de Paris, CNRS, Paris, France Werner Collmar Max Planck Institute for Extraterrestrial Physics, Giessenbachstrasse 1, 85748 Garching, Germany Maximilien J. Collon cosine, Sassenheim, The Netherlands Bertrand Cordier Lab AIM – CEA, CNRS, Université Paris-Saclay, Université de Paris, Gif-sur-Yvette, France L. Corrales Department of Astronomy, University of Michigan, Ann Arbor, MI, USA Juan Cortina CIEMAT, Madrid, Spain Enrico Costa Istituto di Astrofisica e Planetologia Spaziale – INAF, Roma, Italy E. Costantini SRON Netherlands Institute for Space Research, The Netherlands

Leiden,

Anton Pannekoek Astronomical Institute, University of Amsterdam, Amsterdam, The Netherlands

Contributors

xli

Zigao Dai Department of Astronomy, University of Science and Technology of China, Hefei, China Jacqueline M. Davis NASA Marshall Space Flight Center, Huntsville, AL, USA Alessandro De Angelis Department of Physics and Astronomy “Galileo Galilei”, University of Padua, Padua, Italy INFN and INAF, Padua, Italy IST/LIP, Lisboa, Portugal Barbara De Marco Departament de Fìsica, EEBE, Universitat Politècnica de Catalunya, Barcelona, Spain Emma de Oña Wilhelmi Deutsches Elektronen Synchrotron DESY, Zeuthen, Germany Nathalie Degenaar Anton Pannekoek Institute for Astronomy, University of Amsterdam, Amsterdam, The Netherlands Ettore Del Monte Istituto di Astrofisica e Planetologia Spaziali (IAPS), Roma, Italy INFN – Roma Tor Vergata, Roma, Italy Carlos Delgado CIEMAT, Madrid, Spain J. W. den Herder NWO-I/SRON and the University of Amsterdam, Leiden, The Netherlands Konrad Dennerl Max-Planck-Institut für extraterrestrische Physik, Garching, Germany Brian Dennis Solar Physics Laboratory, Goddard Space Flight Center, Greenbelt, MD, USA Casey T. DeRoo Department of Physics and Astronomy, University of Iowa, Iowa City, IA, USA Tiziana Di Salvo Dipartimento di Fisica e Chimica – Emilio Segré, Universitá di Palermo, Palermo, Italy Sebastian Diebold Institut für Astronomie und Astrophysik, Eberhard Karls Universität Tübingen, Tübingen, Germany Roland Diehl Max Planck Institut für extraterrestrische Physik, Germany

Garching,

W. B. Doriese United States Department of Commerce, National Institute of Standards and Technology (NIST), Boulder, CO, USA Jeremy J. Drake Center for Astrophysics | Harvard & Smithsonian MS-03, Cambridge, MA, USA Guillaume Dubus University of Grenoble Alpes, CNRS, IPAG, Grenoble, France

xlii

Contributors

Lorenzo Ducci Institut für Astronomie und Astrophysik Tübingen, Kepler Center for Astro and Particle Physics, University of Tübingen, Tübingen, Germany ISDC Data Center for Astrophysics, Université de Genève, Versoix, Switzerland W. R. Dunn Department of Physics and Astronomy, University College London, London, UK The Centre for Planetary Science at UCL/Birkbeck, London, UK Michael A. DuVernois Dept of Physics & Wisconsin IceCube Particle Astrophysics Center (WIPAC), University of Wisconsin, Madison, WI, USA M. Ehle European Space Agency (ESA), European Space Astronomy Centre (ESAC), Madrid, Spain M. Elvis Center for Astrophysics | Harvard & Smithsonian, Cambridge, MA, USA Manel Errando Department of Physics, Washington University in St. Louis, St. Louis, MO, USA Paolo Esposito Scuola Universitaria Superiore IUSS Pavia, Palazzo del Broletto, Pavia, Italy INAF–Istituto di Astrofisica Spaziale e Fisica Cosmica di Milano, Milano, Italy Yuri Evangelista IAPS/INAF, Rome, Italy Giuseppina Fabbiano Harvard-Smithsonian Center for Astrophysics (CfA), Cambridge, MA, USA Sergio Fabiani Istituto di Astrofisica e Planetologia Spaziali (IAPS), Roma, Italy INFN – Roma Tor Vergata, Roma, Italy Taotao Fang Department of Astronomy, Xiamen University, Xiamen, China Eric D. Feigelson Department of Astronomy and Astrophysics, Center for Astrostatistics, Penn State University, Pennsylvania, PA, USA Charly Feldman School of Physics and Astronomy, University of Leicester, Leicester, UK Hua Feng Department of Astronomy, Tsinghua University, Beijing, China Marco Feroci Istituto di Astrofisica e Planetologia Spaziali, Istituto Nazionale di Astrofisica, Rome, Italy Elizabeth Ferrara NASA/GSFC and University of Maryland, Greenbelt, MD, USA Desiree Della Monica Ferreira DTU Space – Technical University of Denmark, Kongens Lyngby, Denmark Ivo Ferreira European Space Agency, ESTEC, Noordwijk, The Netherlands

Contributors

xliii

C. Ferrigno ISDC/University of Geneva, Versoix, Switzerland Chiara Feruglio INAF Osservatorio Astronomico di Trieste, Trieste, Italy Institute for Fundamental Physics of the Universe, Trieste, Italy Alexis Finoguenov Department of Physics, University of Helsinki, Helsinki, Finland Fabrizio Fiore INAF-Osservatorio Astronomico di Trieste, Trieste, Italy Carlo Fiorini Dipartimento di Elettronica, Informazione e Bioingegneria, Politecnico di Milano, Milano, Italy Sezione di Milano, Istituto Nazionale di Fisica Nucleare, Milano, Italy Henrike Fleischhack Catholic University of America, Washington, DC, USA NASA/GSFC, Greenbelt, MD, USA CRESST II, Greenbelt, MD, USA Francesca Fornasini Stonehill College, North Easton, MA, USA Peter Friedrich Max-Planck-Institut für extraterrestrische Physik, Germany

Garching,

Y. Fukazawa Department of Physical Sciences, Hiroshima University, HigashiHiroshima, Hiroshima, Japan Weiqun Gan Chinese Academy of Sciences, Purple Mountain Observatory, Nanjing, China He Gao Department of Astronomy, Beijing Normal University, Beijing, China Jessica Gaskin NASA Marshall Space Flight Center, Huntsville, AL, USA J. Gelfand NYU Abu Dhabi, Abu Dhabi, UAE Keith Gendreau NASA/GSFC, Greenbelt, MD, USA Marat Gilfanov Max-Planck-Institute for Astrophysics, Space Research Institute, Garching, Germany Space Research Institute, Moscow, Russia David Girou cosine, Sassenheim, The Netherlands Margherita Giustini Centro de Astrobiologia (CAB), CSIC-INTA, Madrid, Hertfordshire, UK Andrea Goldwurm Université Paris Cité, CNRS, CEA, Astroparticule et Cosmologie, Paris, France Département d’Astrophysique/IRFU/DRF, CEA-Saclay, Gif-sur-Yvette, France Rosario González-Riestra Serco Gestión de Negocios S.L., ESAC, Madrid, Spain

xliv

Contributors

Jordan Goodman University of Maryland, College Park, MD, USA Luciano Gottardi NWO-I/SRON Netherlands Institute for Space Research, Leiden, The Netherlands Aleksandra Gros Université Paris-Saclay, Université Paris Cité, CEA, CNRS, AIM, Gif-sur-Yvette, France Martín A. Guerrero Instituto de Astrofísica de Andalucía, IAA-CSIC, Granada, Spain H. Moritz Günther Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology, Cambridge, MA, USA Alejandro Guzman University of Tübingen Institute for Astronomy and Astrophysics, Tübingen, Germany K. Hagino Kanto Gakuin University, Kanazawa-ku, Yokohama, Japan Graeme P. Hall School of Physics and Astronomy, University of Leicester, Leicester, UK Hubert Halloin Université de Paris, CNRS, Astroparticule et Cosmologie, Paris, France David Hanna Physics Department, McGill University, Montreal, QC, Canada Laura A. Hayes European Space Agency (ESA), European Space Research and Technology Centre (ESTEC), Noordwijk, The Netherlands Margarita Hernanz Institute of Space Sciences (ICE-CSIC), Barcelona, Spain Ryan C. Hickox Department of Physics and Astronomy, Dartmouth College, Hanover, NH, USA Martin Hilchenbach Max Planck Institute for Solar System Research, Justus-vonLiebig-Weg, Göttingen, Germany Julie Hlavacek-Larrondo Physics Department, Université de Montréal, Montréal, QC, Canada Werner Hofmann Max-Planck-Institut für Kernphysik, Heidelberg, Germany Andrew D. Holland Centre for Electronic Imaging, The Open University, Milton Keynes, UK Jaesub Hong Center for Astrophysics, Harvard & Smithsonian, Cambridge, MA, USA Deirdre Horan Laboratoire Leprince-Ringuet, CNRS/IN2P3, Institut Polytechnique de Paris, Palaiseau, France Rene Hudec Faculty of Electrical Engineering, Czech Technical University in Prague, Prague, Czech Republic

Contributors

xlv

Petra Huentemeyer Michigan Technological University, Houghton, MI, USA Stanley D. Hunter NASA/Goddard Space Flight Center, Greenbelt, MD, USA Juhani Huovelin Department of Physics, University of Helsinki, Helsinki, Finland Daniela Huppenkothen SRON Netherlands Institute for Space Research, Leiden, The Netherlands Gordon J. Hurford Space Sciences Laboratory, University of California, Berkeley, CA, USA Rosario Iaria Dipartimento di Fisica e Chimica – Emilio Segré, Universitá di Palermo, Palermo, Italy Adam Ingram School of Mathematics, Statistics and Physics, Newcastle University, Newcastle upon Tyne, UK A. F. Iyudin Skobeltsyn Institute of Nuclear Physics, Moscow State University, Moscow, Russia B. D. Jackson SRON Netherlands Institute for Space Research, Groningen, The Netherlands Xiankai Jiang Chinese Academy of Sciences, Purple Mountain Observatory, Nanjing, China R. P. Johnson Department of Physics, Santa Cruz Institute for Particle Physics, University of California at Santa Cruz, Santa Cruz, CA, USA Thomas W. Jones School of Physics and Astronomy, University of Minnesota, Minneapolis, MN, USA E. Jourdain UPS-OMP, IRAP, Université de Toulouse, Toulouse, France Philip Kaaret Department of Physics and Astronomy, University of Iowa, Iowa City, IA, USA Jelle Kaastra SRON, Leiden, The Netherlands Jari J. E. Kajava Serco for ESA, ESA/ESAC, Madrid, Spain Department of Physics and Astronomy, University of Turku, Turku, Finland Emrah Kalemci Faculty of Engineering and Natural Sciences, SabancıUniversity, Istanbul, Turkey Gottfried Kanbach Max Planck Institute for Extraterrestrial Physics, Garching, Germany Erin Kara MIT Kavli Institute for Astrophysics and Space Research, Cambridge, MA, USA Vinay L. Kashyap Center for Astrophysics, Harvard & Smithsonian, Cambridge, MA, USA

xlvi

Contributors

Joel H. Kastner Center for Imaging Science, School of Physics and Astronomy, and Laboratory for Multiwavelength Astrophysics, Rochester Institute of Technology, Rochester, NY, USA S. T. Kay Jodrell Bank Centre for Astrophysics, Department of Physics and Astronomy, The University of Manchester, Manchester, UK Jamie A. Kennea Department of Astronomy and Astrophysics, The Pennsylvania State University, University Park, PA, USA Carolyn Kierans NASA Goddard Space Flight Center, Greenbelt, MD, USA Kiranmayee Kilaru Marshall Space Flight Center, Huntsville, AL, USA Dong-Woo Kim Center for Astrophysics | Harvard & Smithsonian, Cambridge, MA, USA Marcus Kirsch ESA, European Space Operations Centre (ESOC), Darmstadt, Germany Fabian Kislat University of New Hampshire, Durham, NH, USA Mózsi Kiss Department of Physics, KTH Royal Institute of Technology, Stockholm, Sweden The Oskar Klein Centre for Cosmoparticle Physics, AlbaNova University Center, Stockholm, Sweden Merlin Kole DPNC, University of Geneva, Geneva, Switzerland Peter Kretschmar European Space Agency (ESA), European Space Astronomy Centre (ESAC), Madrid, Spain Säm Krucker University of Applied Sciences and Arts Northwestern Switzerland, Windisch, Switzerland Space Sciences Laboratory, University of California, Berkeley, CA, USA Matthew W. Kunz Department of Astrophysical Sciences, Princeton University, Princeton, NJ, USA E. Kuulkers European Space Agency (ESA), European Space Research and Technology Centre (ESTEC), Noordwijk, The Netherlands Irfan Kuvvetli DTU-Space, Kongens Lyngby, Denmark C. Labanti Osservatorio di Astrofisica e Scienza dello spazio (OAS-INAF), Bologna, Italy Boris Landgraf cosine, Sassenheim, The Netherlands Erwin Lau Smithsonian Astrophysical Observatory, Cambridge, MA, USA P. Laurent CEA/DRF/IRFU/DAp, CEA Saclay, Saclay, France

Contributors

xlvii

D. J. Lawrence Johns Hopkins University Applied Physics Laboratory, Laurel, MD, USA Hadar Lazar Space Sciences Laboratory, University of California, Berkeley, CA, USA Bret Lehmer University of Arkansas, Fayetteville, AR, USA Arto Lehtolainen Department of Physics, University of Helsinki, Helsinki, Finland Fabian Leuschner Institute for Astronomy and Astrophysics Tübingen, Tübingen, Germany Yuan Li University of North Texas, Denton, TX, USA Simon T. Lindsay School of Physics and Astronomy, University of Leicester, Leicester, UK Zhixing Ling National Astronomical Observatories, Chinese Academy of Sciences, Beijing, China Congzhan Liu Key Laboratory of Particle Astrophysics, Institute of High Energy Physics, Chinese Academy of Sciences, Beijing, China Ugo Lo Cicero Osservatorio Astronomico di Palermo “G. S. Vaiana”, Istituto Nazionale di Astrofisica, Palermo, Italy Francesco Longo Università degli Studi di Trieste, Trieste, Italy Lorenzo Lovisari INAF – Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Bologna, Italia Center for Astrophysics, Harvard & Smithsonian, Cambridge, MA, USA Alexander Lowell Space Sciences Laboratory, University of California, Berkeley, CA, USA Fangjun Lu Key Laboratory of Particle Astrophysics, Institute of High Energy Physics, Chinese Academy of Sciences, Beijing, China Key Laboratory of Stellar and Interstellar Physics and School of Physics and Optoelectronics, Xiangtan University, Xiangtan, Hunan, China Wenbin Lu Departments of Astronomy and Theoretical Astrophysics Center, University of California, Berkeley Berkeley, CA, USA Department of Astrophysical Sciences, Princeton University, Princeton, NJ, USA D. H. Lumb Centre for Electronic Imaging, Open University, Milton Keynes, UK Elisabeta Lusso Dipartimento di Fisica e Astronomia, Università di Firenze, Firenze, Italy INAF-Osservatorio Astrofisico di Arcetri, Firenze,Italy

xlviii

Contributors

Jonathan Mackey Dublin Institute for Advanced Studies, Astronomy & Astrophysics Section, Dunsink Observatory, Dublin, Ireland Rosalia Madonia Institute of Astronomy and Astrophysics, University of Tübingen, Tübingen, Germany Kristin K. Madsen CRESST and X-ray Astrophysics Laboratory, NASA Goddard Space Flight Center, Greenbelt, MD, USA Keiichi Maeda Department of Astronomy, Kyoto University, Sakyo-ku, Kyoto, Japan Vincenzo Mainieri European Southern Observatory, Garching bei München, Germany Petra Majewski Semiconductor Laboratory of the Max-Planck-Society, Munich, Germany Christian Malacaria International Space Science Institute (ISSI), Switzerland

Bern,

Denys Malyshev Institut für Astronomie und Astrophysik Tübingen, Eberhard Karls Universität Tübingen, Tübingen, Germany Alessio Marino Dipartimento di Fisica e Chimica – Emilio Segré, Universitá di Palermo, Palermo, Italy Astrophysics & Planetary Sciences, Institute of Space Sciences (ICE, CSIC), Barcelona,Spain Craig B. Markwardt NASA/GSFC, Greenbelt, MD, USA Adrian Martindale School of Physics and Astronomy, University of Leicester, Leicester, UK J. M. Mas-Hesse Centro de Astrobiología (CSIC-INTA), Madrid, Spain J. A. B. Mates United States Department of Commerce, National Institute of Standards and Technology (NIST), Boulder, CO, USA Smita Mathur The Ohio State University, Columbus, OH, USA Max Mattero Department of Physics, University of Helsinki, Helsinki, Finland Ben J. Maughan H. H. Wills Physics Laboratory, University of Bristol, Bristol, UK Michael J. McKee School of Physics and Astronomy, University of Leicester, Leicester, UK Norbert Meidinger Max Planck Institute for Extraterrestrial Physics, Garching, Germany

Contributors

xlix

François Mernier European Space Agency (ESA), European Space Research and Technology Centre (ESTEC), Noordwijk, The Netherlands Aline Meuris Université Paris-Saclay, Université Paris Cité, CEA, CNRS, AIM, 91191 Gif-sur-Yvette, France Tatehiro Mihara RIKEN, Wako, Saitama, Japan Razmik Mirzoyan Max-Planck-Institute for Physics, Munich, Germany National Academy of Sciences of Republic of Armenia, Yerevan, Armenia A. M. W. Mitchell Friedrich-Alexander-Universität Erlangen-Nürnberg, Erlangen, Germany Tsunefumi Mizuno Hiroshima Astrophysical Science Center, Hiroshima University, Higashi-Hiroshima, Hiroshima, Japan Lars Mohrmann Max-Planck-Institut für Kernphysik, Heidelberg, Germany Alexander A. Moiseev University of Maryland, College Park, MD, USA M. Molina IASF/INAF, Milano, Italy Alberto Moretti INAF Astronomical Observatory Brera, Milano, Italy Hideyuki Mori Japan Aerospace Exploration Agency/Institute of Space and Astronautical Science, Sagamihara, Kanagawa, Japan Sara E. Motta INAF – Osservatorio Astronomico di Brera, Merate, Italy Karri Muinonen Department of Physics, University of Helsinki, Helsinki, Finland Reshmi Mukherjee Department of Physics & Astronomy, Barnard College, Columbia University, New York, NY, USA Fabio Muleri INAF-IAPS, Rome, Italy Daniel Müller European Space Agency (ESA), European Space Research and Technology Centre (ESTEC), Noordwijk, The Netherlands Johannes Müller-Seidlitz Max Planck Institute for Extraterrestrial Physics, Garching, Germany David Murphy Centre for Space Research and School of Physics, University College Dublin, Dublin, Ireland Alexander Mushtukov Astrophysics, Department of Physics, University of Oxford, Oxford, UK Leiden Observatory, Leiden, The Netherlands Sophie Musset European Space Agency (ESA), European Space Research and Technology Centre (ESTEC), Noordwijk, The Netherlands Kazuhiro Nakazawa Nogoya University, Nogoya, Japan

l

Contributors

Emanuele Nardini INAF – Arcetri Astrophysical Observatory, Firenze, Italy Lorenzo Natalucci IAPS/INAF, Rome, Italy Joonas Nättilä Center for Computational Astrophysics, Flatiron Institute, New York, NY, USA Physics Department and Columbia Astrophysics Laboratory, Columbia University, New York, NY, USA Hitoshi Negoro Nihon University, Tokyo, Japan Fabrizio Nicastro Istituto Nazionale di Astrofisica (INAF) – Osservatorio Astronomico di Roma, Rome, Italy Department of Astronomy, Xiamen University, Xiamen, China Yuken Ohshiro Institute of Space and Astronautical Science/JAXA, Sagamihara, Japan Takashi Okajima NASA’s Goddard Space Flight Center, Greenbelt, MD, USA Stan Owocki University of Delaware, Newark, DE, USA Paolo Padovani European Southern Observatory, Germany

Garching bei München,

Frits Paerels Columbia Astrophysics Laboratory, Columbia University, New York, NY, USA K. L. Page School of Physics & Astronomy, University of Leicester, Leicester, UK Alessandro Papitto INAF—Osservatorio Astronomico di Roma, Monteporzio Catone, Roma, Italy Mark Pearce Department of Physics, KTH Royal Institute of Technology, Stockholm, Sweden The Oskar Klein Centre for Cosmoparticle Physics, AlbaNova University Center, Stockholm, Sweden James F. Pearson School of Physics and Astronomy, University of Leicester, Leicester, UK A. L. Peirson Kavli Institute for Particle Astrophysics and Cosmology, Stanford University, Stanford, CA, USA Silvia Pellegrini Department of Physics and Astronomy, University of Bologna, Bologna, Italy Jeremy Perkins NASA/GSFC, Greenbelt, MD, USA Pierre-Olivier Petrucci University of Grenoble Alpes, CNRS, IPAG, Grenoble, France

Contributors

li

Santina Piraino Institute of Astronomy and Astrophysics, University of Tübingen, Tübingen, Germany Carlotta Pittori INAF/OAR, Monte Porzio Catone (RM), Italy SSDC/ASI, Roma, Italy Michael J. Pivovaroff Lawrence Livermore National Laboratory, Livermore, CA, USA Gabriele Ponti INAF-Osservatorio Astronomico di Brera, Merate, Italy Max-Planck-Institut für extraterrestrische Physik, Garching, Germany Katja Poppenhaeger Leibniz Institute for Astrophysics Potsdam, Germany

Potsdam,

Institute for Physics and Astronomy, University of Potsdam, Potsdam, Germany G. W. Pratt CEA, CNRS, AIM, Université Paris-Saclay, Université Paris Cité, Gif-sur-Yvette, France M. Prest Università dell’Insubria, Como, Italy Istituto Nazionale di Fisica Nucleare, Sezione di Milano, Italy David A. Principe Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology, Cambridge, MA, USA Nicolas Produit Astronomy Department, University of Geneva, Versoix, Geneva, Switzerland Gerd Pühlhofer Institute for Astronomy and Astrophysics Tübingen, Tübingen, Germany Brian D. Ramsey NASA Marshall Space Flight Center, Huntsville, AL, USA Riccardo Rando University of Padova and I.N.F.N. Padova, Padova, Italy Gregor Rauw Space sciences, Technologies and Astrophysics Research (STAR) Institute, Université de Liège, Liège, Belgium Fabio Reale Dipartimento di Fisica e Chimica, Universita’ di Palermo, Palermo, Italy INAF-Osservatorio Astronomico di Palermo, Palermo, Italy O. J. Roberts Science and Technology Institute, Universities Space Research Association, Huntsville, AL, USA Pedro Rodríguez-Pascual Serco Gestión de Negocios S.L., ESAC, Madrid, Spain Suzanne Romaine Center for Astrophysics, Harvard & Smithsonian, Cambridge, MA, USA

lii

Contributors

J.-P. Roques CNRS, IRAP, Toulouse, France UPS-OMP, IRAP, Université de Toulouse, Toulouse, France Simon Rosen Serco Gestión de Negocios S.L., ESAC, Madrid, Spain James M. Ryan University of New Hampshire, Durham, NH, USA Pascal Saint-Hilaire Space Sciences Laboratory, University of California, Berkeley, CA, USA Takayuki Saito Institute for Cosmic Ray Research, The University of Tokyo, Kashiwa, Japan Bianca Salmaso INAF Astronomical Observatory Brera, Merate, Lecco, Italy Heiko Salzmann Institute for Astronomy and Astrophysics Tübingen, Tübingen, Germany Andrea Santangelo Institute of Astronomy and Astrophysics, University of Tübingen, Tüebingen, Baden-Württemberg, Germany Maria Santos-Lleó European Space Agency (ESA), European Space Astronomy Centre (ESAC), Madrid, Spain Manami Sasaki Dr. Karl Remeis Sternwarte, Erlangen Centre for Astroparticle Physics, Friedrich-Alexander-Universität Erlangen-Nürnberg, Bamberg, Germany Norbert Schartel European Space Agency (ESA), European Space Astronomy Centre (ESAC), Madrid, Spain P. Christian Schneider Hamburg Observatory, Hamburg, Germany Matthias R. Schreiber Departamento de Física, Universidad Técnica Federico Santa María, Valparaíso, Chile Millennium Nucleus for Planet Formation (NPF), Valparaíso, Chile Giuseppe Di Sciascio Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Roma Tor Vergata, Rome, Italy Luisa Sciortino Dipartimento di Fisica e Chimica “E. Segrè”, Università degli Studi di Palermo, Palermo, Italy Salvatore Sciortino INAF-Osservatorio Astronomico di Palermo, Palermo, Sicily, Italy A.W. Shaw Department of Physics, University of Nevada, Reno, NV, USA Albert Y. Shih Solar Physics Laboratory, Goddard Space Flight Center, Greenbelt, MD, USA Michael H. Siegel Department of Astronomy and Astrophysics, The Pennsylvania State University, University Park, PA, USA

Contributors

liii

Thomas Siegert Institut für Theoretische Physik und Astrophysik, Universität Würzburg, Würzburg, Germany Aneta Siemiginowska Center for Astrophysics, Harvard & Smithsonian, Cambridge, MA, USA Kulinder Pal Singh Tata Institute of Fundamental Research, Mumbai, India Indian Institute of Science Education and Research Mohali, Punjab, India J. Sitarek Faculty of Physics and Applied Informatics – Department of Astrophysics, University of Lodz, Lodz, Poland Gerry Skinner University of Birmingham, Birmingham, UK Clio Sleator U.S. Naval Research Laboratory, Washington, DC, USA Michael Smith Telespazio, ESAC, Madrid, Spain Randall Smith Harvard-Smithsonian Center for Astrophysics, Cambridge, MA, USA Stephen Smith NASA Goddard Space Flight Center, Greenbelt, MD, USA Paolo Soffitta IAPS/INAF, Rome, Italy Sean Spooner University of New Hampshire, Durham, NH, USA Konstantin D. Stefanov Centre for Electronic Imaging, The Open University, Milton Keynes, UK Beate Stelzer Institut für Astronomie & Astrophysik, Eberhard Karls Universität Tübingen, Tübingen, Germany G. Stratta IAPS/INAF, Rome, Italy INFN-Roma, Rome, Italy INAF/OAS, Rome, Italy Martin Stuhlinger Serco Gestión de Negocios S.L., ESAC, Madrid, Spain Yang Su Chinese Academy of Sciences, Purple Mountain Observatory, Nanjing, China Yuanyuan Su University of Kentucky, Lexington, KY, USA Jianchao Sun Key Laboratory of Particle Astrophysics, Institute of High Energy Physics, Chinese Academy of Sciences, Beijing, China H. Tajima Solar-Terresterial Enviornment Laboratory, Nagoya University, Nagoya, Japan Institute for Space–Earth Environmental Research, Nagoya University Furo-cho, Chikusa-ku, Nagoya, Japan

liv

Contributors

Tadayuki Takahashi Kavli Institute for the Physics and Mathematics of the Universe (WPI), The University of Tokyo, Kashiwa, Chiba, Japan Harvey Tananbaum Center for Astrophysics | Harvard & Smithsonian, Cambridge, MA, USA Toru Tanimori Graduate School of Science Kyoto University, Kyoto, Japan Vincent Tatischeff CNRS/IN2P3, IJCLab, Université Paris-Saclay, Orsay, France Marco Tavani INAF/IAPS, Roma, Italy Università degli Studi di Roma Tor Vergata, Roma, Italy INFN Roma Tor Vergata, Roma, Italy Consorzio Interuniversitario Fisica Spaziale (CIFS), Torino, Italy Andrew M. Taylor Deutsches Elektronen Synchrotron DESY, Zeuthen, Germany B. J. Teegarden NASA Goddard Space Flight Center, Greenbelt, MD, USA Paola Testa Harvard-Smithsonian Center for Astrophysics, Cambridge, MA, USA David J. Thompson NASA Goddard Space Flight Center, Greenbelt, MD, USA Tuomo V. Tikkanen School of Physics and Astronomy, University of Leicester, Leicester, UK Martin Tluczykont Institute of Experimental Physics, University of Hamburg, Hamburg, Germany Francesco Tombesi Department of Astronomy, University of Maryland, College Park, MD, USA Department of Physics, University of Rome “Tor Vergata”, Rome, Italy INAF Osservatorio Astronomico di Roma, Monteporzio Catone, Rome, Italy NASA Goddard Space Flight Center, Greenbelt, MD, USA John A. Tomsick Space Sciences Laboratory, University of California, Berkeley, CA, USA Johannes Treis Max Planck Institute for Solar System Research, Justus-vonLiebig-Weg, Göttingen, Germany Hiroshi Tsunemi Osaka University, Toyonaka, Osaka, Japan Sergey Tsygankov Department of Physics and Astronomy, University of Turku, Turku, Finland Pietro Ubertini IAPS/INAF, Rome, Italy

B. J. Teegarden: retired.

Contributors

lv

Asif ud-Doula Penn State Scranton, Dunmore, PA, USA Alexey Uliyanov School of Physics, University College Dublin, Dublin, Ireland Melville P. Ulmer Department of Physics, Northwestern University, Evanston, IL, USA Sabina Ustamujic INAF-Osservatorio Astronomico di Palermo, Palermo, Italy Giuseppe Vacanti cosine, Sassenheim, The Netherlands Andrea Vacchi National Institute for Nuclear Physics INFN – Italy, Trieste (I) Branch, Trieste, Italy Rosa Valiante INAF-Osservatorio Astronomico di Roma, Monteporzio Catone, Italy INFN, Sezione di Roma I, Roma, Italy E. Vallazza Istituto Nazionale di Fisica Nucleare, Sezione di Milano Bicocca, Milan, Italy Eva Verdugo-Rodrigo European Space Agency (ESA), European Space Astronomy Centre (ESAC), Madrid, Spain Jacco Vink Anton Pannekoek Institute for Astronomy & GRAPPA, University of Amsterdam, Amsterdam, The Netherlands SRON National Institute for Space Research, Leiden, The Netherlands Enrico Virgilli Istituto Nazionale di Astrofisica INAF-OAS, Bologna, Italy Fabio Vito INAF-Osservatorio di Astrofisica e Scienza dello Spazio, Bologna, Italy Mark Vogelsberger Massachusetts Institute of Technology, Cambridge, MA, USA Stephen Walker Department of Physics and Astronomy, The University of Alabama in Huntsville, Huntsville, AL, USA C. Wang National Space Science Center, Chinese Academy of Sciences, Haidian District, Beijing, China Fa-Yin Wang Key Laboratory of Modern Astronomy and Astrophysics, Ministry of Education, Beijing, China School of Astronomy and Space Science, Nanjing University, Nanjing, China Natalie A. Webb Institute de Recherche en Astrophysique et Planétologie, Toulouse, France Jianyan Wei Key Laboratory of Space Astronomy and Technology, National Astronomical Observatories, Chinese Academy of Sciences, Beijing, People’s Republic of China University of Chinese Academy of Sciences, Beijing, China

lvi

Contributors

Jun-Jie Wei Purple Mountain Observatory, Chinese Academy of Sciences, Nanjing, China School of Astronomy and Space Sciences, University of Science and Technology of China, Hefei, China Martin C. Weisskopf NASA-MSFC, Alabama, USA Belinda J. Wilkes Center for Astrophysics | Harvard & Smithsonian, Cambridge, MA, USA School of Physics, University of Bristol, Bristol, UK Brian J. Williams X-Ray Astrophysics Laboratory, NASA Goddard Space Flight Center, Greenbelt, MD, USA Richard Willingale University of Leicester, Leicester, UK Colleen A. Wilson-Hodge NASA Marshall Space Flight Center, Huntsville, AL, USA Jian Wu Chinese Academy of Sciences, Purple Mountain Observatory, Nanjing, China Xue-Feng Wu Purple Mountain Observatory, Chinese Academy of Sciences, Nanjing, China School of Astronomy and Space Sciences, University of Science and Technology of China, Hefei, China Di Xiao Purple Mountain Observatory, Chinese Academy of Sciences, Nanjing, China Yunxiang Xiao Key Laboratory of Particle Astrophysics, Institute of High Energy Physics, Chinese Academy of Sciences, Beijing, China Yupeng Xu Key Laboratory of Particle Astrophysics, Institute of High Energy Physics, Chinese Academy of Sciences, Beijing, China University of Chinese Academy of Sciences, Beijing, China Hiroya Yamaguchi Institute of Space and Astronautical Science/JAXA, Sagamihara, Japan G. Yang Department of Physics and Astronomy, Texas A&M University, College Station, TX, USA George P. and Cynthia Woods Mitchell Institute for Fundamental Physics and Astronomy, Texas A&M University, College Station, TX, USA Yun-Wei Yu Institute of Astrophysics, Central China Normal University, Wuhan, China

Contributors

lvii

Weimin Yuan National Astronomical Observatories, Chinese Academy of Sciences, Beijing, China Anna Zajczyk Center for Space Sciences and Technology, University of Maryland Baltimore County, NASA Goddard Space Flight Center, Center for Research and Exploration in Space Science and Technology, Baltimore, MD, USA Roberta Zanin CTA Observatory, Bologna, Italy Andreas Zezas University of Crete, Crete, Greece Bin-Bin Zhang Key Laboratory of Modern Astronomy and Astrophysics, Ministry of Education, Beijing, China School of Astronomy and Space Science, Nanjing University, Nanjing, China Chen Zhang National Astronomical Observatories, Chinese Academy of Sciences, Beijing, China Fan Zhang Key Laboratory of Particle Astrophysics, Institute of High Energy Physics, Chinese Academy of Sciences, Beijing, China Shuang-Nan Zhang Key Laboratory for Particle Astrophysics, Institute of High Energy Physics, CAS, Beijing, China University of Chinese Academy of Sciences, Chinese Academy of Sciences, Beijing, China Zhe Zhang Chinese Academy of Sciences, Purple Mountain Observatory, Nanjing, China Irina Zhuravleva Department of Astronomy and Astrophysics, University of Chicago, Chicago, IL, USA Andreas Zoglauer Space Sciences Laboratory, University of California, Berkeley, CA, USA John ZuHone Center for Astrophysics | Harvard & Smithsonian, Cambridge, MA, USA

Part I Introduction to X-ray Astrophysics

1

A Chronological History of X-ray Astronomy Missions Andrea Santangelo, Rosalia Madonia, and Santina Piraino

Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Early Years of X-Ray Astronomy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Rockets and Balloons in the 1960s and 1970s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ROCKETS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . BALLOONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Uhuru and the Others, Opening the Age of the Satellites in the Early 1970s . . . . . . . . . . . . . . UHURU . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . APOLLO 15 AND APOLLO 16 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . SAS-3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . HEAO-1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Late 1970s and the 1980s: The Program in the USA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . EINSTEIN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Late 1970s and the 1980s: The Program in Europe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . COPERNICUS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ANS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ARIEL V . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . COS-B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ARIEL VI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . EXOSAT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Late 1970s and the 1980s: The Program in Japan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . HAKUCHO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . HINOTORI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . TENMA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . GINGA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Late 1970s and the 1980s: The Program in Russia and India . . . . . . . . . . . . . . . . . . . . . . . FILIN / SALYUT-4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . SKR -02 M . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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A. Santangelo · R. Madonia () · S. Piraino Institute of Astronomy and Astrophysics, University of Tübingen, Tübingen, Germany e-mail: [email protected]; [email protected]; [email protected] © Springer Nature Singapore Pte Ltd. 2024 C. Bambi, A. Santangelo (eds.), Handbook of X-ray and Gamma-ray Astrophysics, https://doi.org/10.1007/978-981-19-6960-7_147

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A. Santangelo et al. XVANTIMIR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ARYABHATA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

BHASKARA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Golden Age of X-Ray Astronomy, From the 1990s to the Present . . . . . . . . . . . . . . . . . . . THE PROGRAM IN THE USA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ULYSSES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . BBXRT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . RXTE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . USA ONBOARD ARGOS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . THE PROGRAM IN EUROPE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ROSAT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . BEPPOSAX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . THE PROGRAM IN JAPAN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ASCA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . SUZAKU . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . HITOMI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . THE PROGRAM IN RUSSIA AND INDIA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . GRANAT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . IRS - P 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Appendix 1. List of the Rrockets Launched from 1957 to 1970 . . . . . . . . . . . . . . . . . . . . . . . . . Appendix 2. List of the Balloon Missions Launched by the MIT Group . . . . . . . . . . . . . . . . . . Appendix 3. List of the Balloon Missions Launched by Worldwide Institution . . . . . . . . . . . . Appendix 4. Balloons Flown by AIT and MPI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Appendix 5. Transatlantic Balloons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Abstract

In this chapter, we briefly review the history of X-ray astronomy through its missions. We follow a temporal development, from the first instruments onboard rockets and balloons to the most recent and complex space missions. We intend to provide the reader with detailed information and references on the many missions and instruments that have contributed to the success of the exploration of the X-ray universe. We have not included missions that are still operating, providing the worldwide community with high-quality observations. Specific chapters for these missions are included in a dedicated section of the handbook.

Keywords

X-rays astronomy · X-rays balloons · X-rays rockets · X-ray space missions · History of x-ray astronomy

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Introduction The Earth’s atmosphere is not (fortunately!) transparent to X-rays. In the figure published in 1968 by Riccardo Giacconi and colleagues (Giacconi et al. 1968), a figure in many ways now historical, the attenuation of the electromagnetic radiation penetrating the atmosphere due to atmospheric absorption is presented as a function of the wavelength (see Fig. 1). To explore the universe in X-rays or in the soft gammas, it is therefore necessary to fly instrumentation onboard rockets, balloons, or satellites, and this presented new technological challenges at the end of the 1950s. The development of X-ray astronomy therefore had to wait for the development of rockets capable of carrying instrumentation into the upper layers of the atmosphere. Its history thus coincides with the “space race,” which began after the end of World War II and experienced a decisive acceleration with the launch of Sputnik in 1957 and Yuri Gagarin’s first human space flight ever on April 12, 1961 (Santangelo and Madonia 2014).

Fig. 1 Atmospheric absorption as a function of the wavelength (bottom axis). The solid lines indicate the fraction of the atmosphere, expressed in unit of 1 atmosphere pressure (right vertical axis) or in terms of altitude (left vertical axis), at which half of the incoming celestial radiation is absorbed by the atmosphere. Whereas radio and visible wavelength (blue rectangle) can reach without being absorbed the Earth’s surface, infrared, ultraviolet, and X-rays are strongly absorbed. (Credit High Energy Astrophysics Group, University of Tübingen)

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Following the best-known narrative, one usually traces the birth of X-ray astronomy to the program of the AS&E-MIT and especially to the flight of the rocket launched by Giacconi, Paolini, Rossi, and Gursky on June 18 1962 from White Sands (New Mexico), which led to the discovery of the first celestial source of X-rays, Sco X-1 (Giacconi et al. 1962). However, the story, as we will see later, is more complex. This paper, although detailed, is not exhaustive; further read could be found in Giacconi’s book “Secrets of the Hoary Deep” (Giacconi 2008), in Hirsh’s “Glimpsing an Invisible Universe” (Hirsh 1983), and in the review chapter of Pounds “Forty years on from Aerobee 150: a personal perspective” (Pounds 2002).

The Early Years of X-Ray Astronomy At the beginning of the twentieth century, there was great interest among scientific communities in the study of the Earth’s atmosphere. The emanation power of newly discovered radioactive elements, with new types of radiation, and the discovery of cosmic rays (then called “penetrating radiation”) are probably the main reason for this interest. Whether or not some layer of the upper atmosphere could be ionized was of particular interest for investigation (How suggested by Swann (1916a): The subject of the ionization of the upper atmosphere is one of extreme importance to students (SIC). From various points of view there are indications that the upper atmosphere is to be treated as a region of high electrical conductivity.

He further wrote Swann (1916b): both of Terrestrial Magnetism and of Atmospheric Electricity, and from various points of view there are indications that this region of the atmosphere is to be treated as one of relatively high electrical conductivity).

Working on radio waves, Tuve and Breit (1925) noted an interference phenomenon hypothetically due to the existence of an ionized reflecting layer in the upper atmosphere (the Kennelly-Heaviside layer or E layer) (Tuve 1967). The work of Tuve and Breit started a new research’s branch that in the end brought to the invention of the Radar. Between 1925 and 1930, Edward O. Hulburt published different papers on the reflecting properties of the Kennelly-Heaviside layer of the atmosphere (Taylor and Hulburt 1926; Hulburt 1928). He suggested that this should have been related to some Sun activity, because the ionization of the atmosphere could only be due to absorption of the Sun’s ultraviolet light or, more likely, X-rays. When, immediately after World War II, the US military offered research organizations and scientific institutions the opportunity to fly scientific instruments aboard V-2 rockets, developed during the war by Wernher von Braun and Edward Hulburt, head of the Naval Research Laboratory (NRL), enthusiastically accepted the offer to further investigate the reflective power of the atmosphere. Herbert Friedman was working in Hulburt’s department. He was interested in studying the Sun’s UV and X-rays to understand their role in the formation of the ionosphere. Using a combination of filters and gas mixtures, Friedman built several photomultiplier tubes, each sensitive in a narrow frequency range. With the V-2 number

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49 flight, launched in September 1949 from White Sands (Hirsh 1980), Friedman and colleagues confirmed the hypothesis that the ionization of the atmosphere above 87 km was due to solar X-rays emitted by the Sun’s corona (Friedman et al. 1951). For the first time, X-ray instrumentation had been launched above the Earth’s atmosphere. Further developments in the field were obtained, thanks to the construction of a new type of rocket, the Aerobee series, by James van Allen. Using Aerobee rockets, Friedman and colleagues conducted a series of night flights to search for stellar sources that, as the sun, could emit UV and X-ray radiation (Friedman et al. 1951; Kupperian et al. 1959). Only an upper limit of 10−8 ergs cm−2 s−1 Å−1 was obtained. Herbert Friedman (see Fig. 2) was a pioneer of X-ray astronomy: he obtained the first X-ray image of the Sun with a pinhole camera and flew the first Bragg spectrometer for measuring hard X-rays. The first satellite, SOLRAD, for long-term monitoring of the sun was also conceived and developed by Friedman. The prewar interest in the physics of the upper atmosphere and its interaction with the solar radiation was also strong in the UK, at the Imperial College and at the University College London (UCL). Pioneers of ionospheric physics and geomagnetism were Sir Edward Appleton, Sydney Chapman, John Ashworth Ratcliffe, Harrie Massey, and his student David Bates, and James Sayers. In 1942,

Fig. 2 Left: Herbert Friedman (1916–2000) was certainly a pioneer in X-ray research of the celestial sources. Right: Friedman’s US patent No. 2,475,603, for an adaptation of the tube used in a Geiger-Mueller counter. Thanks to a reduced background, Friedman’s tube design increased the counter’s sensitivity to weak sources. The details of the figure can be found at (Friedman 2023). (Credit: Public Domain)

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the Gassiot Committee, a committee concerned with upper atmospheric research, of the Royal Society began to cooperate with the Meteorological Research Committee in order to consider the use of rockets for a program for atmospheric physics (Pounds 2010). The war and the postwar economic difficulty of the nation slowed down the program, but eventually the common interest of military institutions and scientific groups gave the scientific community the possibility to fly instrumentation onboard of rockets and later satellites. Most remarkable was the agreement between the head of the physics department at UCL, Harrie Massey (According to Pounds “... Sir Harrie Massey ... was the key player in establishing the UK as the clear leader – after the USA and the Soviet Union – in the early years of space research (Pounds 2010)) and Sir Arnold Hall, director of the Royal Aircraft Establishment (RAE) Farborough (We cite Pounds (2010): “[...] on 13 May 1953, when the chairman of the Gassiot Committee was about to leave for Shenley to play in the annual UCL staff-students cricket match. Massey’s response to the question, ‘would there be interest in using rockets available from the Ministry for scientific research?’ was an immediate ‘yes’ [...]”). The result was the funding of the Skylark Program and the formation of space research group at UCL (Robert Boyd), Imperial College (Percival Albert Sheppard), Birmingham University (James Sayers), Queen’s University of Belfast (David Bates and Karl George Emeleus), and University College Wales, Aberystwyth (William Granville Beynon). The early Skylark missions were dedicated to the study of the Sun, the Lyman-α and X-ray emission, as well as the study of the upper atmosphere, as already said. The International Geophysical Year (1957/1958) was a motivating occasion for the development of projects and studies. Indeed, the first successful test launch of a Skylark rocket occurred on February 13, 1957, from Woomera Range, Adelaide, Australia. The choice of Woomera was due to the personal Australian relationships of H. Massey (Massey was born on May 16, 1908, in Invermay, Victoria, Australia). Nine months later on November 13, the first Skylark rocket with a scientific payload was launched from Woomera. The program was very successful, new instruments for X-ray were developed by a group of young scientists of the UCL, among them was Ken Pounds who, in 1960, received an assistant lectureship at Leicester with a 3-year grant of £13006 from the Department of Scientific and Industrial Research. This generous fund was indubitably a consequence of the launch of the Sputnik I. The two new instrument developed by UCL and then the Leicester group were as follows: a photographic emulsion, protected in an armored steel cassette with the filter mounted behind aluminum and beryllium foils (“This device was flown successfully in over 20 Skylark flights during the 1960s, providing the first direct broadband X-ray spectra over a wide range of solar activity (Pounds 1986)”), and a proportional counter spectrometer (PCS) that, according to Ken Pounds, was to became the workhorse detector in X-ray astronomy (Pounds 2010). The studies of solar X-rays were pioneered in the Netherlands by Kees de Jager, who started a laboratory for space science at the University of Utrecht. He was supported by the atomic physicist Rolf Mewe, who developed theoretical models

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for data interpretation. Also, the cosmic-ray working group at the University of Leiden, in the 1960s, worked on X-ray with rockets and balloons in collaboration with the Nagoya University and ISAS in Japan. Eventually in 1983, these groups, together with the Groningen University, joined in the SRON (Stichting Ruimte Onderzoek Nederland) with the aim to develop instruments for space science missions. As already mentioned, the turning point for space activities, in general, and therefore for X-ray astronomy was the so-called Sputnik shock of 1957. New opportunities appeared and space research was welcomed and financed. In the USA, in September 1959, Bruno Rossi, chairman of the board of the American Science & Engineering (AS&E), a start-up high-tech company formed in Cambridge a year earlier by Martin Annis, suggested to Riccardo Giacconi, who was called from Princeton to become head of the Space Science Division of the AS&E, to develop some research program on X-ray astronomy. In the next few months, on February 1960, two proposals were submitted to the newly formed NASA: one, rather visionary, to develop an X-ray telescope (Wolter type) and another for a rocket mission to investigate the emission (or scattering) of X-rays from the Moon and from the Crab Nebula. NASA accepted the first proposal and refused the second one. In an oral interview, Nancy Roman, of NASA, said that this proposal was not funded because, in her mind, it was impossible to detect such emission (Roman 1980) (According to Nancy Roman: “Yes. The first X-ray work was ’62, if I remember right, and that was funded by the Air Force. I didn’t fund it. I guess you can blame me for being too good a scientist or you can blame me for not having foresight. Giaconni came to me with a proposal to fly an experiment to measure solar X-rays scattered off the Moon, and it was, to me, absolutely clear that that was impossible. Still is.[...] If they had come to me to say they wanted to do a sky survey in X-ray, I think, admittedly in hindsight, that I would have supported them, because I was very much aware of the desirability of finding out something about new wave length regions. But I could not see supporting an experimental rocket to measure reflected solar X-rays from the moon.” Note that the misspelling of the name of Giacconi is already in the original transcript). Nevertheless, certain of the importance of rocket mission and waiting for the realization of the telescope, Giacconi sent the proposal to the Air Force Cambridge Research Laboratory that, on the contrary to NASA, funded a series of rocket launches. The first and second Aerobee rocket launch failed, but the third one was very successful: it changed the history of astronomy and our perception of the universe. It is fair to mention that in December 1960, a year before the discovery of Sco X-1, Philip Fisher, of the Lockheed Company, had submitted a proposal to NASA to search for cosmic X-ray sources (Fisher 1960). Nevertheless, the launches of the Lockheed rockets (Aerobee 4.69 and 4.70) occurred on September 30, 1962, and March 15, 1963, after the discovery of Sco X-1. However, according to Fisher (2009), his results were not properly taken into account and cited in the subsequent scientific meetings focused on X-Ray astronomy.

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Rockets and Balloons in the 1960s and 1970s ROCKETS On June 18, 1962, an air force Aerobee rocket was launched from White Sands Missile Range in New Mexico with the aim and the appropriate instrumentation to search for X-ray emission from celestial objects. The pioneer AS&E-MIT experiment discovered the first extra solar source of X-rays (see Fig. 3), a diffuse X-ray background component, and the probable existence of a second source in the proximity of the Cygnus constellation (Giacconi et al. 1962). The payload consisted of three Geiger counters, each composed of seven mica windows of 20 cm2 comprising area; the detectors had a sensitivity between 2 and 8 Å. As predicted by Nancy Roman, no X-rays from the Moon were observed. That was just the beginning: an intense program based on rocket launches was started. Rockets observed for only a few minutes, from a maximum altitude of ∼200 km. The list of the rocket experiments launched until 1970 is included in “Appendix 1. List of the Rrockets Launched from 1957 to 1970”. The large majority of rocket launches was performed by US scientists. However, the UK participated to the early race of X-ray astronomy, with the Skylark launches. In particular, Skylark launches SL118 and SL119, from Woomera, Australia, provided for the first time a survey of X-ray sources in the Southern Hemisphere.

BALLOONS The short fly-time of the sound rockets was a clear limit for the study of the X-ray sources, especially once their variability was revealed. With the use of aerostatic

Fig. 3 The discovery plot which marked the beginning of X-ray astronomy. The azimuthal distribution of the count rates of the Geiger-Müller detectors flown in the June 1962 flight is shown. (Credit Giacconi et al. 1962)

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balloons, long-duration observations on the order of hours became possible, even if from a lower altitude. Different research groups undertook intense and fruitful balloon campaigns. In particular, the group at MIT of George W. Clark, Gordon P. Garmire, and Minoru Oda, on leave from Tokyo University, was involved in a robust and successful program for X-ray sky observations with balloons. A detailed list of the MIT Balloon flights is reported in “Appendix 2. List of the Balloon Missions Launched by the MIT Group”. The efforts to fly balloon mission for X-ray astronomy were undertaken by other institutions worldwide. In particular, the following groups were rather active: Leiden University; the GIFCO group at Bologna University and the TESRE Institute of the Consiglio Nazionale delle Ricerche (CNR); the Centre d’Etudes Nucléaires (CEN) de Saclay (France); the Tata Institute in Mumbai (India); the Rice University, Houston (Texas); the Adelaide University (Australia); and Nagoya University (Japan). A detailed list of the Balloon flights launched by these institutions is reported in “Appendix 3. List of the Balloon Missions Launched by Worldwide Institution”. We wish to mention in particular that a balloon program in the hard X-rays (20–200 keV) was pursued by the Institut für Astronomie und Astrophysik der Universität Tübingen (AIT) and the Max Planck-Institut für Extraterrestrische Physics in Garching (MPE) from 1973 to 1980 with nine successful balloon flights from Texas and Australia (Staubert et al. 1981). The program was led by Joachim Trümper who started German X-ray astronomy in Tübingen before moving to the directorship at MPE. A detailed list of the balloon flights launched by these institutions is reported in “Appendix 4. Balloons Flown by AIT and MPI”. The instruments were built and operated by MPE and AIT and consisted of scintillation counters with NaI(Tl) crystals (Kendziorra et al. 1974; Reppin et al. 1978). The close cooperation between AIT and MPI continued in the 1980s with the construction and operation of the high-energy X-ray experiment (HEXE) used during three successful balloon campaigns (May 1980 and September 1981 launched from Palestine/Texas, as well as November 1982 launched from Uberaba/Brazil). At the beginning of the 1970s, the main worldwide available balloon launch site was the NSBF facility in Palestine, Texas, USA. In the period between 1967 and 1976, the average flight duration was about 10–15 h, with a few exceptions (four flights lasted 40–60 h and only one, in 1974, up to 120 h). The opening in 1975 of the stratospheric balloon launch base of Trapani-Milo in Sicily provided the opportunity to use transatlantic flights, with long and stable durations, and the capability to carry payloads with mass up to 2–3 tons at altitudes above 38– 42 km, perfect to realize X-ray investigations of cosmic sources (Ubertini 2008). The flight campaign started with a precursor flight operated by the Italian TrapaniMilo ground operation crew and a launch team from NSBF-NASA. The payload had a total weight of 1500 kg, out of which was 500 kg of scientific experiments and flight services. The flight started on August 5, 1975, and safely landed on the US East Coast after a flight of 81 h. Several successful balloon experiments were performed by the Istituto di Astrofisica Spaziale of Rome (IAS), in collaboration with others Italian and international institutes (Among them are the Istituto di Fisica Cosmica of Milan (IFC), the Laboratorio di Tecnologie e Studio delle Radiazioni Extraterrestri of Bologna (TESRE), the Istituto di Fisica Cosmica con Applicazione

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all’Informatica of Palermo (IFCAI), and international institutions, such as the University of Southampton and RAL (the UK), TATA Institute (Mumbai, India), Tübingen University (Germany), ADFA (Australia), CNES (France), INTA (Spain), etc. (Ubertini 2008)). The list of the major transatlantic balloon missions is reported in “Appendix 4. Balloons Flown by AIT and MPI”.

Uhuru and the Others, Opening the Age of the Satellites in the Early 1970s The first satellite designed for cosmic X-ray observation was the US Vanguard 3 satellite, launched on September 18, 1959. It operated until December 11, 1959. The payload consisted of ion chambers provided by NRL that were intended to detect (solar) X-rays (and Lyman-alpha). Unfortunately as noted in Friedman (1960) “the Van Allen Belt radiation swamped the detectors most of the time and no useful X-ray data were obtained.” On October 13, 1959, the US Explorer 7 satellite was launched from Cape Canaveral. It operated until August 24, 1961, and, like Vanguard 3, carried, among other experiments, ion chambers provided by NRL. The goal was to detect (solar) X-rays (and Lyman-alpha). Unfortunately, no useful X-ray data were obtained similar to the case of Vanguard 3 (Friedman 1960).

UHURU The Small Astronomical Satellite 1 (SAS-1) was the first of small astronomy satellites developed by NASA and was entirely devoted to the observations of cosmic X-ray sources (see Fig. 4). It was launched on December 12, 1970, from the Italian San Marco launch platform off the coast of Kenya, operated by the Italian Centro Ricerche Aerospaziali. December 12 was the seventh anniversary of the independence of Kenya, and in recognition of the kind hospitality of the Kenyan people, Marjorie Townsend, the NASA mission project manager, named the successfully launched mission “Uhuru,” Swahili term for “freedom.” Uhuru was launched into a nearly equatorial circular orbit of about 560 km apogee and 520 km perigee, with an inclination of 3◦ and an orbital period of 96 min. The mission ended in March 1973. The X-ray detectors consisted of two sets of large-area proportional counters sensitive (with more than 10 percent efficiency) to X-ray photons in the 1.7–18 keV range. The lower limit was determined by the attenuation of the beryllium windows of the counter plus a thin thermal shroud, needed to maintain the temperature stability of the spacecraft. The upper energy limit was determined by the transmission properties of the filling gas. Pulse-shape discrimination and anticoincidence techniques were used to reduce the particle background and highenergy photons (Giacconi et al. 1971). The main features of the mission are reported in Table 1.

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Fig. 4 Left: Marjorie Townsend discusses the SAS-1 X-ray Explorer Satellite’s performance with Bruno Rossi during preflight tests at NASA’s Goddard Space Flight Center. Marjorie Townsend was the first woman to become a satellite project manager at NASA. Right: a schematic of the satellite. All major basic elements of an X-ray satellite are shown. (Credit NASA) Table 1 Uhuru

Instrument Bandpass (keV) Eff Area (cm2 ) Field of view (FWHM) Timing resolution (s) Sensitivity (ergs cm−2 s−1 )

Set 1 1.7–18 840 0.52◦ × 5.2◦ 0.192 1.5×10−11

Set 2 1.7–18 840 5.2◦ × 5.2◦ 0.384

The main science achievement of Uhuru was, with no doubt, the completion of the first X-ray all-sky survey up to a sensitivity of 0.5 mCrab (between 10 and 100 times better than what achievable with rockets). Uhuru detected 339 X-ray sources of different classes: X-ray binaries, supernova remnants, Seyfert galaxies, and clusters of galaxies, for which diffuse X-ray emission was discovered (Forman et al. 1978) (Fig. 5).

APOLLO 15 AND APOLLO 16 On July 26, 1971, the Apollo 15 lunar mission carried, inside the Scientific Instrument Module (SIM) of the Service Module, an X-ray fluorescence spectrometer (XRFS (Jagoda et al. 1974; Adler et al. 1975)) and a gamma-ray spectrometer (GRS), with the aim to study the composition of the lunar surface. Similarly, on April 16, 1972, the same suite of instruments was flown on Apollo 16. The XRFS was manufactured by the AS&E. The main objective was indeed to study the Moon’s surface from lunar orbit, in order to better understand the Moon’s overall chemical composition (see Gloudemans et al. 2021). On the way back from the Moon to the

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Fig. 5 The map of the X-ray sky after Uhuru, according to the fourth Uhuru catalog. (Figure adapted from Forman et al. 1978)

Fig. 6 The Scientific Instrument Module of Apollo 15. (Credit HEAG@UCSD High Energy Astrophysics Group at UCSD 2023)

Earth (i.e., during the “trans-Earth coast”), the XRFS observed parts of the X-ray sky. The prime objective of the Apollo observations during the trans-Earth coast was to understand the nature of the X-ray sources discovered earlier (e.g., Cyg X-1, Sco X-1), by observing them continuously for approximately half an hour to an hour, which was unique at that time. UHURU could only observe for approximately 1 or 2 min per sighting. Preliminary results were reported in the Apollo 15 and 16 Preliminary Science Reports (Adler et al. 1972a, b). Further results from the transEarth coast observations include a mysterious (type I?) burst seen by Apollo 15 (see Kuulkers et al. 2009) and a gamma-ray burst seen by Apollo 16 (Metzger et al. 1974; Trombka et al. 1974) (Fig. 6).

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SAS-3 The second small satellite for X-ray astronomy SAS-3 was launched on May 7, 1975 again from the Italian San Marco launch facility. Its initial orbit was equatorial. SAS-3 was designed as a spinning satellite. The spin rate was controlled by a gyroscope that could be commanded to stop rotation. In this way, all instruments could be pointed providing about 30 min of continuous exposures on sources, such as a pulsars, bursters, or transients. The nominal spin period was 95 min, which was also the orbital period having an inclination of 3◦ and an altitude of 513 km. The scientific payload (Mayer 1975), designed and built at MIT, consisted of four X-ray instruments (see Fig. 7): • Two rotating modulation collimator systems (RMCS Schnopper et al. 1976), each of which had an effective area of 178 cm2 and consisted of a modulation collimator and proportional counters active in the energy bands of 2–6 and 6–11 keV. The collimator had an overall FOV of 12◦ ×12◦ , with a FWHM of 4.5 arcmin, centred on the direction parallel to the spin axis (satellite +Z-axis). • Three crossed slat collimators (SME Buff et al. 1977), each with a proportional counter. They were designed to monitor a large portion of the sky in a wideband of directions centred on the plane perpendicular to the rotation axis of the satellite. Each detector had an on-axis effective area of 75 cm2 . The collimators defined three long, narrow FoVs, which intersected on the +Y axis and were inclined with respect to the YZ plane of the satellite at angles of −30◦ , 0◦ , and +30◦ , respectively. During the scanning mode, an X-ray source would appear in the three detectors. Three lines could then be obtained, and their intersection determined the source position. The central collimator had a field of view of 2◦ ×120◦ with FWHM 1◦ ×32◦ . The left and right collimators had narrower but similar responses, i.e., 0.5◦ ×32◦ (FWHM) and 1.0◦ ×100◦ (FW). The proportional counters were filled with argon and were sensitive in the range

Fig. 7 Left: a schematic diagram of the instruments of the science payload. SAS3 was already a complex mission. Note that it also had onboard a set of four grazing-incidence concentrators. Right: an artistic impression of the SAS-3 satellite. (Credit NASA)

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5–15 keV. In addition, the central detector featured a xenon counter, located behind the argon detector, that extended the energy range to 60 keV. Over the energy range 1.5–6 keV, 1 count/s was equivalent to 1.5 × 10−10 erg cm−2 s−1 for a Crab-like spectrum. In any given orbit, at the nominal 95 min spin period, 60% of the sky was scanned by the centre slat detector with an effective area from 300–1125 cm2 . • Three tube collimators (TC Lewin et al. 1976), sensitive to X-rays in the range 0.4–55 keV, located above and below, each of which with an effective area of 80 cm2 . The third was along “the left” with an effective area of 115 cm2 of the slat collimators, that defined a 1.7◦ circular FOV. The tube collimator above the slat collimator was inclined at an angle of 5 degrees above the Y-axis and could therefore be used as a background reference for the other tube collimators aligned along the Y-axis. • One low-energy detector system (LEDS Hearn et al. 1976) to the right of the slat collimators. It consisted of a set of four grazing incidence, parabolic reflection concentrators with two independent gas-flow counters, sensitive to X-rays in the range 0.15–1.0 keV, and with an effective area of 20 cm2 . The major scientific objectives were reaching a position accuracy of bright X-ray sources to ∼15 arcs; studying a selected sample of sources over the energy range 0.1–55 keV; and searching the sky for X-ray novae, flares, and other transient phenomena. The science highlights of the mission included the discovery of a dozen X-ray burst sources (Lewin et al. 1976), among which include the Rapid Burster (Marshall et al. 1979); the first discovery of X-ray from an highly magnetic White Dwarf (WD) binary system, AM Her (Hearn and Richardson 1977); the discovery of X-ray from Algol and HZ 43 (Schnopper et al. 1976); the precise location of about 60 X-ray sources; and the survey of the soft X-ray background (0.1–0.28 kev) (Marshall and Clark 1984).

HEAO-1 In 1977, NASA started launching a series of very large scientific payloads called high-energy astronomy observatories (HEAO). They were launched by Atlas Centaur rockets. The payloads were about 2.5 m×5.8 m in size and ∼3000 kg in mass (Bradt 1992; Tucker 1984; Peterson 1975). The telemetry rate was large, ∼6, 400 bits/s compared to the 1,000 bits/s typical of earlier satellites. The first of these missions, HEAO-1 (HEAO-A before launch), surveyed the X-ray sky almost three times over the 0.2 keV–10 MeV energy band and provided nearly constant monitoring of X-ray sources near the ecliptic poles. More detailed studies of a number of objects were made through pointed observations lasting typically 3–6 h. HEAO-1 operated from August 12, 1977, to January 9, 1979, in a satellite orbit at 432 km, with an inclination of 23◦ and a period of 93.5 min. The science payload included four major instruments (for the details see Table 2):

0.25–25 1350–1900

1◦ ×4◦ -1◦ ×0.5◦

FOV

A1(LASS)

Payload Detector Energy range (keV) Eff area (cm2 )

Table 2 HEAO-1 payload A2(CXE) LED 0.15–3 2×400 MED 1.5–20 800 1.5◦ ×3◦ 3◦ ×3◦ 3◦ ×6◦

HED 2.5–60 3×800 4◦ ×4◦

A3(MC) MC1 0.9–13.3 2×400 300

MC2

1.7◦ ×20◦

A4 LED 15–200 2×100

17◦

MED 80–2000 4×45

37◦

HED 120–10000 100

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• A1 – a large-area sky survey experiment (LASS) consisting of a proportional counter array (seven modules), sensitive in the 0.25–25 keV energy range, designed to survey the sky for discrete sources (Friedman 1979). • A2 – a smaller proportional counter array, the cosmic X-ray experiment (CXE), designed principally to study the diffuse X-ray background from 0.215–60 keV (Rothschild 1979; Boldt 1987). It consisted of six proportional counters: – Low-energy detectors (LED), two detectors operating in the 0.15–3.0 keV energy range – Medium-energy detector (MED) operating in the 1.5–20 keV range – High-energy detector (HED), three detectors in the 2.5–60 keV energy range • A3 – a Modulation Collimator (MC) experiment, covering the energy range of 0.9–13.3 keV, with two detectors (MC1and MC2). It was designed to determine accurate (∼1′ ) celestial positions (Gursky et al. 1978). • A4 – a high-energy experiment, the hard X-ray/low-energy gamma-ray experiment (Matteson 1978; Peterson 1975), extending to ∼10 MeV, consisting in seven inorganic phoswich scintillator detectors: – Low-energy detectors, two detectors in the 15–200 keV range – Medium-energy detectors operating in the 80 keV–2 MeV range – High-energy detector in the range 120 keV–10 MeV Comprehensive catalogs of X-ray sources (one for each experiment) were obtained (see Fig. 8). The LASS and the occasional pointed mode, with 1◦ × 4◦ FWHM collimation, enabled the studies of the rapid temporal variability, with,

Fig. 8 The HEAO-1 A-1 X-ray source catalog includes results from the first 6 months of data from HEAO-1, during which time a scan of the entire sky was completed. It contains positions and intensities for 842 sources. Half of the sources remained unidentified at the time of catalog publication (1984). (Credit NASA)

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e.g., the discovery of aperiodic variability in Cyg X-1 down to a timescale of 3 ms (Meekins et al. 1984), the first eclipse in a low-mass binary system (X1658-298) (Cominsky and Wood 1984, 1989), the 5-Hz quasiperiodic oscillation (QPO) in the “normal-branch” mode of Cyg X-2 (Norris and Wood 1987), and the variability on the timescale of tens of milliseconds in an X-ray burst (Hoffman et al. 1979). The CXE experiment provided a complete flux-limited high galactic latitude survey (85 sources), which yielded improved X-ray luminosity functions for active galactic nuclei and clusters of galaxies (Piccinotti et al. 1982), a classification among AGN types (Mushotzky 1984), and a measurement of the diffuse X-ray background from 3–50 keV (Marshall et al. 1980; Boldt 1987). The celestial positions, accurate to about 1 arcmin, obtained with the MC experiment, led to several hundred optical identifications and source classifications. The results from the high-energy instrument included the observation of the high-energy spectra of AGN, which were key for understanding the origin of the diffuse background (Rothschild et al. 1983); the discovery of the binary system, LMC X-4, with ∼30 d periodic on-off states; and the second example (after Her X-1) of cyclotron absorption in a binary system, 4U0115+63 (Wheaton et al. 1979).

The Late 1970s and the 1980s: The Program in the USA Thanks to Uhuru and HEAO-1, a new sky had been revealed, and X-ray astronomy entered a new mature phase, thanks to collimators and proportional counters. A key step forward was now necessary: X-ray focusing. A step that had been prepared by Riccardo Giacconi since the beginning of the 1960s, with robust R&D plans.

EINSTEIN All efforts to develop X-ray focusing telescopes resulted in a proposal to NASA for a focused large orbiting X-ray telescope (LOXT), whose team was assembled by Giacconi in 1970. Indeed, the second of NASA’s three high-energy astrophysical observatories, HEAO-2, renamed Einstein after launch, revolutionized X-ray astronomy, thanks to its Wolter type-I grazing-incidence X-ray focusing optics (Wolter 1952) (see Fig. 9). It was the first high-resolution imaging X-ray telescope launched into space (Giacconi et al. 1979). Focusing enabled not only a much better position constraint but also was key to dramatically reduce the particle background, since the volume of the detector was now significantly smaller than before. The HEAO2 sensitivity was then several hundred times better than any previous mission. Thanks to its few arcsec angular resolution, tens of arcmin field of view, and greater sensitivity, it was now possible to study the diffuse emission, to image extended objects, and to detect a large number of faint sources. It was a revolutionary mission in X-ray astronomy, and its scientific outcome completely changed our view of the X-ray sky. Einstein operated from November 12, 1978, to April 26, 1981, in a satellite orbit at 465–476 km, with 23.5◦ inclination and a period of 94 min. The

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Fig. 9 Left: a schematic view of the Einstein satellite. Right: the Einstein view of the galactic center of the Andromeda Galaxy (M31). The power of focusing appears in the many point sources resolved. (Both figures credit NASA) Table 3 HEAO 2 science payload Payload Bandpass (keV) Eff area (cm2 )

WolterType 1 IPC HRI 0.4–4 0.15–3 100 5–20

SSS 0.5–4.5 200

Field of view (FOV)

75′

25′

6′

Spatial resolution

∼1′

∼2′′

E ∆E

3–25

FPCS 0.42–2.6 0.1–1 6′ 1′ × 20′ 2′ × 20′ 3′ × 30′ 50–100∗ 100–1000∗∗

MPC 1.5–20 667

OGS

1.5◦

∼20%

∼50

scientific payload consisted of four instruments covering the energy range 0.2– 20 keV, which could be rotated, one at a time, into the focal plane of the optics (see Table 3 for the details of the instrument parameters): • An imaging proportional counter (IPC Gorestein et al. 1981; Giacconi et al. 1979), operating in the 0.4–4.0 keV with high sensitivity • A high-resolution imager (HRI Grindlay et al. 1980) operating in the 0.15– 3.0 keV range • A solid-state spectrometer (SSSn Holt 1976) in the 0.5–4.5 keV range with moderate sensitivity • A focal plane crystal spectrometer (FPCS Lum et al. 1992) in the 0.42–2.6 keV E E of 50–100 for E0.4 keV. Einstein also carried a non-focusing monitor proportional counter array (MPC, Gaillardetz et al. 1978) to measure the higher-energy emission (2–15 keV) of bright

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sources in the view direction of the main telescopes, and an objective grating spectrometer (OGS Harris 1984), with 500 mm−1 & 1000 mm−1 ; energy resolution E ∆E ∼50 was used in conjunction with HRI. Many fundamental and far-reaching results were obtained (NASA’s HEASARC 2023): The high spatial resolution morphological studies of supernova remnants The many faint sources resolved in M31 and the Magellanic Clouds The first study of the X-ray emission from the hot intra-cluster medium in clusters of galaxies revealing cooling inflow and cluster evolution The discovery of X-ray jets from Cen A and M87 aligned with radio jets The first medium and deep X-ray surveys On top of this, Einstein discovered thousands of “serendipitous” sources. Einstein was also the first X-ray NASA mission to have a Guest Observer Program.

The Late 1970s and the 1980s: The Program in Europe COPERNICUS Copernicus or Orbiting Astronomical Observatory 3 (OAO-3) was a collaborative effort between the USA (NASA) and the UK (SERC). The main instrument onboard was the Princeton University UV telescope (PEP) consisting of a Cassegrain telescope with an 80 cm primary mirror, a 7.5 cm secondary, and a Paschen-Runge spectrometer. In addition, the mission carried an X-ray astronomy instrument developed by the Mullard Space Science Laboratory (MSSL) of UCL. OAO-3 was launched on August 21, 1972, into a circular orbit of 7,123 km radius and an inclination of 35◦ . Although some of the instruments ceased to work, it operated for almost 9 years until February 1981. The University College of London X-ray Experiment (UCLXE) consisted of four co-aligned X-ray detectors observing in the energy range 0.7–10 keV, the collimated proportional counter (CPC), and three Wolter type-0 grazing-incidence telescopes (WT-0). At the focus of the telescopes, two proportional counters (PC1, PC2) and one channel photomultiplier (CHP) were used. In Table 4, we report the main parameters of the instruments (Bowles et al. 1974). Science highlights of the mission were the following: the discovery of several long period pulsars (e.g., X Per) (White et al. 1976), the discovery of absorption dips in Cyg X-1 (Mason et al. 1974), the long-term monitoring of pulsars and other bright

Table 4 Aside an instrument for UV astronomy, Copernicus carried onboard four X-ray detectors

Instrument Bandpass (nm) Eff area (cm2 ) FOV (FWHM)

CPC 0.1–0.3 17.8 –

Energy range (keV)

0.7–10

WT-0 PC 1 0.3–0.9 5.5 1′ 3′ 10′

PC 2 0.6–1.8 12.5 2′ 6′ 10′

CHP

2–7 22.9 10′

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X-ray binaries (Branduardi et al. 1978), and the observed rapid intensity variability from Cen A (Davison et al. 1975). ANS

ANS (Astronomische Nederlandse Satelliet) was a collaboration between the Netherlands Institute for Space Research (NIRV) and NASA. Launched on August 30, 1974, the mission reentered the atmosphere on June 14, 1977. Its orbit should have been circular with a radius of 500 km, but due to a failure of the first-stage guidance, the final orbit was highly inclined (98◦ ) and elliptic (258 km perigee and 1173 km apogee) with a period ∼99 min. ANS took onboard three instruments: an ultraviolet telescope spectrometer (UVT) (vanDuinen et al. 1975) by the University of Groningen; a soft X-ray experiment (SXX), den Boggede et al. (1975) developed by the University of Utrecht, that consisted of two parts known as Utrecht soft and medium X-ray detectors; and a hard X-ray experiment (HXX) (Gursky et al. 1975) of the AS&E-MIT group. In particular, the UVT instrument consisted of a Cassegrain telescope followed by a grating spectrometer of the Wadsworthtype; the Utrecht soft X-ray (USXD) consisted of a grazing-incidence parabolic collector, while the Utrecht medium X-ray detector (UMXD) was a 1.7 µ titanium proportional counter; and the HXX experimental package contained three major components: a collimator assembly, a large-area detector (LAD) unit, and a Bragg crystal spectrometer (BCS) tuned for detection of the silicon lines. The details of these experiments are summarized in Table 5. ANS scientific highlights include the discovery of X-ray bursts; flash of X-rays of several seconds, emitted by neutron stars in binary accreting systems (Heise et al. 1976); the detection of X-rays from Stellar Coronae (Capella) (Mewe et al. 1975); and the first detection of X-ray flares from UV Ceti and YZ CMi (Heise et al. 1975)

ARIEL V The Ariel V Satellite, developed by a joint collaboration of the UK and the USA, was launched from the San Marco platform on October 15, 1974, into a low inclination (2.8◦ ), near-circular orbit at an altitude of ∼520 km. The orbital period was 95 min. The mission ended on March 14, 1980. The British Science Research Council managed the project for the UK, the NASA GSFC for the USA. Ariel V Table 5 ANS UVT Instrument Bandpass (keV) Bandpass (Å) Eff area (cm2 ) FOV (FWHM)

1550 Å–3300 Å 266 2.5′ ×2.5′

SXX

HXX

USXD

UMXD

LAD

BCS

0.2–0.28

1–7

1–30

1–4.2

144 34′

45 38′ ×75′

40 10′

3◦

6 3◦

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was dedicated to the monitoring of the X-ray sky. The science payload included six instruments. Four, aligned with the spin axis, were devoted to a detailed study of a small region of the sky within ∼10◦ of the satellite pole. The set included the following: a rotation modulation collimator (RMC or Exp-A), consisting of rotation collimators and three different detectors, a photo-multiplier, an electron multiplier, and a proportional counter; a high-resolution proportional counter spectrometer (Exp-C); a Bragg crystal spectrometer (Exp-D), operating in the energy band 2–8 keV, that used a honeycomb collimator; and a scintillator telescope (ST or ExpF). The remaining two instruments were arranged in a direction perpendicular to the spin axis. The all-sky monitor (ASM or Exp-G), the only experiment of the mission developed by the USA, utilized two X-ray pinhole cameras to image the sky in order to monitor transient X-ray phenomena and all the strong X-ray sources for long-term temporal effects; the Sky Survey Instrument (SSI or Exp-B) (Villa et al. 1976) consisted of two pairs of proportional counters (LE and HE) (Smith and Courtier 1976). Ariel V performed long-term monitoring of numerous X-ray sources. It also discovered several long period (minutes) X-ray pulsars (White et al. 1978) and several bright X-ray transients probably containing a black hole (e.g., A0620-00=Nova Mon 1975) (Pound et al. 1976; Elvis et al. 1975). It also discovered iron line emission in extragalactic sources (Sanford et al. 1975) and established Seyfert I galaxies (AGN) as a class of X-ray emitters. In Table 6, we report details of the scientific payload of the mission.

COS-B Cos-B was an ESA mission built by the so-called Caravane Collaboration that included the following: the Laboratory for Space Research, Leiden, the Netherlands; Istituto di Fisica Cosmica e Informatica del CNR, Palermo, Italy; Laboratorio di Fisica Cosmica e Tecnologie Relative del CNR, Milano, Italy; Max-PlanckInstitut fur Extraterrestrische Physik, Garching, Germany; Service d’Electronique Physique, CEN de Saclay, France; and Space Science Department of ESA, ESTEC, Noordwijk, the Netherlands. The principal scientific objective was to provide a view of the gamma-ray universe; nevertheless, it took onboard a proportional counter sensitive to 2–12 keV

Table 6 Ariel V payload consisted of six instruments: four were aligned with the spin axes (Exp A, Exp C, Exp D, Exp F), and two were offset (Exp G, Exp B) Aligned A (RMC) Instrument Bandpass (keV) Eff area (cm2 ) FOV (FWHM) Energy range (keV)

0.3–30 – 10◦ -20◦ 0.7-10

C

D

F (ST)

1.3–28.6 – 3.5◦

2–8 –

26–1200 8

Offset G (ASM) 3–6

B (SSI) LE

HE

1.2–5.8 290

2.4–19.8

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Table 7 Ariel VI featured two X-ray instruments onboard the SXT and the MXPC

Experiment Bandpass (keV) Eff area (cm2 ) FOV (FWHM)

SXT Grazing telescope + Xe prop. counter 0.1–2 65 1.2◦ –4.6◦

MXPC

1–50 300 3◦

X-rays. As one can read in Bennet (1990) ,“This detector was intended to provide synchronization of possible pulsed gamma-ray emission from pulsating X-ray sources. The pulsar synchronizer was also used for monitoring the intensity of radiation from X-ray sources.”

ARIEL

VI

UK6, named Ariel VI after launch, was launched from the Wallops Island Launch Center in the USA on June 2, 1979. The orbit was elliptical with an apogee of 650 km and a perigee of 600 at an inclination of 55 ◦ . Ariel VI was a national UK mission but, in comparison with the success of its predecessor Ariel V, much less successful due to the problems caused by the interference with powerful military radars. In fact, strong magnetic fields severely hammered the command encoder and the pointing operations. Ariel VI carried three scientific instruments: one was a cosmic-ray experiment consisting of Cerenkov and gas scintillation counters and the other two were X-ray instruments. The soft X-ray telescope (here SXT), developed by MSSL in collaboration with the University of Birmingham, consisted of four grazing-incidence hyperboloid mirrors that reflected X-rays through an aperture/filter to four continuous-flow propane gas detectors (Cole et al. 1981). The medium X-ray proportional counter (MXPC) developed by the Leicester University consisted of four multilayered Xe proportional counters (Hall et al. 1981). Ariel VI continued to observe until February 1982. Table 7 shows some of the features of the X-ray instruments. Although partially, the observations carried with Ariel VI brought some results like the observation of phase variable iron line emission of the source GX 1+4 (Ricketts et al. 1982) or the spectral observation of Active Galaxies (Hall et al. 1981).

EXOSAT

The European Space Agency’s (ESA’s) X-ray Observatory, EXOSAT (Taylor et al. 1981), was active from May 1983 to April 1986. It was launched into a highly eccentric orbit (e∼ 0.93) with a 90.6 h period, inclination of 73◦ , at an apogee and perigee of 191,000 km and 350 km, respectively (at the beginning of the mission). This – at that time – peculiar orbit was chosen to enable long (from 76 h or 90 h),

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Table 8 EXOSAT’s science payload: the LE, ME, and GSPC LE Instrument Bandpass (keV) Eff area (cm2 ) FOV Angular res (FWHM) Energy res (FWHM)

CAM

PSD

0.04–2 0.1–2 0.4–10 – 2.2◦ 1.5◦ on axis 12′′ none

50′′ ∆E/E= 44/E (keV)1/2 %

ME Spectrometer – 1–50

GSPC

–

1800

∼10–100

–

45′ × 45′

45′

21% at 6 keV (Ar)

27/E (keV)1/2 %

2–20

18% at 22 keV (Xe)

uninterrupted observations during a single orbit. Due also to the great distance from the Earth (∼50, 000 km), EXOSAT was almost always visible from the ground station at Villafranca in Spain during science instruments operations. The payload of the satellite consisted of the low-energy telescopes (LE), composed of two identical Wolter-I telescopes. Each could operate in imaging mode by means of channel multiplier array (CMA) or position-sensitive detector (PSD) or in spectroscopy mode with gratings behind the optics and the CMA in the focal plane DeKorte et al. (1981); the medium-energy instrument (ME), the main instrument in the lunar occultation mode (Turner et al. 1981); and the gas scintillation proportional counter (GSPC Peacock et al. 1981). The characteristics of the instruments are shown in Table 8. During the performance verification phase, the PSDs of the two LE failed. About half a year later, one of the channel plates failed. However, overall the LE functioned up to the end, and discoveries were made using the X-ray grating spectrometers (built by SRON) (Bleeker and Verbunt 2013; Bleeker 2022). Most notable were the discoveries of quasiperiodic oscillations (QPOs) of low mass X-ray binaries, the soft excesses from AGN, the red and blue shifted iron K line from SS433, the characterization of many orbital periods of low mass X-ray binaries, and the new transient sources. The scientific highlights of the EXOSAT mission are reported in a special issue of the Memorie della Società Astronomica Italiana (MSAI 1988).

Late 1970s and the 1980s: The Program in Japan Japan, thanks to the leadership of Minoru Oda, contributed to X-ray astronomy with several missions, becoming a well-recognized country in space science. The first of those missions was CoRSa-b renamed, after the successful launch, Hakucho.

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Table 9 HAKUCHO (CoRSa-b). The payload carried three instruments for the detection of very soft (VSX), soft (SFX), and hard (HDX) X-rays VSX Instrument VXP Bandpass (keV) 0.1–1 Eff Area (cm2 )

∼78

FOV (FWHM)

6.3◦ × 2.9◦

SFX VXV

17.6◦

HDX

CMC

FMC

69

1.5–30 FMC 1 40 32 FMC 2 83 5.8◦ 4.4◦ × 10.0◦

24.9◦ × 2.9◦

SVC

10–100 ∼ 45 50.3◦ × 1.7◦

HAKUCHO

Hakucho, Japanese for swan (like one of the archetypal X-ray sources, Cyg X-1) developed by the Institute of Space and Astronautical Science (ISAS), was launched from the Kagoshima Space Center on February 21, 1979. It was placed into a nearcircular orbit with an apogee of 572 km, a perigee of 545 km, an inclination of 29.9◦ , and an orbital period of 96 min (Oda 1980). It was the second of the series CoRSa (Cosmic Radiation Satellite) (Unfortunately the first of the satellite of the series Corsa-a failed to reach the orbit). The mission ended on April 16, 1985. Its main goal was the study of transient phenomena using three different instruments: the very soft X-ray experiment (VSX), based on four units of proportional counters with very thin polypropylene windows. Two of the counters were oriented along the spin axis (VXP) and two were offset (VXV); the soft X-ray instrument (SFX) included six proportional counters with Beryllium windows. Two were equipped with a coarse modulation collimator (CMC), two with a fine modulation collimator (FMC), and the last two aimed at scanning the sky (SVC) operated in offset mode; the hard X-ray (HDX) detector consisted of two Na(T1) scintillators with an offset of 2.7◦ . Table 9 summarizes the principal characteristics of the mission payload (Inoue et al. 1980). Hakucho data led to the discovery of many burst sources and the soft X-ray transient sources Cen X-4 and Apl X-1.

HINOTORI Hinotori, Japanese for phoenix or firebird, was the first of the series of Astra satellites. It was dedicated to the study of solar phenomena, in particular to solar flares during the solar maximum. It was launched from the Kagoshima Space Center (now Ichinoura) on February 21, 1981, and operated until October 8, 1982. The orbit was near-circular with an apogee altitude of 603 km, a perigee of 548 km, an inclination of 31.3◦ , and a period of 96.20 min. For the solar flare studies, Hinitori carried onboard the solar X-ray telescope (SXT), equipped with two sets of bigrid modulation collimators for the imaging of the hard X-ray emission, using the rotating modulation collimator technique. In addition, the solar X-ray aspect sensor (SXA) was a system of collimating lenses to determine the flare position with a

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Table 10 HINOTORI (ASTRO-A). The payload consisted of a solar flare telescope (SXT), an analyzer (SXA), a spectrometer for soft X-ray (SOX), monitors for hard X-rays (HXM), and gamma-rays (SGR), for both solar flares (FLM) and for particle emission (PXM) SXT Instrument Bandpass (keV) Area (cm2 ) Ang. res (FWHM) Time res (ms) Energy res

113

SXA SOX SOX 1 1.72– 1.99 Å 6.69 Å

30′′

5′′

17–40

∼ 6×103

SOX 2

1.83– 1.89 Å 2.36 Å

6–10×103 2mÅ

0.15 m Å

FLM HXM SGR HXM 1 HXM 2 2–12 17–40 40–340 200– 6,700 0.5 57 62

125

7.8

125

PXM 100– 800 2.2

128ch/4s 125/ch 0.1 E1/2 MeV

resolution of 5 arcsec. The soft X-ray crystal spectrometer (SOX, Tanaka et al. 1982) enabled the spectroscopy of X-ray emission lines from highly ionized iron during a flare. It consisted of coarse (SOX1) and fine (SOX2) Bragg spectrometers. Three additional instruments enabled the monitoring of the flares over a large energy band: the soft X-ray flare monitor (FLM), the hard X-ray flare monitor (HXM), and the solar gamma-ray detector (SGR Yoshimori et al. 1983). The FLM was a gas (Xe) scintillation proportional counter, while the HXM and SGR detectors were NaI(T1) and CsI(T1) scintillation counters, respectively. The eight counters of the HXM instrument had different characteristics as reported in Table 10 (Tanaka 1983). In addition to the aforementioned instruments, Hinotori hosted a particle ray monitor (PXM), a plasma electron density measurement instrument (IMP), and a plasma electron temperature measurement instrument (TEL). All instruments were co-aligned with the spacecraft spin (Z) axis that was set 1◦ off the sun center, and therefore no additional driving mechanism for the detectors was necessary. The main scientific results of Hinotori include the following: the time profile and spectrum of the X-ray flares (Tanaka 1987; Yoshimori 1990), monitoring of the electron flux above 100 keV, discovery of high-temperature phenomena reaching up to 50 million ◦ C, and clouds of light-speed electrons floating in coronas (Oyama et al. 1988).

TENMA

Tenma, Japanese for Pegasus, developed by ISAS, was the second satellite of the ASTRO series (ASTRO-B) and the second Japanese satellite for X-ray astronomy. It was launched on February 1983 and placed into a near-circular orbit with an apogee of 501 km, a perigee of 497 km, and an inclination angle of 31.5 degrees. The orbital period was 96 min. Its scientific payload consisted of four instruments:

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Table 11 Tenma.The payload consisted of four instruments: the SPC, the XFC, the TSM, and a the RBM/GBD monitor SPC Instrument Bandpass (keV) Energy res (FWHM) Area (cm2 ) (FOV) FWHM

SPC - A

SPC - B

XFC SPC - C

2–60 9.5% at 5.9 keV 320 80 3.1◦ 2.5◦ 3.8◦

TSM

RBM/GBD

HXT

ZYT

0.1–2

2–25

1.5–25

10–100

15 1.4◦ ×5◦

114 40◦ ×40◦

280 2◦ ×25◦

14 1sr

a scintillation proportional counter (SPC), an X-ray focusing collector (XFC), a transient sources monitor (TSM), and a radiation belt and gamma-ray monitor (RBM/GBD, Tanaka et al. 1984). In particular, the SPC, devoted to spectral and temporal studies, consisted of ten GSPC divided in three groups (SPC-A, B, C) of four, four, and two units, respectively. The XFC, consisting of mirrors and position-sensitive proportional counters, was designed to observe very soft X-ray sources. The TSM served as an X-ray monitor because of its wide FOV. It included two detector groups: an Hadamard X-ray telescope system (HXT) and a scanner counting system (ZYT). Two small scintillation counters monitored the non-X-ray background and the gamma-ray burst emissions. The entire payload was mostly aligned with the stabilized spin-axes (Z) of the satellite. Detailed information about the instruments are reported in Table 11. Tenma observations continued intermittently until November 11, 1985. The main results of the mission were the discovery and the study of the iron line region of many classes of sources. Tenma science highlights include the following: the discovery of hot plasma of several tens of millions of degrees located along the galactic plane (Koyama 1989); the discovery of the iron absorption line in the energy spectra of X-ray bursts, which was red-shifted in the strong gravitational field of the neutron star (Waki et al. 1984; Suzuki et al. 1984; Inoue 1985); and the identification in low-mass X-ray binaries of X-ray emission regions on the surface of the neutron star and in the accretion disk (Mitsuda et al. 1984).

GINGA Ginga, Japanese for galaxy, ASTRO-C before launch, was launched on Feb 5, 1987, and operated until November 1, 1991. Astro-C was the result of a collaboration between Japanese research institutions, the University of Leicester and the Rutherford-Appleton Laboratory in the UK and the Los Alamos National Laboratory (USA). Ginga followed a near-circular orbit at a perigee distance of 505 km and an apogee of 675 km. It was originally planned to make a circular orbit of 630 km, but atmospheric conditions at launch constrained the satellite into an elliptic orbit. The inclination of the orbit was 31◦ , and the period was 96 min.

1 A Chronological History of X-ray Astronomy Missions Table 12 Ginga (ASTRO-C). The primary instrument onboard was the LAC. The ASM and the GBD completed the payload

29 GBD

Instrument Bandpass (keV) Energy res (FWHM) Area (cm2 ) FOV (FWHM)

LAC 1.5–37 18% at 6 keV 4500 0.8◦ × 1.7◦

ASM 1–20

1.5–500

70 1◦ × 45◦

63 60 all sky

PC

SC

The primary mission objective was the study of the time variability of X-rays from active galaxies, such as Seyfert galaxies, BL Lac objects, and quasars in the energy range 1.5–30 KeV. Accurate timing analysis of galactic X-ray sources was also one of the goals of the mission (Makino and Astro-C Team 1987). The payload of the satellite consisted of three instruments: a large-area proportional counter (LAC, Turner et al. 1989), an all-sky monitor (ASM, Tsunemi et al. 1989), and a gamma-ray burst detector (GBD, Murakami et al. 1989). The LAC consisted of eight multicells proportional counters. The ASM consisted of two identical gas proportional counters. Each counter was equipped with a collimator, which had three different FOVs. The GBD included two detectors: a proportional counter and a scintillation spectrometer. The characteristics of these instruments are summarized in Table 12.

The Late 1970s and the 1980s: The Program in Russia and India The X-ray astronomy program of the Soviet Union had modest beginnings in the 1970s with the FILIN X-ray experiment aboard the Salyut-4 space station. It continued in the 1980s with experiments onboard the Astron (1983-1988) and Mir (1987-2000) space stations. This latter program had a strong European involvement. These programs generally suffered from a limited observation time allocation because of other commitments of the manned spacecraft. During the late 1970s and into the 1980s, the Soviet program was focused on studies of gamma-ray bursts. The Konus experiments on the Venera 11-14 spacecraft yielded major advances in this field (Mazets et al. 1981; Higdon and Lingenfelter 1990). A notable result at X-ray wavelengths was the discovery of an unusual gamma burst on March 5, 1979, with sustained X-ray emission that exhibited periodic pulsations (Mazets et al. 1979).

FILIN / SALYUT -4

The FILIN X-ray instrument aboard the manned orbiting space station Salyut4 (December 1974) consisted of three detectors sensitive in the 2–10 keV range (Babichenko et al. 1977) and a smaller proportional counter for soft X-ray studies (0.2–2 keV), with a rather large FOV (see Table 13).

30 Table 13 FILIN. The x-ray instrument onboard the Salyut-4 space station

A. Santangelo et al. Instrument Bandpass (keV) Area (cm2 ) FoV (FWHM)

sFilin Filin 0.2–2 2–10 40 450 3◦ × 10◦

Gas-flow proportional counters were used as the detectors. A gas-flow system supplied a gas mixture for the counters. To determine the source coordinates, two star sensors were installed. The X-ray detectors, all-optical sensors, and the gasflow system were mounted on the outside of the station, while the power supply and electronics were inside. Scanning observations were carried out for about 1 month and pointed observations for about 2 months; studies included observations of Sco X-1, Her X-1, and Cyg X-1 (Babichenko et al. 1977) and the X-ray nova A0620-00 (Bradt 1992; Martynov et al. 1975).

SKR -02 M

The experiment SKR-02M on the Astron station (1983) consisted of a large proportional counter of effective area ∼0.17 m2 sensitive from 2 to 25 keV (Babichenko et al. 1990). The field of view was 3◦ × 3◦ (FWHM). Data were sent via telemetry in ten energy channels. Results have been reported from studies of the Crab Nebula and the Crab Pulsar, Her X-1, A0535 + 26, and Cen X-3 (Babichenko et al. 1990). The prolonged low state of Her X-1 in 1983 was studied, and the 1984 turn-on was reported (Giovanelli et al. 1984).

XVANTIMIR

The Röntgen X-ray observatory was launched in 1987 aboard the Kvant module, which docked to the MIR space station. The complement of detectors (Sunyaev et al. 1990b) included a sensitive high energy 15–200 keV X-ray experiment (HEXE, Reppin et al. 1985), a coded-mask system for imaging high-energy photons (TTM, Brinkman et al. 1985), and a gas scintillation proportional counters (GSPC, Smith (1985)). It also carried two gamma-ray experiments, which reached down to 30–40 keV (Sunyaev et al. 1990b). Röntgen was an international endeavor with contributions from Germany, UK, ESA, and the Netherlands. The highlight of the mission was the discovery and study (with Ginga) of the X-ray emission from SN1987A (Sunyaev 1987). A high-energy tail in the spectrum of the X-ray nova GS2000 + 25 was discovered (Sunyaev 1988a), further indicating its similarity to the black-hole candidate A0620-00. Timing results for the Her X-1 pulsar in 1987–1988 showed it to be continuing its spin up (Sunyaev 1988b). The principal characteristics of the Röntgen X-ray observatory are reported in Table 14.

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Table 14 Röntgen X-ray observatory Instrument Energy range (keV) Energy resolution (FWHM) Area (cm2 ) FOV (FWHM)

TTM 2–32 18% at 6 keV 600 7.8◦ × 7.8◦

GSPC 4–100 10.5% at 6 keV 300 3◦ × 3◦

HEXE 15–200 30% at 60 keV 800 1.6◦ × 1.6◦

ARYABHATA

Aryabhata, named after the Indian mathematician and astronomer of the fifth century, was the first satellite of India completely designed and built by the Indian Space Research Organization (ISRO). It was launched on April 19, 1975, from the Russian rocket launch site Kapustin Yar. Its orbit had a perigee of 563 km, an apogee of 619 km, and an inclination of 50.7◦ . The period was of 96.46 min. The mission ended on March 1981, and the satellite reentered the Earth’s atmosphere on February 10, 1992. Three instruments dedicated to aeronomy, solar physics, and Xray astronomy were onboard. The X-ray detector consisted of a proportional counter filled with a mixture of Ar, CO2 , and He and operated in a parallel mode, in the energy range from 2.5 to 115 keV. The effective area was ∼15.4 cm2 and the FOV, circular, with 12.5◦ (FWHM). In particular Aryabhata made observation of Cyg X-1, finding a hardening in its spectrum, Rao et al. (1976), and of other two X-ray sources, namely, GX17+2 and GX9+9 (Kasturirangan et al. 1976).

BHASKARA

Two satellites Bhaskara I and II were developed by ISRO and named after the two famous Indian mathematicians Bhaskara (or Baskara I) of the seventh century and Bhaskara II (or Bhaskaracharya, Bhaskara the teacher) of the twelfth century. We will report here only about Bhaskara I, since Baskara II didn’t carry X-ray instruments. Bhaskara I was launched on June 7, 1979, from Kapustin Yar. Its orbital perigee and apogee were 512 km and 557 km respectively; the inclination was of 50.7◦ and period 95.20 min. The mission ended on February 17, 1989, after almost 10 years. The main objectives of the mission were as follows: (1) to conduct observations of the earth yielding data for hydrology, forestry, and geology applications; (2) to conduct ocean-surface study using a SAtellite MIcrowave Radiometer (SAMIR); and (3) among other minor investigations, to conduct investigation in X-ray astronomy. The X-ray instrument consisted by a pinhole X-ray survey camera operating in the energy range between 2 and 10 keV with the purpose of observing transient sources and long-term variability of steady sources. At the image plane of the camera, there was a position-sensitive proportional counter, the detector operated with success during the first month after launch. However, it had to be turned off, and when, after some time, was turned on again, it didn’t operate correctly; the reason of the malfunction was never found.

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The Golden Age of X-Ray Astronomy, From the 1990s to the Present The 1990s can be considered as a sort of renaissance of X-ray astronomy. It consisted of years of significant missions that brought X astronomy into its full maturity. The decade begins with the launch of the Soviet mission Granat (December 1989) and of the German mission ROSAT (June 1990) and soon after the Japanese ASCA. In the mid-1990s, BeppoSAX and RXTE were launched, and in the late 1990s, Chandra and XMM-Newton.

THE PROGRAM IN THE USA ULYSSES

The Ulysses mission was a joint mission between NASA and ESA to explore the solar environment at high ecliptic latitudes. Launched on October 6, 1990, it reached Jupiter for its “gravitational slingshot” in February 1992. It passed the south solar pole in June 1994 and crossed the ecliptic equator in February 1995. In addition to its solar environment instruments, Ulysses also carried onboard plasma instruments to study the interstellar and Jovian regions as well as two instruments for studying X- and gamma-rays of both solar and cosmic origins. The mission could send data in four different telemetry modes at rates of 128, 256, 512, and 1024 b/s. The time resolution of the gamma-ray burst instrument depended on the chosen data rate. The maximum telemetry allocation for the instrument was about 40 b/s. The Ulysses solar X-ray and cosmic gamma-ray burst experiment (GRB) had three main objectives: study and monitor solar flares, detect and localize cosmic gamma-ray bursts, and in situ detection of Jovian auroras. Ulysses was the first satellite carrying a gamma burst detector, which went outside the orbit of Mars. This resulted in a triangulation baseline of unprecedented length, thus allowing major improvements in burst localization accuracy. The instrument was turned on November 9, 1990. The GRB consisted of two CsI scintillators (called the hard Xray detectors) and two Si surface barrier detectors (called the soft X-ray detectors). The detectors were mounted on a 3 m boom to reduce background generated by the spacecraft’s radioisotope thermoelectric generator. The hard X-ray detectors operated in the range 15–150 keV. The detectors consisted of two 3 mm thick by 51 mm diameter CsI(Tl) crystals mounted via plastic light tubes to photomultipliers. The hard detector varied its operating mode depending on the measured count rate, the ground command, or a change in spacecraft telemetry mode. The trigger level was normally set for 8 sigma above background corresponding to a sensitivity 2×10−6 erg cm−2 s−1 (Boer et al. 1990). When a burst trigger was recorded, the instrument switched to high-resolution data, recording a 32-kbit memory for a slow telemetry readout. Burst data consisted of either 16 s of 8-ms resolution count rates or 64 s of 32-ms count rates from the sum of the two detectors. There were also

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16 channel energy spectra from the sum of the two detectors (taken either in 1-, 2-, 4-, 16-, or 32-second integration). During “wait” mode, the data were taken either in 0.25 or 0.5 s integration and four energy channels (with shortest integration time being 8 s). Again, the outputs of the two detectors were summed. The soft X-ray detectors consisted of two 500 µm thick, 0.5 cm2 area Si surface barrier detectors. A 100 mg cm−2 beryllium foil front window rejected the low-energy X-rays and defined a conical field of view of 75◦ (half-angle). These detectors were passively cooled and operated in the temperature range −35 ◦ C to −55 ◦ C. This detector had six energy channels, covering the range 5–20 keV. Ulysses results have been mainly about the Sun and its influence on nearby space (Marsden and Angold 2008).

BBXRT

The Broadband X-ray telescope (BBXRT, Serlemitsos et al. 1984) was flown on the Space Shuttle Columbia (STS-35) as part of the ASTRO-1 payload (December 2, 1990–December 11, 1990). It was designed and built by the Laboratory for highenergy astrophysics at NASA/GSFC. BBXRT was the first focusing X-ray telescope operating over a broad energy range 0.3–12 keV, with moderate-energy resolution (90 eV at 1 keV and 150 eV at 6 keV). It consisted of two identical co-aligned telescopes each with a segmented Si(Li) solid-state spectrometer (detector A and B) with five pixels. The telescope consisted of two sets of nested grazing-incidence mirrors, whose geometry was close to the ideal paraboloidal/ hyperboloidal surfaces (modified Wolter type-I). This simplified fabrication and made possible nesting many shells to yield a large geometric area. The effective on-axis areas was 0.03 m2 at 1.5 keV and 0.015 m2 at 7 keV. The focal plane consisted of a five-element lithium-drifted silicon detector with an energy resolution of about 100 eV FWHM. Despite operational difficulties with the pointing systems, the BBXRT obtained high-quality spectra from some 50 selected objects (Serlemitsos et al. 1992), both galactic and extragalactic. Results included the resolved iron K line in the binaries Cen X-3 and Cyg X-2 (Smale et al. 1993), evidence of line broadening in NGC 4151 (Weaver et al. 1992), and the study of cooling flow in clusters (Arnaud et al. 1998). Details are reported in Table 15.

R XTE The Rossi X-ray Timing Explorer (RXTE, Bradt et al. 1993) was launched on December 30, 1995, from the NASA Kennedy Space Center. The mission was managed and controlled by NASA/GSFC. RXTE featured unprecedented time resolution in combination with moderate spectral resolution to explore the time variability of the X-ray sources. Timescales from microseconds to months were studied in the spectral range from 2 to 250 keV. Originally designed for a required lifetime of 2 years with a goal of five, RXTE completed 16 years of observations (!) before being decommissioned on January 5, 2012.

34 Table 15 BBXRT

A. Santangelo et al. Instrument Bandpass (keV) Eff area (cm2 ) (at 1.5 keV) Eff area (cm2 ) (at 7 keV) FOV (diameter) Central pixel FOV diameter Angular resolution Energy resolution (eV, FWHM) at 1 keV Energy resolution (eV, FWHM) at 6 keV

BBXRT on STS-35 0.3–12 765 300 17.4′ 4′ 2′ –6′ 90 150

The spacecraft was designed and built by the Applied Engineering and Technology Directorate at NASA/GSFC. The launch vehicle was a Delta II rocket that put RXTE into a low-Earth circular orbit at an altitude of 580 km, corresponding to an orbital period of about 90 min, with an inclination of 23 degrees. Operations were managed at GSFC. The mission carried onboard two pointed, collimated instruments: the proportional counter array (PCA, Zhang et al. 1993) developed by GSFC to cover the lower part of the energy range, and the high-energy X-ray timing experiment (HEXTE, Gruber et al. 1996) developed by the University of California at San Diego, covering the upper energy range. The PCA was an array of five proportional counters with a total collecting area of 6,500 cm2 . Each unit consisted of a layer propane veto; three layers of xenon, each split in two; and a xenon veto layer. HEXTE consisted of two clusters each containing four NaI/CsI phoswich scintillation counters. Each cluster could “rock” along mutually orthogonal directions to provide background measurements (1.5 or 3.0 degrees away from the source) every 16 to 128 s. Automatic gain control was provided by using a 241Am radioactive source mounted in each detector’s field of view. Part of the RXTE scientific payload was an all-sky monitor (ASM) from MIT that scanned about 80% of the sky every orbit, allowing monitoring at timescales of 90 min or longer. The ASM (Levine et al. 1996) consisted of three wide-angle shadow cameras equipped with proportional counters with a total collecting area of 90 cm2 . The main details of the mission are reported in Table 16. RossiXTE was an extremely successful and productive mission. Science highlights include the following: the discovery of kilohertz quasiperiodic oscillations (KHz QPOs) in NS systems (van der Klis et al. 1996)and high-frequency QPOs in BH systems (Morgan et al. 1997); the discovery of the first accreting millisecond pulsar, SAX J1808.4–3658 (Wijnands and van der Klis 1998), followed by several more accreting millisecond pulsars; the detection of X-ray afterglows from gammaray bursts (Bradt et al. 2003); and the observation of the bursting pulsar over a broad range of luminosity, providing stringent test of accretion theories.

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Table 16 Rossi XTE Instrument Bandpass (keV) Eff area (cm2 ) FOV Time resolution Energy resolution Spatial resolution Sensitivity (milliCrab) Background

Table 17 USA onboard ARGOS

ASM 2–10 90 6◦ × 90◦ e.u. 80% of the sky in 90 min 3′ × 15′ 30

PCA 2–60 6 500 1◦ 1 µs

HEXTE 15–250 2×800 1◦ 8 µs

2) reflections, again reducing the area in the double reflection spot. Figure 6 demonstrates how the variation of the value of ξ , and therefore the thickness of the MPOs, affects the area, gain, and FWHM of the MPO. Here, the gain is a measure of the focusing power of the optic and is the ratio between the total collecting area and the area in the double reflection spot. As shown in Fig. 6, the optimum value of ξ at 1 keV is 1.25. This simplifies Equation 3, at 1 keV, to (4)

0

0

arc min 1 2 3 4 5

area cm2 20 40 60

6 7

L = 2.5dF /r

0.8

1.0

1.2

1.4

1.6

1.8

0.8

1.0

1.2

1.4

1.6

1.8

x

Open symbols -No central MPO

0.0 0.5 1.0 1.5 2.0 2.5

gain cm2/arc min2

x

Solid symbols - Central MPO included Squares - Analysis beam = 2 x FWHM Circles - Analysis beam = FWHM Optimum x = 1.25 0.8

1.0

1.2

1.4

1.6

1.8

Fig. 6 The derivation of the relationship between the MPO’s redial position and optimum thickness is L = 2ξ dF /r. ξ is a scaling factor and all simulations were completed at 1.0 keV. The top left pane details the change in on-axis area as a function of ξ , which is strongly governed by the thickness of the MPO. The top right pain shows the change in the on-axis FWHM of the double reflection spot given ξ , and finally the bottom pane shows the change in gain, the focusing power of the optic, at various values of ξ

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Limitations of MPOs If you have a perfect MPO, which is perfectly spherical, with perfectly smooth pores all pointing to exactly the same position on a curved focal plane at exactly the correct focal distance, the minimum PSF size you could achieve would be the width of the pores at that optic-to-detector distance. The angular size of the pore at the focal length of the optic is the fundamental limit of the resolution of an MPO. If every pore is identical and all point to the same position on the focal plane, then the beam from each pore will pile up on top of each other, perfectly, to the width of a pore. In reality this is not the case, and there are many deformations in the form of the MPO which limit the resolution. The full details of the majority of the deformations can be found in Willingale et al. (2016), but they are summarized here. The three intrinsic aberrations associated with the lobster eye geometry, which limit the angular resolution performance of the optic, independent of the technology used to construct the pore array, are spherical aberrations, the geometric pore size, and diffraction limits. Nonintrinsic aberrations include slumping and formation of the multifibers. Slumping introduces additional radial tilt and shear errors as the pores are stretched and compressed to form the correct profile. Misalignment of multifibers to one another and deformations at the multifiber boundaries and within the multifibers themselves contribute to the total angular resolution. In addition, the pore surface roughness further increases the angular resolution of the MPO. The combination of the above errors imposes a theoretical limit on the angular resolution of ∼2 arcmin for a single MPO; however, the majority of MPOs have an angular resolution far larger than this. The MPOs are slumped by a technique that sandwiches the MPOs between convex and concave diamond-turned mandrels of the appropriate radius of curvature. Equal pressure and heat are applied to both mandrels and across the full surface in order to prevent the shearing of the channels with respect to each other. After slumping, the MPOs and mandrels are left to cool to room temperature which keeps the MPO form. Unfortunately, trying to slump a square MPO onto a sphere causes deformations in the form of the optic. If you think of trying to wrap a basketball with a square piece of paper, at the center, the fit is very good, but toward the corners you get crinkles and folds which distort your piece of paper. This is similar to what happens to an MPO, and the end result is that the form of the corner regions of the optics is not as good as at the center. You can also end up with an astigmatism in the optic where the radius of curvature in one axis does not match that in the other axes. Both of these effects have a massive influence on the net focal length of the optic and the PSF size and shape. At lower energies, the structure of the corners has a strong influence on the PSF, but the astigmatism can affect the PSF at all energies. In addition to the effect of the slumping on individual MPOs, the variation of RoC between the MPOs combined within an assembly will have an effect on the full optic assembly PSF. The optic-to-detector distance of best focus for the optic assembly is governed by the RoC and the form of the frame, but the size of the PSF

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of the assembly is governed by the individual MPOs. If none of the MPOs have the same RoC as the frame, then they will all be out of focus by varying amounts, and this will increase the size of the PSF.

Current Missions Several missions over the next few years are using this technology in order to take advantage of the large FoV and lightweight nature of these optics for various scientific goals, including planetary science and astronomy. Below is a description of some of the current selected missions.

BepiColombo The first instrument is the Mercury Imaging X-ray Spectrometer (MIXS) (Bunce et al. 2020) on board the ESA-JAXA mission BepiColombo. Although it was launched in October of 2018, it will not insert into its scientific orbit around Mercury, its destination, until late 2025–early 2026. MIXS consists of two instruments, the telescope MIXS-T and the wide-field collimator MIXS-C, shown on the left and right, respectively, on the MIXS optical bench in Fig. 7. MIXS-T uses the radial packing of 20 µm square pores and two consecutive sector MPOs, slumped with different radii of curvature to simulate a Wolter geometry (Willingale et al. 1998). In order to create the 1 m focal length, the front sectors have a RoC of 4 m and the rear sectors have a RoC of 1.3 m. The FoV of MIXS-T is ∼1.1◦ and consists of 36 tandem, sector pairs. The inner ring sectors have a thickness of 2.2 mm, the

Fig. 7 The flight MIXS instrument on the optical bench. The MIXS-T is on the left of the bench, and approximates the Wolter geometry. The MIXS-C is on the right of the bench and is a collimator in a 2 × 2 MPO geometry

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middle ring optics are 1.3 mm thick, and the outer ring optics are just 0.9 mm thick. The MIXS-C instrument uses 20 µm, square pore, square packed MPOs which are 40 × 40 mm in size and 1.2 mm thick. These MPOs have been slumped to a radius of curvature of 550 mm and give a FoV of ∼10◦ . The complete MIXS instrument on its optical bench weighs ∼11 kgs. By using these two instruments side by side, an elemental map of the Mercurian surface using X-ray fluorescence from the solar wind (Fraser et al. 2010) will be created.

SVOM The Space-based multiband astronomical Variable Objects Monitor (SVOM) (Mercier et al. 2014) is a Chinese-French mission to be launched in 2023. It is comprised of four spaceborne instruments, including the Microchannel X-ray Telescope (MXT) (Götz et al. 2015). The MXT’s main goal is to precisely localize and spectrally characterize X-ray afterglows of GRBs. The MXT is a narrow-fieldoptimized, lobster eye X-ray focusing telescope, consisting of an array of 25 square MPOs, with a focal length of 1.14 m and working in the energy band 0.2–10 keV. The design of the MXT optic (MOP) is optimized to give a 1◦ detector-limited FoV, but the optic has the unique characteristics of a lobster eye design, with a wide FoV >6◦ , and a PSF which is constant over the entire FoV. The MPOs on the Flight Module (FM) MOP have a pore size of 40 µm giving the optimum thicknesses across the aperture of 2.4 mm in the center and 1.2 mm at the edges. The left of Fig. 8 shows the completed FM MOP. Each MPO is 40 × 40 mm square, and there is a 2 mm gap between each MPO on the frame. The total mass of the fully assembled optic was measured to be 1.43 kg. Einstein Probe Einstein Probe (Yuan 2019) is a Chinese Academy of Science (CAS) mission due for launch in 2023, with its primary goals to discover high-energy transients and monitor variable objects. The mission consists of two instruments, the wide-field

Fig. 8 Left: the flight MXT optic, a 25 MPO array narrow-field lobster eye optic. Right: the full flight MXT lobster eye telescope. (© T De Prada CNES)

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Fig. 9 Left: A qualification WXT module installed in the PANTER beamline, MPE, Germany, prior to calibration. Right: X-ray image with the source centered on the module showing all four MPO quadrants focusing. Image taken with Cu-L (0.93 keV) X-rays at PANTER using the TRoPIC camera (Freyberg et al. 2008). (Image courtesy of MPE)

X-ray telescope (WXT), a lobster eye X-ray telescope consisting of 12 identical modules, and the follow-up X-ray telescope (FXT) (Vernani et al. 2020), which is a traditional Wolter X-ray telescope. The FXT has been jointly developed by the CAS, the European Space Agency (ESA), and the Max Planck Institute for Extraterrestrial Physics (MPE). Each of the WXT modules is comprised of 36 MPOs in a 6 by 6 array (left of Fig. 9), with a 375 mm focal length, a total FoV of more than 3600 square degrees, and an angular resolution goal of 5 arcmin per module and working in the energy range of 0.5–4 keV. Each of the 12 WXT modules has a focal plane comprised of 4 CMOS detectors in a 2 by 2 array. The modules are aligned so that each 3 by 3 quadrant of MPOs focuses onto a single CMOS detector, thus creating 4 discrete telescopes per module with overlapping FoVs (right of Fig. 9).

SMILE Solar wind Magnetosphere Ionosphere Link Explorer (SMILE) (ESA 2020) is a joint mission between the ESA and CAS to investigate the dynamic response of the Earth’s magnetosphere to the impact of the solar wind. From an elliptical polar orbit, it will combine soft X-ray imaging of the Earth’s magnetopause and magnetospheric cusps with simultaneous UV imaging of the Northern aurora, and will monitor in situ the solar wind and magnetosheath plasma conditions so as to set the imaging data into context. It is due for launch in late 2024 or early 2025 with four separate instruments on board, including the Soft X-ray Imager (SXI). The SXI is an elongated lobster eye telescope with an array of 4 by 8 MPOs. Each MPO is 40 × 40 mm, with iridium-coated 40 µm pores and a focal length of 300 mm. The high charge state solar wind ions in collision with hydrogen produce photons at soft X-ray (and EUV) energies within the 0.2–2.5 keV band. The focal plane consists of 2 CCDs and the instrument has a FoV of 26.5◦ by 15.5◦ . The wide FoV enables SXI to spectrally map the location, shape, and motion of Earth’s magnetospheric

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Fig. 10 Clockwise from left: Exploded CAD diagram of the SXI instrument. CAD diagram of the complete instrument. The structural thermal model of the full instrument during vibration testing. Simulation of a typical event and as seen by SXI after 5-min exposure

boundaries. Figure 10 shows an exploded CAD diagram of the SXI instrument on the left, the structural thermal model of the full instrument during vibration testing on the top right, and a simulation of the data expected on the bottom right.

Lobster Eye Optics in MFO/Schmidt Arrangement Schmidt Objectives The lobster eye geometry X-ray optics offer an excellent opportunity to achieve very wide fields of view. One-dimensional lobster eye geometry was originally suggested by Schmidt (1975), based upon flat reflectors. The device consists of a set of flat reflecting surfaces. The plane reflectors are arranged in a uniform radial pattern around the perimeter of a cylinder of radius R. X-rays from a given direction are focused to a line on the surface of a cylinder of radius R/2 (Fig. 11). The azimuthal angle is determined directly from the centroid of the focused image. At glancing angle of X-rays of wavelength 1 nm and longer, this device can be used for the

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Fig. 11 The arrangements of Angel MPO (left), Schmidt MFO 1D (middle), and Schmidt 2D lobster eye optics (Sveda 2003)

focusing of a sizable portion of an intercepted beam of parallel incident X-rays. Focusing is not perfect and the image size is finite. On the other hand, this type of focusing device offers a wide FoV, of up to a maximum of the half sphere of the coded aperture. It is possible to achieve an angular resolution on the order of one tenth of a degree or better. Two such systems in sequence, with orthogonal stacks of reflectors, form a double-focusing device. Such a device offers a FoV of up to 1000 square degrees at a moderate angular resolution. It is obvious that this type of wide-field X-ray telescope could play an important role in future X-ray astrophysics. These innovative very wide-field X-ray telescopes have only recently been suggested for space-based applications. One of the first proposals was the All Sky Supernova and Transient Explorer (ASTRE, Gorenstein (Gorenstein 1979, 1987)). This proposal included a cylindrical coded aperture outside of the reflectors, which provide angular resolution along the cylinder axis. The coded aperture contains circumferential open slits that are 1 mm wide and are in a pseudorandom pattern. The line image is modulated along its length by the coded aperture. The image is cross-correlated with the coded aperture to determine the polar angle of one or more sources. The FoV of this system can be, in principle, up to 360◦ in the azimuthal direction and nearly 90% of the solid angle in the polar direction. To create this mirror system, a development of double-sided flats is necessary. There is also potential for extending the wide-field imaging system to higher energy with the application of multilayers or other coatings in analogy to those described for flat reflectors in the K-B geometry. The angular resolution of the lobster eye optics in the Schmidt arrangement is a function of spacing between the reflecting plates and focal length. In the Schmidt arrangement, the lobster eye consists of plates of thickness t, and depth d (Fig. 12). Spacing between plate planes is s, focal length f , radius r, and focal point F , and β is the angle between optical axis and focused photons. Beam A (Fig. 12) shows the situation where the plate is fully illuminated, and the cross section of the plate is maximal (effective reflection). Beam B is the last beam that can be reflected into the focal point. Beams that are further from the optical axis reflect more than once (critical reflection). If reflected twice from the same set of plates, the photon does not reach the focal point and continues parallel to the incoming photon direction (Sveda 2003).

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Fig. 12 The schematic arrangement of the Schmidt lobster eye type X-ray optics used for simple equations derivation (Sveda 2003)

If t ≪ s ≪ d ≪ f , we can derive the following simple equations (Sveda 2003; Inneman 2001), where α is the estimate of the angular resolution: r 2 (s − t) βE = d f =

βL = 2βE α∼

2s s = r f

The design concept is different for lobster eye systems based on two reflections, a single reflection on a horizontally oriented surface (pore wall or mirror) and a single reflection on a horizontally oriented surface. Particularly, this is a case of Schmidt lobster eye. A paper by Tichý et al. (2019) presents analytical formula allowing direct computing of the effective collecting area for those systems by the formula:

L(r, s, t, ζ ) = 2r

 R(2ζ ) − 2 R(ζ ) + R(0) s  , s+t ζ

(5)

  ¯ )dθ is an arbitrary second antiderivative where  R(θ ) := R(θ )dθ dθ = R(θ of R. Radius of the system measured to mirror center is denoted r, s represents mirror spacing (or pore width), and t is mirror (pore wall) thickness. The effective collecting area equals L2 for the Angel system and L1 L2 for the Schmidt system, where L1 and L2 are related to individual mirror stacks as they have different radii and they may differ in other parameters. The value ζ is the ratio between mirror (pore) depth d and s. The optimal value of this ratio is given by the reflectivity function for given surface and photon energy only. The paper by Tichý et al. (2009) presents the detailed procedure for how the optimal value of this ratio can be analytically calculated. In addition, a paper by Tichý and Willingale (2018) presents a formula for the optimal value of s as s = −t +

 2Rtζ + t 2

(6)

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Here, R = (r + d/2) is the radius of the system measured to the front aperture (d is the mirror depth). This solves a common problem when focal length is limited, e.g., by available space in a spacecraft. Mirror (pore wall) thickness t should be as small as possible but must be large enough to achieve sufficient stress endurance, etc (Fig. 13). The 1D and 2D lobster eye Schmidt modules are illustrated in Fig. 14. To test the design and assembly of lobster eye modules in Schmidt geometry, various test modules were manufactured and tested (Table 1, Fig. 15). The first lobster eye X-ray Schmidt telescope prototype (midi) consisted of 2 perpendicular arrays of flats (36 and 42 double-sided flats 100 × 80 mm each).

Fig. 13 The Schmidt objective midi test module with 100 × 80 mm plates (left) and its optical tests (right)

Fig. 14 The schema of Schmidt lobster eye modules, 1D (left) and 2D (right) arrangements

Table 1 The parameters of selected test Schmidt lobster eye modules assembled and tested. The distance parameter means the separation between reflecting foils. The parameters size, plate thickness, distance, length, and focal distance f are given in mm, resolution in arcmin, FoV in degrees, and optimal energy in keV Module Size Plate thickness Macro 300 0.75 Middle 80 0.3 Mini 1 24 0.1 Mini 2 24 0.1 Micro 3 0.03

Distance

Length

Eff. angle

f

Resolution FoV Energy

10.8 2 0.3 0.3 0.07

300 80 30 30 14

0.036 0.025 0.01 0.01 0.005

6000 400 900 250 80

7 20 2 6 4

16 12 5 5 3

3 2 5 5 10

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Fig. 15 The visual tests for the 1D (left) and 2D lobster eye modules (right) in Schmidt arrangements

The flats were 0.3 mm thick and gold-coated. The focal distance was 400 mm from the midplane. The FoV was about 6.5 degrees (Fig. 13). The results of optical and X-ray tests indicated a performance close to those provided by mathematical modeling (ray tracing). X-ray testing was carried out in the test facility of the X-ray astronomy group at the University of Leicester. At a later date, test modules with a Schmidt geometry were designed and developed using 0.1-mm-thick gold-coated glass plates that were 23 × 23 mm, with a 0.3 mm spacing. The aperture/length ratio is 80. A single module has 60 plates. Two analogous modules represent the 2D system for laboratory tests, providing focus-to-focus imaging with focal distances of 85 and 95 cm. The innovative gold coating technique resulted in a final surface micro-roughness rms to 0.2–0.5 nm. Various modifications of this arrangement have been designed both for imaging sources at final distances (for laboratory tests) and for distant sources (the corresponding double-focusing array has f = 250 mm and FoV = 2.5 deg). In parallel, numerous ray tracing simulations have been performed, allowing for a comparison between theoretical and experimental results (Figs. 16, 17, 18, 19, and 20). Following the aforementioned developments, even smaller (micro) lobster eye modules were constructed and tested in both visible light and X-rays. As an example, we show X-ray test results for the mini and micro lobster eye modules (Fig. 21). These results show the on-axis and off-axis imaging performance of the lobster eye module tested. For mosaics of X-ray test images for various energies see Fig. 22 and for various off-axis angles at 4.5 keV see Fig. 23.

Substrates for Lobster Eye Lenses in Schmidt/MFO Arrangement In general, there is growing need for large segmented X-ray foil telescopes of various geometries and geometrical arrangements. The requirement of minimizing the weight of future large X-ray space telescopes and at the same time achieving large collecting area for future large astronomical telescopes can be met with thin X-ray-reflecting foils (i.e., thin, lightweight, multiple layers that can be easily nested to form precise high-throughput mirror assemblies). This includes the large

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Fig. 16 The large Schmidt lobster eye module macro with aperture of 30 × 30 cm (left) and its optical image in visible light (right)

Fig. 17 The LE Mini and LE Micro modules

Fig. 18 The various sizes of Schmidt MFO lobster modules manufactured by Rigaku Prague. (Photo courtesy of Rigaku Prague)

4 Lobster Eye X-ray Optics Fig. 19 The schematic assembly of 1D lobster eye Schmidt sub-modules and 2D lobster modules

159 Sub-module A

Sub-module B

module (Schmidt arrangement)

Fig. 20 The calculated on-axis gain dependence on energy for lobster eye modules in Schmidt geometry. The f = 375 mm, gold-coated plates 100 microns thick (Sveda 2003)

modules of the Wolter 1 geometry, the large Kirkpatrick-Baez (further referred to as K-B) modules (as they can play an important role in future X-ray astronomy projects as a promising and less laborious to produce alternative), as well as the large lobster eye modules in the Schmidt arrangements. Although these particular X-ray optics modules differ in the geometry of foils/shells arrangements, they do not differ much from the point of the view of the foil/shell production and assembly, and also share all the problems of calculations, design, development, weight constraints, manufacture, assembling, testing, etc. It is evident that these problems are common and rather important for the majority of the large aperture Xray astronomy space-based observatories. Most of the future space projects require light material alternatives (Hudec 2011). We (Czech team with participation of the first author of this chapter) have developed various prototypes of the abovementioned X-ray optics modules based

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Fig. 21 The point-to-point focusing system, lobster eye Schmidt micro (3×3×0.03 mm mirrors), source-detector distance 160 mm, 8 keV photons, left, X-ray experiment vs. simulation, point-topoint focusing system, lobster eye Schmidt mini (25×25×0.1 mm; source-detector distance 1.2 m; 8 keV photons; image width, 2×512 pixels; 24 micron pixel; gain, 570 (measured) vs. 584 (model) (right)

Fig. 22 X-ray images for various energies from MFO Schmidt lobster eye mini, f = 25 cm, Palermo X-ray test facility (Tichý et al. 2009)

on high-quality X-ray-reflecting gold-coated float glass foils (Hudec et al. 2000). The glass represents a promising alternative to electroformed nickel shells used in Wolter optics, the main advantage being much lower specific weight (typically 2.2 g cm−3 if compared with 8.8 g cm−3 for nickel). For the large prototype modules of dimensions equal to or exceeding 30 × 30 × 30 cm, mostly glass foils of thickness of 0.75 mm have been used, although in the future this thickness can be further reduced down to 0.3 mm and perhaps even less (we have successfully designed,

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Fig. 23 Mosaic of X-ray (at 4.5 keV) images for various off-axis positions (demonstrating the offaxis imaging performance), lobster eye REX2 2D module (83 gold-coated glass foils 148 × 57 × 0.42 mm each, FoV 4.7 × 4.3 deg.) (Pina et al. 2021)

Fig. 24 The experimental HORUS modules with Si wafers (Stehlikova et al. 2021)

developed, and tested systems based on glass foils as thin as 30 microns, albeit for much smaller sizes of the modules). More recently, silicon wafers with superior flatness and micro-roughness are serving as alternative substrates for lobster eye MFO modules. The recent HORUS experiment can serve as an example. HORUS has 4 modules, 2 modules with Au surface and 2 modules with Ir surface; each module has 17 silicon foils, i.e., in total 4 × 17 Si wafers 0.625 mm thick, with an aperture of 85 × 65 mm f = 2 m. The goal is to experimentally compare different reflective layers (Fig. 24).

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These substrates, both glass foils and silicon wafers, can be used in various Xray optics arrangements using MFO technology, mostly lobster eye and K-B (Hudec et al. 2006b, 2009).

The Application and the Future of Lobster Eye Telescopes in Schmidt Arrangements It is obvious that the lobster eye Schmidt MFO prototypes confirm the feasibility to design and develop these telescopes with currently available technologies. Considerations for fabricating and assembling a wide-field space-based X-ray observatory include: (1) Reduction of the micro-roughness and slope errors of the reflecting surfaces to optimize the angular resolution and reflectivity/efficiency of the system. The past development has already led to significant micro-roughness improvement (to 0.2–0.5 nm for glass substrates and 0.1 nm for silicon substrates) (2) The design and construction of larger or multiple modules to achieve a larger FoV (of order of 1000 square degrees and/or more) and enhance the collecting area (3) Reduction in the spacing and plate thickness (Schmidt arrangement) to improve imaging performance (angular resolution and system efficiency) and (4) Advanced, alternative layer applications, and/or other approaches applied to the reflecting surfaces to improve the reflectivity and to extend the energy bandpass to higher energies. The application of very wide-field Schmidt MFO X-ray imaging systems could be without doubt very valuable in many areas of X-ray and gamma-ray astrophysics. Results of analyses and simulations of lobster eye X-ray telescopes have indicated that they will be able to monitor the X-ray sky at an unprecedented level of sensitivity, an order of magnitude better than any previous X-ray all-sky monitor. Limits as faint as 10−12 erg cm−2 s−1 for daily observation in the soft X-ray range (typically 1–10 keV) are expected to be achieved, allowing monitoring of all classes of X-ray sources, including X-ray binaries, fainter classes such as AGNs, coronal sources, cataclysmic variables, as well as fast X-ray transients including GRBs and the nearby Type II supernovae (Hudec et al. 2006a, 2008, 2012). For pointed observations, limits better than 10−14 erg cm−2 s−1 (0.5–3 keV) could be obtained, sufficient enough to detect X-ray afterglows to GRBs (Sveda et al. 2004; Hudec et al. 2013).

Lobster Eye Laboratory Modifications The lobster eye soft X-ray optics, originally proposed and designed for astronomical (space) applications, has potential for numerous laboratory applications. As an example, lobster eye optics can be modified for efficient collection of laserplasma radiation for wavelengths longer than 8 nm (Sveda et al. 2006). The optics for this application consist of two orthogonal stacks of ellipsoidal mirrors forming a double-focusing device (Sveda et al. 2006). The ellipsoidal surfaces were covered

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by a layer of gold that has relatively high reflectivity at the wavelength range that is 8–20 nm up to an incident angle of around 10 degrees. The width of the mirrors forming the optics assemblies is 40 mm. As can be noticed, the spacing between adjacent mirrors increases with the distance from the axis. The curvature of the mirrors and the spacing between them were optimized using ray tracing simulations to maximize the optics aperture and to minimize the size of the focal spot.

Hybrid Lobster Eye The lobster eye Schmidt MFO configuration described in the previous sections is a wide-field, relatively low angular resolution optics. Achieving finer angular resolution is challenging given the current limitations of the technological limitation related to the mirror thickness and minimum spacing (Sveda et al. 2005). One possible solution to improving angular resolution is to invoke the typical use case of the standard lobster eye configuration as an all-sky monitor (ASM) for X-ray astronomy. The lobster eye is used onboard a space-based platform and will continuously scan the sky. If an area of the sky is outside the FoV of the optics, it will be inside the FoV sometime later because of scanning. This operational scenario allows for a smaller FoV in the scanning direction, which in turn permits finer angular resolution. The desired optics would have a wide FoV and moderate angular resolution in one direction, and a smaller FoV and better angular resolution in another. It is necessary to use curved mirrors to achieve better angular resolution. However, this puts constraints on the mirror dimensions. A combination of the standard one-dimensional lobster eye optics in one direction and K-B parabolic mirrors in the other direction meets the desired requirements (Sveda et al. 2005), shown in Fig. 25. Preliminary results of this configuration indicate that the hybrid lobster eye works as intended, i.e., it improves the angular resolution in one direction while still having a wide FoV in another. However, the blurring increases rapidly with the off-axis distance in the direction where there is focusing from the parabolic mirrors. Fig. 25 The sketch of the hybrid lobster eye with two plotted rays. Only one parabolic mirror is schematically plotted here. Typically, multiple reflecting surfaces have to be used (Sveda et al. 2005)

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Consequently, it is reasonable to think about such optics for pointed observations if the source and image are expected to be highly asymmetric. The effect of blurring is reduced for scanning observations; hence, the increase in angular resolution is achievable. There is a loss of sensitivity with this configuration, which translates to a significant decrease in the limiting flux. This fact, combined with manufacturing difficulties, makes this configuration of limited use for space-based applications. However, there is potential for use in laboratory applications (Sveda 2006).

Space Experiments with Lobster Eye MFO X-ray Optics The lobster eye optics in the Schmidt/MFO arrangement was placed onboard the Czech nanosatellite VZLUSAT-1 and onboard the NASA Water Recovery Rocket experiment. More systems are in study and/or in preparation for future space missions. For example, the HORUS double test module was designed and tested recently in order to compare modules with various reflective layers; see Fig. 24 (Stehlikova et al. 2021).

VZLUSAT-1 The small lobster eye telescope onboard the VZLUSAT-1 nanosatellite uses the first lobster eye MFO Schmidt X-ray optics in space. The first Czech technological CubeSat satellite VZLUSAT-1 was designed and built during the 2013–2016 period. It was successfully launched into low Earth orbit at an altitude of 505 km on June 23, 2017, as part of international mission QB50 onboard a PSLV C38 launch vehicle. The satellite was developed in the Czech Republic by the Czech Aerospace Research Centre, in cooperation with Czech industrial partners and universities (Dániel et al. 2016). The payload fits into a 2U CubeSat (extended to 3U in space) and includes a 1D (Pína et al. 2015, 2016) miniature X-ray telescope with a Timepix detector in its focal plane (Baca et al. 2016). The main mission goal is the technological verification of the system (Urban et al. 2017; Dániel et al. 2016). However, there is potential for science as the telescope will view bright celestial sources as part of its mission (Blazek et al. 2017). The satellite represents the fifth satellite in space with Czech X-ray optics onboard. The 1D lobster eye module onboard VZLUSAT-1 has focal length of 250 mm and is composed of 116 wedges and 56 reflective double-sided gold-plated foils (thickness 145 microns). The input aperture is 29 × 19 mm2 ; outer dimensions are 60 × 28 × 31 mm3 . The active part of the foils is 19 mm in width and 60 mm in length, and the energy range is 3–20 keV. Images of the optics are shown in Fig. 26. REX Rocket Experiment The Rocket EXperiment 1 (REX1) was a secondary payload instrument on the Water Recovery X-ray Rocket (WRX-R) experiment. WRX-R was launched from the Kwajalein Atoll in the Marshall Islands on April 4, 2018. WRX-R was the first astrophysics sounding rocket mission to use a newly developed NASA water

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Fig. 26 The miniature 1D Schmidt lobster eye module for VZLUSAT1 CubeSat (Urban et al. 2017)

recovery system for astronomical payloads as a cost-effective alternative to typical land recoveries that also may result in payload damage (Miles 2017). The WRX-R was led by the Pennsylvania State University (PSU), USA. The primary payload was the soft X-ray spectroscope of PSU. WRX-R’s primary instrument was a grating spectrometer that consisted of a mechanical collimator, an X-ray reflection grating array, a grazing incidence mirror, and a hybrid CMOS detector. The Czech team provided the REX1 optical instrument as a secondary payload (Urban et al. 2021; Dániel et al. 2017, 2019). It was the first time that an X-ray lobster eye telescope was flown in a rocket experiment to observe an astrophysical object. The design of the REX1 instrument for the WRX-R was based on the concept of an optical baffle, which is normally used for NASA Sounding rocket experiments. This is a simple construction of a quill-shaped boulder with the anchor on one side of the block base, where the baffle is attached to the sounding rocket. The REX1 optical instrument consisted of two parts – vacuum chamber and hermetically sealed box. The vacuum part contained two (one 1D and one 2D) Xray telescopes with Timepix pixel detectors (Pína et al. 2019). The modules were assembled using Multi-Foil Technology (MFT). The material of the housing of the optical module was an aluminum alloy. The 1D X-ray lobster eye system with a focal length of 250 mm had a FoV of 3.3 × 2.0 degrees and spanned the spectral range from 3 to 20 keV. The 1D lobster eye module was composed of 116 wedges and 56 reflective double-sided gold-plated glass foils (thickness of 145 µm). The gold coating allows the material to reflect incoming X-ray photons that have shallow incident angles of 0.5 deg or less. The input aperture was 29 × 19 mm2 , while the outer dimensions were 60 × 28 × 31 mm. The active area of the module was 19 mm in width and 6 mm in length and the energy range was 3–20 keV. The second lobster eye telescope was a 2D X-ray system with a focal length of 1065 mm. The FoV of this system was 0.8 × 0.8 deg with spectral range from

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Fig. 27 The 1D and 2D Schmidt lobster eye modules REX for rocket flight experiment (Urban et al. 2021)

3 to 10 keV. The 2D lobster eye X-ray optics of REX was composed of two 1D sub-modules where one-sided gold-plated glass foils were in the vertical plane of the horizontal arrangement. Each sub-module consisted of 55 pieces of thin at glass foils (thickness of 0.34 mm) which were arranged so that the focal length was around 1.0 m. The external dimensions of the module was approximately 80×80×170 mm. Both REX1 lobster eye modules can be seen in Fig. 27. The second generation of the optical system for the Rocket Experiment (REX2) is currently under study (Pina et al. 2021). This optical device is based on the successful mission REX1 described above. The purpose of REX2 is to verify the Xray optical system that consists of a wide-field 2D X-ray lobster eye assembly with an uncooled Quad Timepix3 detector (512×512 px @ 55 microns and spectrometer (active area 7 mm2 , resolution 145 eV @ 5.9 keV)). The 2D X-ray lobster eye optics is a combination of two 1D lobster eye modules with a focal length of up to 1 m and a FoV larger than 4.0 × 4.0 deg. The proposed optical system has imaging capabilities (2.5–20 keV) and spectroscopy capabilities (0.2–10 keV). The optical system was recently tested in an X-ray vacuum chamber (Pina et al. 2021).

Kirkpatrick-Baez Optics In this section we briefly describe Kirkpatrick-Baez (K-B) X-ray optics. From the standpoint of manufacturing, there is a significant number of similarities to lobster eye optics in MFO Schmidt arrangements as both are based on multiple thin foils. Although the Wolter systems are generally well known, Hans Wolter was not the first who proposed X-ray imaging systems based on the reflection of X-rays. In fact, the first grazing incidence system to form a real image was proposed by Kirkpatrick and Baez in (1948). This system consists of a set of two orthogonal parabolas in the configuration shown in Fig. 28. The first reflection focuses to a line, which the second surface focuses to a point. This was necessary to avoid the extreme astigmatism suffered by a single mirror but was still not free from geometric aberrations. The system is nevertheless attractive for the ease of constructing the reflecting surfaces. These surfaces can be produced as flat plates and then

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Fig. 28 The configuration of the K-B X-ray objective according to Kirkpatrick and Baez (1948)

mechanically bent to the required curvature. In order to increase the aperture, a number of mirrors can be nested together, but it should be noted that such nesting introduces additional aberrations. This configuration is used mostly in experiments not requiring large collecting area (solar, laboratory). Recently, however, large modules of K-B mirrors have been suggested also for stellar X-ray experiments (Hudec et al. 2018a,b). Despite this fact, astronomical X-ray telescopes flown so far on satellites mostly used the Wolter 1 type optics. However, K-B was used in several rocket experiments in the past, and in addition to that, they were proposed and discussed for use on several satellite experiments. Alternately, in the lab, K-B systems are in frequent use, e.g., at synchrotron facilities. In order to increase the collecting area (the frontal area), a stack of parabolas of translation can be constructed for astrophysical applications. However, in contrast to the single double-plate system, the image of a point-like source starts to become increasingly extended in size as the number of plates involved increases. Wolter type I telescopes bend the incident ray direction two times in the same plane, whereas the two bendings in K-B systems occur in two orthogonal planes, which for the same incidence angle on the primary mirror requires a longer telescope (Aschenbach 2009).

K-B Systems in Astronomical Applications As an alternative to Wolter optics-based instruments, van Speybroeck et al. (1971) designed several K-B telescope configurations that focus the X-rays with sets of two orthogonal parabolas of translation. According to van Speybroeck et al. (1971), the crossed parabola systems should find application in astronomical observations such as high sensitivity surveys, photometry, and certain kinds of spectroscopy where a large effective area rather than high angular resolution is the most important factor. The design of a K-B grazing incidence X-ray telescope to be used to scan the sky would allow for the distribution of the reflected X-rays and spurious images over the FoV to be analyzed. Kast (1975) has shown that in order to obtain maximum

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effective area over the FoV, it is necessary to increase the spacing between plates for a scanning telescope as compared to a pointing telescope. Spurious images are necessarily present in this type of lens, but they can be eliminated from the FoV by adding properly located baffles or collimators. X-ray telescopes of the type suggested by Kirkpatrick and Baez (1948) have several advantages over other types of X-ray telescopes for a general sky survey for low-energy X-ray sources. These telescopes use two orthogonal sets of nested parabolas of translation (perpendicular to one another) to provide 2D focusing of an X-ray image. Although their angular resolution for axial rays is somewhat worse compared with telescopes using successive concentric figures of revolution, they can be constructed more easily and have greater effective area (van Speybroeck et al. 1971). Note that more recent papers give somewhat different findings, namely, that the K-B Si stacks provide an alternative solution with a reduced on-axis collecting area but wider field of view and comparable angular resolution (Willingale and Spaan 2009). In either case, these telescopes, in general, can be constructed more easily. The design of K-B-type telescopes has been discussed by several authors, e.g., van Speybroeck et al. (1971), Gorenstein et al. (1973), Weisskopf (1973), and results have been reported from several experiments using 1D focusing from a single set of plates (Gorenstein et al. 1971; Catura et al. 1972; Borken et al. 1972). For a more recent status, see Hudec (2010) and Hudec et al. (2018a).

K-B as a Segmented Mirror Segmentation can also be applied to an array of K-B stacked orthogonal parabolic reflectors (Fig. 29). As shown in Fig. 29, a large K-B mirror can be segmented into rectangular modules of equal size and shape (Gorenstein et al. 1996). A segmented K-B telescope has the advantage of being highly modular on several levels. All segments are rectangular boxes with the same outer dimensions. Along a column, the segments are nearly identical and many are interchangeable with each other. All reflectors deviate from flatness only slightly. On the other hand, the Wolter reflectors are highly curved in the azimuthal direction, and the curvature varies over

Fig. 29 Kirkpatrick-Baez mirror consisting of orthogonal stacks of reflectors. Each reflector is a parabola in one dimension. A large K-B mirror can be segmented into rectangular modules of equal size and shape (Gorenstein et al. 1996)

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Fig. 30 Principle of K-B MFO telescope (left (Marsikova 2009)) Laboratory samples of advanced K-B MFO modules designed and developed at Rigaku Innovative Technologies Europe (RITE) in Prague (right (Marsikova 2009), photo courtesy Rigaku)

a wide range. Furthermore, within a segment, the K-B reflectors themselves can be segmented along the direction of the optical axis. As shown in Fig. 29, a K-B mirror system can be folded more easily than the Wolter mirror into a compact volume for launch and deployment in space. The examples of assembled K-B modules based on superior quality gold-coated Si wafer substrates are illustrated in Fig. 30.

K-B in Astronomical Telescopes: Recent Status and Future Plans The first attempt to create an astronomical K-B module with silicon wafers was reported by Joy et al. (1994). A telescope module that consisted of 94 silicon wafers with a diameter of 150 mm, uncoated, with thickness of 0.72 mm was constructed. The device was tested both with optical light and with X-rays. The measured FWHM was 150 arc-seconds, which was dominated by large-scale flatness. It should be noted that the surface quality and flatness of Si wafers have improved since this time. Recent efforts toward supporting future larger and precise imaging astronomical X-ray telescopes require reconsidering both the technologies and mirror assembly design. Future large X-ray telescopes require new lightweight and thin materials/substrates such as glass foils and/or silicon wafers (Hudec et al. 2015). Their shaping to small radii, as required in Wolter designs, is not an easy task, while the K-B arrangements have potential to represent a less laborious and hence less expensive alternative because of (i) no need of mandrels, (ii) no need of polishing, and (iii) no need of bending to small radii. The use of K-B arrangement for the proposed IXO project (the proposed joint NASA/ESA/JAXA International X-ray Observatory) was suggested and investigated by Marsikova (2009), Hudec (2011), and Willingale and Spaan (2009). These investigations indicate that if superior quality reflecting plates were used and the focal length is large, an angular resolution of order of a few arcsec could be achieved. Recent simulations further indicate that in comparison with Wolter arrangement, the K-B optics exhibit reduced on-axis collecting area but larger FoV, at comparable angular resolution (Willingale and Spaan 2009). A very important factor is the ease of constructing highly segmented modules based on multiply nested thin reflecting substrates if compared with Wolter design.

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While, e.g., the Wolter design for future large space X-ray telescopes such as Athena requires the substrates to be precisely formed with curvatures as small as 0.25 m, the alternative K-B arrangement uses almost flat or only slightly bent sheets. Hence, the feasibility to construct a K-B module with the required Athena 5 arcsecond HEW resolution at an affordable cost is, in principle, lower than the cost of a Wolter arrangement. Note however that in order to achieve the comparable effective area, the focal length of K-B system is required to be about twice of the focal length of Wolter system (Marsikova 2009; Hudec 2010, 2011).

Conclusion The grazing incidence X-ray optical elements of non-Wolter type (lobster eye and Kirkpatrick-Baez) offer alternative solutions for many future space- and lab-based applications. They can offer cheaper, and/or lighter, alternatives, and also a much larger FoV. At the same time, new computer-based systems allow us to consider alternative designs and arrangements (Nentvich et al. 2017). Although both Angel and Schmidt designs were suggested in the 1970s, both have seen rapid development over the past few years with MPO optics in an Angel arrangement already on selected missions and the Schmidt design using MFOs being proven on rocket and CubeSat experiments. A direct and reliable comparison between MFO and MPO designs of lobster eye X-ray optics is difficult, as in both cases the real optics performance deviates from the theoretical. The necessary slumping of the MPOs introduces additional sources of error (Bannister et al. 2007; Willingale et al. 2016), while the MFO design is harder to assemble. Both designs differ in geometry using both Angel and Schmidt designs, and require different manufacturing and assembling technology. The MFO technology enables a larger effective area with easy deposition of reflective layers, while the MPOs are lighter and are easier to assemble into a large array. The effective area at 10 keV for MFOs is higher than for MPOs although alternative coatings are being investigated for MPOs to improve the higher energy response. The prototypes developed and tested for both arrangements confirm that these lightweight telescopes are fully feasible and can achieve angular resolutions of several arcmin or better over a very wide FoV. While both provide a more modest angular resolution compared to Chandra (Weisskopf 2003) and XMMNewton (Jansen et al. 2001), for example, they can still be used to help solve pressing questions in X-ray astrophysics, and can also be used for other applications such as within laboratories. K-B optics have already found wide applications in synchrotrons, and have demonstrated their performance and advantages. Acknowledgments The authors wish to thank the other members of their research groups. The research leading to these results has received funding from the European Union’s Horizon 2020 Programme under the AHEAD2020 project (grant agreement n. 871158)

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V. Tichý, M. Barbera, R. Hudec, R. Willingale, Effective collecting area of lobster eye optics and optimal value of effective angle. Exp. Astron. 47(1–2), 161–175 (2019). https://doi.org/10.1007/ s10686-019-09622-2 M. Urban, O. Nentvich, V. Stehlikova, T. Baca, V. Daniel, R. Hudec, VZLUSAT-1: Nanosatellite with miniature lobster eye X-ray telescope and qualification of the radiation shielding composite for space application. Acta Astronaut. 140, 96–104 (2017). https://doi.org/10.1016/j.actaastro. 2017.08.004 M. Urban, O. Nentvich, T. Báˇca, I. Veˇrtát, V. Maršíková, D. Doubravová, V. Dániel, A. Inneman, L. Pína, L. Sieger, R.L. McEntaffer, T.B. Schultz, D.M. Miles, J.H. Tutt, REX: X-ray experiment on the water recovery rocket. Acta Astronaut. 184, 1–10 (2021). https://doi.org/10.1016/j. actaastro.2021.03.019, 2011.10072 L.P. van Speybroeck, R.C. Chase, T.F. Zehnpfennig, Orthogonal mirror telescopes for X-ray astronomy. 10, 945–949 (1971). https://doi.org/10.1364/AO.10.000945 D. Vernani, G. Bianucci, F. Marioni, G. Valsecchi, A. Keereman, Y. Chen, M. Cong, Y. Yang, J. Wang, M. Bradshaw, V. Burwitz, P. Friedrich, J. Eder, Follow-up x-ray telescope (fxt) for the einstein probe mission, in Proceedings of SPIE 11444-175 (2020) M.C. Weisskopf, Design of grazing-incidence X-ray telescopes. 1. 12, 1436–1439 (1973). https:// doi.org/10.1364/AO.12.001436 M. Weisskopf, The chandra x-ray observatory: an overview. Adv. Space Res. 32(10), 2005 (2003) N. White, The Gamow explorer: a gamma-ray burst mission to study the high redshift universe. Proc. Yamada Conf. LXXI 1, 51 (2020) S. Wilkins, A. Stevenson, K. Nugent, H. Chapman, S. Steenstrup, On the concentration, focusing, and collimation of x-rays and neutrons using microchannel plates and configurations of holes. Rev. Sci. Instrum. 60, 1026–1036 (1989) R. Willingale, F.H. Spaan, The design, manufacture and predicted performance of KirkpatrickBaez Silicon stacks for the International X-ray Observatory or similar applications, in Optics for EUV, X-Ray, and Gamma-Ray Astronomy IV, ed. by S.L. O’Dell, G. Pareschi. Society of PhotoOptical Instrumentation Engineers (SPIE) Conference Series, vol. 7437 (2009), p. 74370B. https://doi.org/10.1117/12.826225 R. Willingale, G. Fraser, A. Brunton, A. Martin, Hard x-ray imaging with microchannel plate optics. Exp. Astron. 8, 281–296 (1998) R. Willingale, J. Pearson, A. Martindale, C. Feldman, R. Fairbend, E. Schyns, S. Petit, J. Osborne, P. O’Brien, Aberrations in square pore micro-channel optics used for x-ray lobster eye telescopes, in Proceedings of SPIE, vol. 9905 (2016) H. Wolter, Generalized schwarzschild mirror systems with glancing incidence as optics for x-rays. Annalen de Physik 445, 286 (1952) A. Woodhead, R. Ward, The channel electron multiplier and its use in image intensifiers. Inst. Electron. Radio Eng. 47, 545–553 (1977). https://doi.org/10.1049/ree.1977.0079 W. Yuan, Exploring the transient x-ray sky with einstein probe (2019). https://www.cosmos.esa. int/documents/332006/1402684/WYuan_t.pdf

5

Single-Layer and Multilayer Coatings for Astronomical X-ray Mirrors Kristin K. Madsen, David Broadway, and Desiree Della Monica Ferreira

Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . X-Ray Reflection and Refraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Surface Roughness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Single-Layer Thin Film Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Multilayer Thin Film Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Coating and Instrument Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Single-Layer Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Multilayer Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Depositing Thin Film Coatings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Characterization of Thin Film Coatings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . X-Ray Reflectometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Other Characterization Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Environmental Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Stress in Single and Multilayer Coatings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Stress Measurement Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Contributions of Stress in Single-Layer Films . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Methods of Reducing Film Stress . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Stress in Multilayer Thin Films . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Effect of Surface Energy on Film Stress . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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K. K. Madsen CRESST and X-ray Astrophysics Laboratory, NASA Goddard Space Flight Center, Greenbelt, MD, USA e-mail: [email protected] D. Broadway NASA Marshall Space Flight Center (MSFC), Huntsville, AL, USA e-mail: [email protected] D. D. M. Ferreira () DTU Space – Technical University of Denmark, Kongens Lyngby, Denmark e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2024 C. Bambi, A. Santangelo (eds.), Handbook of X-ray and Gamma-ray Astrophysics, https://doi.org/10.1007/978-981-19-6960-7_4

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Abstract

The bandpass of an X-ray telescope is defined by its reflecting surface, which most commonly is a thin film coating, either as a single-layer, bi-layer, or a multilayer coating. Mirror coatings are made to enhance the telescope performance, and by careful design, they can shape the energy response for very specific applications. In this chapter we review the topic of thin film coating essential for the performance of most astrophysical X-ray missions. We discuss the theory behind X-ray reflection and refraction utilized for thin film coatings and address the design challenges for single-layer, bi-layer, and multilayer coating, as well as the properties of the most typical coating materials. We summarize fabrication methods and discuss the measuring techniques in use for characterizing thin film coatings. Important aspects of stability are presented, and we provide a thorough review on the issue stress, which will play an essential role in next-generation high angular resolution imaging telescope. Keywords

X-ray reflective coatings · X-ray multilayer · X-ray reflectometry · DC magnetron sputtering · X-ray telescope design

Introduction The performance of an X-ray optic can be quantified by just two functions: (1) its point spread function (PSF), which is the size and shape of the focused spot, and (2) the energy-dependent effective area, which is the geometric area of the optic multiplied by the efficiency of the mirror (reflectance and obscuration) at each energy: Aeff (E) = Ageometric × Eff(E). The substrate forming the body of the mirror is primarily responsible for image quality, and typical substrates used for X-ray mirrors are electroformed nickel substrates (Jansen et al. 2001; Gehrels et al. 2004), aluminum and aluminum-cobalt substrates (Serlemitsos et al. 1995, 2007; Takahashi et al. 9905), thermally slumped SiO2 (Harrison et al. 2013; Zhang 2009), and pure Si (Zhang et al. 2010) (see Chap. 2.5), all of which can reflect X-rays, but not very effectively. A mirror coating on top is therefore in most cases required to maximize performance. A coating will contribute to the image quality by adding some additional scatter, but the primary function of a mirror coating is to define the bandpass and effective area. X-ray optics leverage the concept of total external reflection, which is the angle at which a light ray can no longer pass the interface into the second medium. This angle is called the critical angle, θc , and since it has a strong dependency on density, heavy materials such as Au and Ir are favored. For most soft X-ray telescopes that operate below 10 keV, a single layer is often enough to ensure performance over the desired bandpass, but when the majority of the reflection angles become larger than the critical, then a multilayer may be required. In its simplest form, a multilayer is a stack of thinly deposited films of alternating material where one of the films is a

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high-Z material and the other of low-Z material. One such pair forms a bi-layer, and a multilayer of N = 10 is composed of 10 such bi-layer pairs, with a nomenclature of high-Z/low-Z, e.g., W/Si. The stack of bi-layers acts as a periodic crystal lattice, and the Bragg condition will create constructive interference according to λm = 2d sin θi , where d is the lattice spacing, θi the incidence angle, and m the order of reflection. Table 1 summarizes key parameters of the X-ray telescope and coatings used on a selection of past, current, and upcoming X-ray missions. There is a roughly even split between Au and Ir, which generally has to do with the fabrication process of the substrates, and for multilayer telescopes, of which there only have been two, Pt/C and W/Si had been the only combinations in use so far. We will in this chapter first review the basic theory behind X-ray reflection and refraction and then discuss the design considerations behind single- and multilayer coatings. We will review the most common deposition techniques and how to characterize the composition of the mirror coating using a variety of nondestructive and destructive techniques. Finally, we will be discussing the very important subject of stress in mirror coatings.

Theory For a recent overview of the theory behind X-ray reflection and scattering, we refer to Als-Nielsen et al. (2011) and for the classical textbook treatment to Born et al. (1999) and summarize here the important concepts for understanding the performance of X-ray mirror coatings.

X-Ray Reflection and Refraction Light propagating through one medium with refraction index, n1 = 1 − δ + iβ that strikes the plane surface of a second medium with index n2 will undergo a change of direction either as reflection back into the same medium or refraction into the other. This fundamental behavior is governed by Snell’s law n1 cos θ1 = n2 cos θ2 ,

(1)

expressed here as the grazing incidence angle to the surface, θ , which is more appropriate for X-rays. If the first medium is a vacuum then θ2 < θ1 and as the angle of incidence continues to decrease there comes a point when the refracted ray is parallel to the surface (θ2 = 0). The angle of θ1 at which this occurs is called the critical angle, and any angle less than this results in total external reflection of the ray. Because the ray does not enter into the second medium but propagates along the surface as an evanescent wave, the index of refraction does not require the absorption term, β, and with n = 1 − δ, where δ = 2πρr0 /k 2 , the angle is given by (see Als-Nielsen et al. 2011, Eq. (3.3))

Bandpass 0.1–12 keV

0.08–10 keV 0.5–4 keV 0.3–12 keV 0.3–80 keV 2–8 keV 3–80 keV 0.1–2.4 6–30 keV 0.2–12 keV 0.3–10 keV 0.1–12 keV

Mission Athena (Bavdaz et al. 2020)

Chandra (Weisskopf et al. 2002)

Einstein-Probe/FXT (Zhu et al. 2021)

XRISM/XMA (Soong et al. 2011; Iizuka et al. 2018)

Hitomi/HXT (Awaki et al. 2017)

IXPE (Ramsey et al. 2021)

NuSTAR (Harrison et al. 2013)

SRG/eRosita (Predehl et al. 2021)

SRG/ART-XC (Pavlinsky et al. 2018)

Suzaku (Mitsuda et al. 2007; Serlemitsos et al. 2007)

Swift/XRT (Burrows et al. 2005, 2000)

XMM-Newton (Jansen et al. 2001)

Wolter-I 4 shells, F = 10 m, Rmax = 1.2 m Wolter-I 54 shells, F = 1.6 m, Rmax = 17.5 cm Conical approximation Wolter-I 203 shells, F = 5.6 m, Rmax = 22.5 cm Conical approximation Wolter-I 213 shells, F = 12 m, Rmax = 22.5 cm Wolter-I 24 shells, F = 4 m, Rmax = 27.2 cm Conical approximation Wolter-I 133 shells, F = 10.14 m, Rmax = 19 cm Wolter-I 54 shells, F = 1.6 m, Rmax = 36 cm Wolter-I 28 shells, F = 2.7 m, Rmax = 14.5 cm Conical approximation Wolter-I 175 shells, F = 4.75 m, Rmax = 20 cm Wolter-I 12 shells, F = 3.5 m, Rmax = 30 cm Wolter-I 58 shells, F = 7.5 m, Rmax = 70 cm

Telescope type Wolter-Schwartzchild SPO, F = 12 m, Rmax = 1.256 m

Table 1 A selection of past, present, and future X-ray observatories with focusing X-ray optics

Au

Au

Au

Ir

No mirror coating substrate NiCo Shells 1–90: Pt/C Shells 91–133: W/Si Au

Pt/C

Au

Au

(B4C, SiC or C) Cr/Ir

Coating Ir + overcoat

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θc =

 √ 2δ = 4πρr0 /k.

181

(2)

The property of total external reflection is of central importance to the design of X-ray optics and ensures almost unity reflection below θc , which conversely limits the bandpass that can be achieved by a telescope of a particular size and focal length as will be discussed in section “Coating and Instrument Design”. Not all X-ray reflectors, however, operate below the critical angle. An incident wave, E, can be decomposed into a reflected and transmitted component with intensities, E + Er = Et . Together with Snell’s law, they give rise to the Fresnel equations: n ≡ n1 /n2

(3) √

sin θ − n2 − cos2 θ Er = √ E sin θ + n2 − cos2 θ Er 2 sin θ t≡ = , √ E sin θ − n2 − cos2 θ

r≡

(4) (5)

with the corresponding intensity reflectance, R = r 2 , and transmittance, T = t 2 . If the second medium is infinitely thick, the transmitted wave is absorbed, and only the reflected component may be detected. If instead the medium has a finite thickness of ∆ and rests on top of an infinite substrate, then the transmitted wave may again reflect and transmit at the interface to the substrate, and the back-reflected component may also again reflect and transmit at the original interface at the surface. This can proceed in an infinite number of ways, and the superposition of all possible combinations forms a geometric series, which has a finite value at infinity. If medium 0 is vacuum, medium 1 the reflective slab, and medium 2 the infinite substrate, the series becomes (as shown in Als-Nielsen et al. 2011, Eq. (3.23)) rslab =

r01 + r12 eiq∆ , 1 − r10 r12 eiq∆

(6)

where q = 2k sin θ is the vertical component of the momentum transfer vector, q = k − k′ . The expression of reflectivity from a homogeneous slab can be extended to describe a multilayer stack. This was done by Parratt (1954), and in this picture the multilayer is considered to be composed of N layers sitting on top of an infinitely thick substrate. The N’th layer is directly on the substrate, and any layer n ≤ N in the stack has a of thickness ∆n . Progressing from the bottom, the N’th layer on top of the substrate is not subject to multiple scattering from lower levels, and therefore the reflectivity from this surface can be calculated using the Fresnel reflectivity, ′ rN,∞ , from Eq. (3). The next layer, N−1, must include both multiple reflection and refraction, and using the expression in Eq. (6) for reflection from a homogeneous

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slab, where r ′ is the Fresnel reflectivity, the recursive formula becomes

rn−1,n =

′ rn−1,n + rn,n+1 eiqn ∆n

′ 1 + rn−1,n rn,n+1 eiqn ∆n

.

(7)

The reflection is in this way calculated from the bottom up until the total reflective amplitude at the interface between vacuum and the top layer, r0,1 is found.

Surface Roughness For a perfectly sharp interface, Snell’s law (Eq. (1)) dictates that the exit angle must be equal to the incident angle, and the reflection from this condition is called specular. In the preceding sections, it was assumed that the interfaces were perfectly flat and sharp, which will always result in specular reflection, but real surfaces have imperfections and will also scatter outside the specular direction. The imperfections are generally referred to as roughness and can coarsely be grouped by length scale: • Micro roughness [nm, µm]: molecular and crystal imperfections and impurities and bond stresses • Intermediate roughness [µm, mm]: crystal imperfections, bulk impurities, surface abrasion, and stress deformations. • Figure error: [mm0

(10)

Most surfaces are a combination of both. The resulting loss in specular reflectance can be approximated by multiplying the Fresnel reflection coefficients with w(s), ˜ s = 4π cos(θ )/λ, which is the Fourier transform of w(z). The modified Fresnel coefficients then take the form r ′ = r w(s), ˜ and the net reflectivity can as before be calculated using Parratt’s recursive formula. Surface roughness can also be described by its lateral correlation length, ξ , that sets a roughness cutoff above which the rms roughness, σ , is independent of the probe size. For the specular reflection, there are two expressions in general use to describe the reflectivity from a surface with rms roughness, σ , valid for different regimes of the correlation length and scattering angle. For large ξ , describing a surface with low spatial frequency, specular reflection from a diffuse interface can be 2 2 cast as r ′ = re−2k0 σ , where k0 is the perpendicular wave component of the incident wave. This form is the static Debye-Waller (DW) factor, derived from the Born approximation (de Boer 1994, 1996), which requires the interaction and scattering to be weak (θ ≫ θc ). For small ξ , describing high spatial surface frequencies for which the angles and roughness are small, we find the Nevot and Corce (NC) solution 2 (Nevot et al. 1980), r ′ = re2k0 k1 σ , with incidence perpendicular wave component, k0 , and perpendicular refracted component, k1 , valid when k0 σ ≪ 1 and k ≪ kc = |k|2 (1 − n). For typical X-ray optics that operate close to the critical angle and have high-frequency low surface roughness, this is the form used to calculate the specular reflectivity. For non-specular scattering, which are rays exiting from a rough surface at angles either smaller or larger than the incidence, the Born approximation is applicable away from the critical angle where the scattering is considered weak and multiple refractions of the photon can be neglected. The non-specular scattering removes energy out of the specular field, but no energy is coupled from the non-specular field back into the specular, which is an incorrect simplification when the interactions are strong. Near the critical angle, total external and internal reflection becomes possible, and the interaction between matter and incident wave can no longer be considered weak. The distorted-wave Born approximation (DWBA) (Sinha et al. 1988; de Boer 1996) takes into account the multiple reflections between the

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interfaces, and it treats the stack of thin films as the ideal state and regards the deviation of the refractive index to that of a smooth surface as the perturbation. Modeling of non-specular reflectivity is done for the characterization of coatings on individual mirrors. They are complicated calculations that require specialized fitting packages and are not practical for deriving the PSF of an actual X-ray optic. The resulting PSF from an assembled optic is due to the non-specular scattering of its individual components, but as it is a superposition of many scattering elements, which can have different surface roughness properties, it is not feasible to attempt to described the PSF by the fitting of hundreds of non-specular scattering components. In practice, therefore, the PSF of an optic is usually described empirically with geometrical perturbation terms applied to a raytrace that is then used to reproduce the observed PSF. The core of the PSF, though, is usually related to micro surface roughness and the wings from figure error often due to deformations and stress introduced by the manufacture and mounting of the mirror.

Materials The X-ray performance of single- and multilayer coatings is determined by the optical properties of the materials and the quality of the interfaces. For the materials discussed here, there are differences in their surface roughness, but for most cases that is a secondary effect, and we will discuss only the material selection from optical properties themselves.

Single-Layer Thin Film Materials Single-layer coatings have optimal performance for materials for which the critical angle is large, and as shown in Table 1, the preferred choice has been Au or Ir, with the IXPE mission being the only listed exception to utilize the NiCo surface of their substrate instead of a mirror coating. Other possibilities are W and Pt, and to illustrate how the materials relate to one another, we show the attenuation of Au, Co, Ir, Ni, W, and Pt with their M-, L-, and K-edges in Fig. 1 (left). Au, Ir, and Pt are all very similar, and due to the cost of Pt, Au and Ir are preferred. The edges of W are shifted toward lower energies, and this impacts the low-energy throughput of soft X-ray instruments which disfavors W. The M- and L-edges of Au and Ir also appear in the soft X-ray bandpass, and it might, therefore, appear as if Co or Ni would be better choices. However, the critical angle of Ni (and Co) is significantly lower as shown in the right panel, where for scale the horizontal lines correspond to the grazing incidence angles for a telescope with focal length, F , and maximum radius, Rmax . For example, a telescope with a focal length of 10 m and maximum radius of Rmax = 40 cm will, if all the mirrors are coated with Ir or Au, operate at total external reflection up to 10 keV. Because effective area is the most easily controlled parameter to maximize

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Fig. 1 Left: Attenuation with coherent scattering. (Data source: NIST XCOM database (Berger 2010)). Right top: Critical angle. Horizontal lines donate the incidence angel of the shell located at R with focal length F. Right bottom: Delta of the critical angle curves of Ir, Pt, and W with respect to Au

sensitivity, the critical angle of the material is more important than the edges, and unless the mission has a soft bandpass for which the Ni and Co critical angles can deliver the required area, or a science goal compromised by the edges, Au and Ir are the best choices for single-layer thin films.

Multilayer Thin Film Materials Optimal performance for multilayers is achieved with materials that have: (1) large differences in their complex indices of refraction; (2) low absorption in the lowZ material, for which the incident radiation can penetrate into the layers of the stack and reflect from as many interfaces as possible; (3) form smooth, sharp, and chemically inert interfaces to minimize non-specular scattering. Requirement (3) is largely the driver as the stable mating of two materials is the first priority, and the typical multilayer families considered for hard X-ray astrophysical applications are Co-, Ni-, W-, and Pt-based coatings. Which combination suits best is a trade between the above requirements. For example, because Pt has the highest K-edge (78.3 keV) and largest bandpass, Pt/C was favored by NuSTAR and Hitomi. However, the Wbased family has both better interfacial roughness and can be deposited more thinly. For this reason, NuSTAR included both Pt/C and W/Si in its design, applying Pt/C only on mirrors that contributed to area between 70 and 80 keV. To overcome the K-edges of Pt and W, future hard X-ray missions may turn to Ni- and Co- solutions for probing energies beyond 80 kev (Madsen et al. 2018).

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Coating and Instrument Design The choice of a mirror coating is a process that involves many parameters, most of which are related to the fabrication process, such as deposition technique, film stress, uniformity, and surface roughness, but if these environmental parameters are removed, the suitable mirror coating for the application and its performance can be inferred from theory. That is the starting place of all design work, and we outline this process below, deferring the discussion of the fabrication itself to sections “Depositing Thin Film Coatings”, “Characterization of Thin Film Coatings”, “Environmental Stability”, and “Stress in Single and Multilayer Coatings”.

Single-Layer Design As discussed in sections “X-Ray Reflection and Refraction” and “Materials”, the phenomena of total external is of central importance to X-ray mirror design. Below the critical angle, the refracted (transmitted) part of the wave propagates along the surface as an evanescent wave. This wave has some curious properties, and although it creates an electromagnetic field into the second medium, there is no net energy crossing the boundary into the medium, i.e., no ray traverses this medium (Born et al. 1999). The 1/e penetration depth of the wave is 1/qc , where qc = 2k sin θc , and the single layer must therefore have a minimum thickness to effectively take advantage of the total external reflection; otherwise the field may interact with the material or substrate below. A thickness of 10 nm is sufficient for materials such as Ir and Au. Figure 2 shows the critical angle, θc , as a function of energy for Ir, Au, Pt, and W for observatories Chandra, NuSTAR, Swift, XMM-Newton, and Athena. The colored bands are the minimum and maximum graze angle of the observatory, and all energies below the critical angle and energy curve will be externally reflected. For example, Chandra has four large radius shells, and the outermost shell only efficiently reflects energies below 3 keV. That shell, however, contributes most of the area, which mitigates the loss from exceeding the critical angle. In contrast, XMM-Newton has a longer focal length, smaller radii optics, and the outermost shell efficiently reflects all energies below ∼7.5 keV. NuSTAR is not a single-layer observatory, but the top layer of the multilayer coatings was made thick enough to ensure total external reflection up to 15 keV from all shells (Madsen et al. 2009). Despite of the condition of total external reflection, absorption at the interface still occurs below θc . Figure 3 shows the reflectance, R; absorbance, A; and transmittance, T, of a 10 -nm-thick Ir coating at θinc = 15 mrad. For a fixed incidence angle, there is a corresponding critical energy, and the dashed lines in the top left plot of Fig. 2 marks that energy (∼5.8 keV) for Ir at 15 mrad. The Ir Mα complex is a very strong feature, and it causes a drop in R by ∼20% where it remains constant up to the critical energy at ∼5.8 keV when the reflectance decreases down to 0.1. As the critical energy is passed, T increases and adds to A in reducing the intensity of R. As a mitigation against the heavy absorption from Ir, a coating of a less dense

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Fig. 2 Critical angle curves as a function of energy for selected missions. The colored bands mark the minimum and maximum graze angles of each instrument, and all angles below the critical angle curve will see total external reflection

Fig. 3 Reflectance, Transmittance, and Absorptance for a 10 nm Ir single-layer. The curves are at a fixed grazing incidence angle of 15 mrad, which is marked as dashed crosshairs in the upper left plot of Figure 2. The first sharp drop at ∼1.9 keV is Mα1 , and the second less sharp drop at ∼5.8 keV from the critical angle. Also shown is the Reflectance of the same 10 nm Ir with a 8 nm overcoat of SiC

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2.5 baseline Ir/B4C + Pt/B4C + Ir/SiC + W/Si + Ir only +

2.0

2.5 2.0 Aeff

Aeff (m2)

1.5 1.5

1.0 1.0 0.5 0.0

0.5

2

4 Energy (keV)

6

8

2

4 6 Energy (keV)

8

10

Fig. 4 Examples effective area models for different examples of coating design considerations for the Athena mission considering uncoated substrates, a single Ir layer coating and the increased performance at low energies by introduction of a soft material top coating layer (left). The introduction of a multilayer coating underneath the single-/bi-layer can enhance the performance at higher energies. In this example the improvement is around 6 keV (Ferreira et al. 2017)

material can be placed on top of Ir. In this example 8 nm of SiC can significantly boost R below the M-edges up until the SiC critical energy at ∼3 keV (see Fig. 1). Above θc,SiC , the ray is transmitted through the SiC layer to the Ir below, and the absorption of SiC further reduces R. This kind of balancing and trade must often be made when optimizing the instrument bandpass of a mirror coating, and ultimately the decisions must be driven by the mission requirements. In the case of the Athena mission, the science goals have a strict requirement for the effective area below 2 keV and at 6 keV. Several materials were investigated, and Fig. 4 shows the design considerations and illustrates the increase in performance at low energies by adding a soft material top coating layer (left). Improvements of the performance at 6 keV cannot be gained by changing material or top layer alone but achieved by introducing a multilayer coating underneath the single layer of heavy material as shown in the left panel (Ferreira et al. 2017). The X-ray photons impinging on the mirror will primarily be reflected by the Ir and only encounter the multilayer for a subset of mirrors above 4 keV, where the constructive interference generated by the multilayer will enhance reflectivity as discussed in the next section.

Multilayer Design A single-layer coating will be effective up its critical angle, beyond which the reflectivity will drop off rapidly as shown in Fig. 3. By utilizing constructive interference from diffraction, such as can be found in crystals, a multilayer coating can boost the reflectivity beyond the critical angle by considerable amounts through careful construction of the individual bi-layer pairs in the stack. The multilayer stack is turned into a crystal-like structure periodic lattice through the deposition of thin layers of different materials consecutively on top of each other. Due to the Bragg

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condition, which is a special case of the general Laue equations, and occurs when the wavelength is comparable to the thickness of the layer, reflection is enhanced for wavelength, λ, graze angles, θ , and the thickness of the bi-layer, d when: nλ = 2d sin θ,

(11)

where n is the diffraction order. A multilayer stack will have its first order (n = 1) Bragg peak at an energy of E=

hc sin θ, 2d

(12)

for a specific θ and subsequent peaks at higher energies, nE. An example of a Pt/C multilayer with N = 10 bi-layers, each of thickness d = 10 nm, is shown in Fig. 5. The shape of the curve comes directly from Eq. (7), and the oscillations between the peaks are called Kiessig (1931), numbering N−2 between two Bragg peaks. The second principle that makes multilayers so effective goes back to the Fresnel equations for which the intensity of the reflection is maximized at interfaces with a large contrast in the refractive index, or, equivalently, the density. Multilayers, therefore, consist of a dense absorber material paired with a light spacer material. The relative thickness of the bi-layer pair is typically optimal at around 40% absorber and 60% spacer, defined as Γ = dabsorb /dtot ∼ 0.4. A stack of constant thickness bi-layers will result in a spectrum with a good response at a narrow set of energies located at the Bragg peaks as shown in Fig. 5 but otherwise have a poor response in between the peaks. By varying the thickness of the bi-layers through the stack, the Bragg peaks can be shifted through the spectrum and a broadband energy response achieved. This can be done in a number of ways, but we will discuss here only those relevant for X-ray astrophysical application.

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Fig. 5 Left: Cartoon of the power-law graded multilayer stack. The top layers, which are the thickest, reflect the lowest energies and the bottom the highest. Right: multilayer performance at a fixed incidence angle of 2.5 mrad for (1) a single-layer (red), (2) a N = 10 bi-layer constant thickness stack (blue), and (3) a power-law depth-graded multilayer stack (green)

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One such depth-graded profile, commonly used for neutron mirrors and used by NuSTAR (Madsen et al. 2009), is the power-law graded stack (Joensen et al. 1995). The bi-layer thickness of the power-law stack is defined by di =

a (b + i)c

i = 1, N

(13)

where N is the number of bi-layers in the stack and a and b constants that are related to the minimum and maximum thickness of the bi-layer. The power-law index, c, controls the relative shifts of the Bragg peaks, and a low c drives them apart, while a high c pushes them together. In the depth-graded structure, the thinnest layers, which reflect the hardest energies, are at the bottom where the photons have the greatest penetration depth, and the thickest layers at the top as shown in the diagram in the cartoon of Fig. 5. For a fixed set of parameters, increasing N will increase reflectivity due to a more continuous distribution of Bragg peaks, up to a point where the absorption becomes dominant and outweighs the benefit of adding layers. Only two X-ray astrophysical missions have flown multilayers, NuSTAR and Hitomi, both optimized for the same bandpass with similar prescriptions. NuSTAR used the depth-graded power-law, and a multilayer prescription is shown in Fig. 5, which demonstrates the advantage over a single-layer and periodic bi-layer with constant spacing for energies beyond the critical angle. Hitomi used a block method (Tamura et al. 2018), and in this structure, rather than continuously changing the thickness of the bi-layers down through the stack, it contains blocks of bi-layers with periodic constant spacing. The principle is the same as for the power-law depth-graded profile, and by changing the bi-layer thickness for each block, the Bragg peaks are shifted through the spectrum as illustrated in Fig. 6. The power-law and block method yield similar responses and using one over the other a matter of preference and fabrication method. 1 First Block Second Block

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Fig. 6 Left: Reflectivity of block (solid line) and individual blocks (dashed lines) at an incidence angle of 0.208◦ . Right: The coating consists of blocks, which have a constant periodic spacing multilayer. The Bragg energy of each block is different, and the reflectivity profile is determined by superposition of each block. (Reprinted from Tamura et al. 2018)

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Fig. 7 A-periodic multilayer of W/SiC with 200 bi-layers. The coating was optimized against the desired response using IMD and measured with a hard X-ray reflectometer at Reflective X-ray Optics LLC (RXO)

A more radical design intended for use in narrow-band applications (Morawe et al. 2002; Aquila et al. 2006) is the a-periodic structure, in which every bi-layer is tuned individually to achieve a desired target response. Figure 7 shows the energy performance of one such a-periodic W/SiC multilayer at an incidence angle of 0.11◦ against its target response. Multilayers are versatile and can be designed for both narrow and broadband applications. Given a stack of N layers with varying thicknesses, the response as a function of energy can be shaped in a number of ways as described above. All designs, however, have to obey the Bragg condition between energy, bi-layer thickness, and angle, and the starting point is to define the necessary bi-layer thickness needed to obtain the desired bandpass. Once a choice of focal length, F , and radius of the optic, R, is made, the graze angles naturally fall out and the minimum and maximum required thickness computed from: dmin =

hc 2Emax sin θmax

(14)

dmax =

hc . 2Emin sin θmin

(15)

This is usually an iterative process where F and R are changed until a feasible set of dmin and dmax are found. As will be discussed in subsequent sections, there is a practical limit to how thinly a coating of a specific material can be deposited without degrading, and, conversely, how thick it can become before stress sets in. The maximum bi-layer thickness is usually not a constraint and should be set such that there is a smooth transition between the multilayer and the energy

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of the critical angle. This forms the set of baseline parameters from which the multilayer prescriptions are then optimized for performance. There are a number of ways they can be optimized, and the general method is to device a figure of merit (FOM) and walk the design parameters through the possible phase space as done in Madsen et al. (2009) and Tamura et al. (2018) using any phase-space optimization routine appropriate for the number of parameters over which the search is to be conducted. To first order, a FOM can be based on the on-axis effective area, but most instruments also include a weighted off-axis angular response, such as wide-field survey instrument types, and there can be several secondary parameters that enter into the FOM based on the specific application of the instrument as well, such as focal length and the PSF with respect to the detector dimensions (Henriksen et al. 2021). The theoretical optimization process has of course to be taken together with the material and fabrication restrictions, which will be the subject of the subsequent sections.

Depositing Thin Film Coatings There are many techniques in use for the fabrication of thin film coatings, and for a thorough review, we refer to Martin (2010). These techniques are often based on physical or chemical processes, where there is physical ejection of material onto a substrate or the chemical species are reduced or decomposed on the substrate surface. The techniques that have been used for mirror production include grindand-polish technique with DC sputtered Ir (Chandra (Bessey et al. 2011)), the nickel electroforming technique coated with Au via evaporation vacuum (XMMNewton (Chambure et al. 1997)), and thermal glass forming technique coated with Pt/C and W/Si multilayers via DC magnetron sputtering (NuSTAR (Christensen et al. 2011)). The choice of the most appropriate technique will depend on the criteria imposed by the specific mission design, e.g., material selection, mirror substrate, and cost. Direct current (DC) magnetron sputtering is a versatile technique which has been used for Chandra, NuSTAR and Hitomi/HXT and is considered both for the Lynx X-ray observatory, under study by NASA, and for the Athena X-ray observatory, the ESA L-class selected mission. It is a physical, vacuum technique, allowing for deposition of both single element materials and compounds. Figure 8 illustrates the principle of the DC magnetron sputtering technique. High voltage is applied between the cathode and anode attracting positive the ions of an inert gas, e.g., Ar, the desired coating material target, is then bombarded with the energetic gas ions leading the target atoms to be ejected and deposited as a thin film coating on the substrate. The thickness of the film is controlled by moving the substrate past the anode, and by having two or more anode targets of different materials inside the chamber, a multilayer can be deposited with adjustable thickness by controlling the speed of the rotation.

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Fig. 8 Magnetron sputtering diagram. (I) high vacuum minimizes contaminants, (II) ions are attracted to the target, (III) target atoms are bombarded, (IV) sputtered atoms travel toward the substrate, (V) sputtered atoms are deposited to substrate surface forming a thin film (Massahi et al. 2021)

DC magnetron sputtering chambers come in a variety of configurations. They are configured to ease the task of achieving good optical performance of the coatings which rely to various degrees on the coating’s uniformity. One technique for encouraging inherent azimuthal coating uniformity is to spin the substrate about a central axis of symmetry. The substrate spinning mechanism is shown for a flat substrate in Fig. 9a for one of the vacuum deposition systems at MSFC (Broadway et al. 2001; Gurgew et al. 2020). To control the thickness gradient along the radial direction, a contoured mask is added. The mask effectively alters the exposure time for points along the substrate’s radial direction according to the arclength of the mask at a given radius. This technique can be used to achieve a desired lateral thickness gradient on the substrate or to obtain uniform coatings. In this configuration, the circular sputtering cathodes Fig. 9b are pointed upward and rotate past the spinning substrate in an oscillatory fashion at a constant angular velocity. The angular velocity dictates the coating thickness of each material. The film thickness distribution can alternatively be controlled without a mask, in which case the cathodes must rotate at a prescribed angular velocity that changes during their passage past the substrate: a technique referred to as velocity profiling. The smaller diameter cathodes are beneficial for reducing the associated target material cost

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when investigating new material combinations for X-ray optics, particularly when precious metals such as Ir, Au, and Pt are used. The deposition system at MSFC can also be configured to house linear cathodes, which are preferred for coating substrates without an axis of azimuthal symmetry, such as segmented substrates, for example. The linear cathode array, shown in Fig. 9c, also illustrates the mask used for controlling film thickness uniformity. The mask functions to alter the spatial distribution of sputtered flux according to its contoured shape by intercepting sputtered material from the target prior to reaching the substrate. An example of a high production yield DC chamber is shown in Fig. 10. This chamber is located at DTU Space (Jensen et al. 2006) and was used to coat over

Fig. 9 Illustration of the magnetron sputtering chamber at MSFC. See detailed description in section “Depositing Thin Film Coatings” and Broadway et al. (2001) and Gurgew et al. (2020)

Fig. 10 The DC magnetron sputtering coating facility at DTU Space. The coating system was built for the coating development and manufacturing of the depth-graded multilayer coatings used on the NuSTAR telescope mirrors (Christensen et al. 2011)

Fig. 11 Overview of deposition parameters that can be optimized and their effects on the coating characteristics (Massahi et al. 2021)

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8000 segmented mirrors with multilayers for the NuSTAR mission (Christensen et al. 2011). Due its ability to coat a large number of substrates (24 per run for NuSTAR), it is considered as prototype for the present Athena coating system. The cathodes for this chamber are 50 -cm-long and fixed vertically in the center pointing outward, while the substrates are mounted on plates on the entire circumference of the chamber wall and spin around the cathodes. The mechanism of growth of the deposited coating is always dependent on the target material, but properties of the thin film coatings fabricated using DC magnetron sputtering will also depend on the coating conditions. Figure 11 shows an overview of parameters that can be optimized to create specific coating conditions. For example, the working gas pressure and substrate temperature directly affect the growth and microstructure of the coating. It is therefore imperative to control the coating conditions to improve film morphology, composition, uniformity, roughness, and stress, for the increased performance and stability of X-ray mirrors (Massahi et al. 2021).

Characterization of Thin Film Coatings X-Ray Reflectometry The most common way to measure the performance of a thin film coating is with X-ray reflectometry (XRR), which directly probes and verifies the coatings response to X-rays. It also serves as a nondestructive and efficient method to determine the characteristic properties of the coating design (thickness of single and multilayers), surface interface roughness, and material properties such as density and composition as was illustrated in Fig. 5. An example of a reflectometer XRR experimental setup, in use at DTU Space, (Technical University of Denmark) is shown in Fig. 12. The layout is common to most reflectometers, where the X-ray photons are first collimated using slits, filtered in energy, and shaped (paralleling the beam) before reflecting off the coated surface of the specimen being tested. The intensity of the reflected beam as a function of energy or angle is a direct product of the film properties, and desired parameters can be derived by employing a curve minimization model-fitting technique of the measured reflectivity, as predicted by Eq. (7) for the assumed thin film design (section “Coating and Instrument Design”) with the appropriately modified Fresnell functions. Typically, the reflected beam is either measured for a fixed energy as a function of grazing incident angle or for a fixed angle as function of energy. Most XRR setups operate at a single energy since the energy scan capability requires powerful continuum sources, generally only available at synchrotron facilities. Figure 13 (left) shows an example of a XRR angle scan at 8 keV for a single-layer thin film coating, and the distance between and width of the Bragg peaks determines the layer

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Fig. 12 The XRR experimental setup at DTU Space. (1) X-ray generator, (2) slit, (3), evacuated tube, (4) Slit, (5) asymmetric cut Ge crystals, (6) attenuation filters, (7) beam shaping slits, (8) sample holder, (9) evacuated tube, (10) position-sensitive detector (Jafari et al. 2020)

thickness and the decrease in intensity as a function of the angle the roughness. The location of the critical angle, which is responsible for the first sharp decrease in intensity, can be used as a measure for the material density and composition. Figure 13 (right) shows an example of an energy scan at a fixed incidence angle for a W/Si NuSTAR flight coating taken at the RaMCaF NuSTAR calibration facility. Here the frequency and amplitude of the undulations that occur right after the critical angle of W (∼25 keV), taken together with the intensity drop at the W K-edge, determine the bi-layer thickness, relative fraction of W of that bi-layer thickness, and density. As discussed in section “Surface Roughness,” the signature of surface roughness is to remove and redistribute the intensity into angles outside of the specular, and the larger the angle and energy, the greater the effect of roughness on the curve. A large dynamic range is therefore desirable to get an accurate estimate of the roughness. XRR setups operating at softpt energies, such as Al-K (1.487 keV), are designed to characterize the soft materials of a thin C, SiC, or B4 C cap layer, which can be used to boost the telescope performance at lower energies (as illustrated in Fig. 3). XRR setups operating at the more typical 8.048 keV from a Cu K alpha source will be insensitive to the top layer and more suitable for the characterization of a complex multilayer structure. Software used for modeling XRR data have been developed by several research teams and are often available as open source (e.g., IMD for IDL, Windt 1998). The modeling of XRR data is often not a simple process, and the complexity of the material and layer structure will reflect in the complexity of the best-fit model. The X-ray beam will always have a footprint on the sample being measured and effects of nonuniformity and surface contamination will introduce features to the measured reflectance.

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Fig. 13 Top: Example of angle scan at 8.048 keV measured at the DTU Space of a 10 nm Ir single-layer coating on an SPO (Svendsen et al. 2020). Bottom: energy scan at fixed angle for a W/Si NuSTAR mirror measure at at the Columbia University RaMCaF facility (Brejnholt et al. 2011)

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Other Characterization Techniques Even though X-ray reflectometry is an extremely useful tool for characterization of X-ray thin film coatings, several other techniques can also be applied to evaluate the true composition of the coatings after the deposition process and access the level of contamination and the possible effect of contamination on coating quality, performance, and stability. Atomic force microscopy (AFM) enables the mapping of the sample surface and will provide information on roughness and contamination of the mirror surface. A nondestructive force is applied by a sharp tip scanning the investigated area resulting in a topographic map of the sample top surface. Figure 14 exemplifies the AFM map of uncoated Si substrates at different processing levels, clearly showing the difference between a smooth and clean surface and a surface with particle contamination. With AFM it is possible to derive the topological roughness which causes non-specular scattering and affects the coating reflectivity. The surface roughness derived from AFM is not directly comparable to the roughness derived by modeling the XRR data as the AFM is only assessing the very top surface, while the XRR derived roughness will also include the effects of interface roughness, accounting for reduction of the reflectivity of X-rays at the interfaces. The composition and morphology of the films can be investigated using a variety of techniques. Among the most popular are X-ray photoelectron spectroscopy (XPS) and transmission electron microscopy (TEM). XPS is based on the photoelectric effect, and by measuring the electron binding energy of the elements in the coating, it enables the investigation of the composition of the coating material, the state of its chemical bonds, and the relative element

Fig. 14 Atomic force microscopy measurements showing a surface with particulate contamination (left) and a smoother surface (right) of uncoated Si substrates at different processing levels of the photo-resist deposition characteristic of SPO technology (see Chap. 2.5) (Massahi et al. 2015)

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Fig. 15 Example of XPS results. (a) Concentration quantification of selective elements for sample A (Ir/B4 C multilayer) using XPS depth profiling. (b) Schematic of the Ir/B4 C multilayer analyzed and the main bonds detected in each individual layer (Jafari et al. 2020)

concentration (Moulder and Chastain 1992; Greczynski and Hultman 2020). XPS is a destructive characterization technique where the measurements reveal the coating composition at several depths of the coating layer controlled by the etching time as shown in Figs. 15 and 16. TEM technique uses a beam of electrons to obtain images at nano- or atomic scales. The sample preparation for TEM measurements is a destructive process where a sufficiently thin slice of the coating and substrate are extracted from the coated sample and measured via a beam of electrons that pass through the sample forming an image (Martin 2010). In the TEM images presented in Fig. 17, it is possible to visualize the morphology of the coatings and the designed multilayer profiles. STEM is a type of TEM where the beam of electrons raster scan the sample allowing for simultaneous composition assessment via energy dispersive Xray spectroscopy (EDS) or electron energy loss spectroscopy (EELS). Figure 16 shows examples of both XPS and EDS measurements. These techniques combined with XRR provide the means for an in-depth understanding of the chemical composition of the coatings, possible contaminants present in the coatings and the effects they might have on the coating performance when combined with the required process for manufacturing of X-ray mirrors. The true composition of mirror coating is specific of each coating facility; therefore it is necessary that a careful composition analysis of the deposited coatings is performed for both quality assurance and telescope calibration.

Environmental Stability Naturally, it is imperative for the success of any mission that the thin mirror coatings are stable over time and robust to the environment of space and its radiation. But they should also be able to withstand short-term extreme conditions that may occur during fabrication and the forces induced during launch. Of particular interest

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Fig. 16 The composition investigated using X-ray photoelectron spectroscopy (XPS) and scanning transmission electron microscopy (STEM) comparison of (left) XPS survey spectra and (right) TEM-EDS results for Ir and B4 C layers (Jafari et al. 2020)

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Fig. 17 Example of a TEM image of periodic Ir/B4 C multilayer (left) and depth-graded multilayer (right) (Jafari et al. 2020)

are the chemical stability, thermal stability, and stress stability of the thin film coatings. The combined studies of the characterizations techniques discussed in section “Characterization of Thin Film Coatings” are used to investigate the short and long-term evolution of coating performance. An example of chemical change of the B4 C overcoat is shown in Fig. 18 (left) where we observe drastic change is the reflectance performance of the X-ray mirror over a year under normal storage condition (Ferreira et al. 2018). The evolution of the coating properties observed through the change in the reflectance curve can be attributed to a density change of the overcoat material and/or oxidation. An example of a Ir/SiC bi-layer coating presenting consistent performance over time is also shown (right). Some of the processes involved in the manufacturing of modern X-ray optics for large telescopes imposes strong challenges to coating stability (Bavdaz et al. 2020). Exposure of coated mirrors to chemicals and high temperatures can affect the coating performance and stability (Ferreira et al. 2018; Svendsen et al. 2021, 2020; Henriksen et al. 2021). The compatibility of post-coating treatments applied to the X-ray mirrors have to take into account the protection of the reflecting coating. Investigation of the effect of chemical exposure and annealing, part of the manufacturing processes using Silicon Pore Optics (SPO) technology (see Chap. 2.5), show that Ir singlelayer coatings are robust and do not have their performance affected. Figure 19 shows the coating reflectance before and after exposures (Svendsen et al. 2021). The effect on a Ir/B4 C bi-layer shows degradation of the B4 C layer from annealing under atmospheric conditions but not when annealed in low vacuum (Henriksen et al. 2021). Monitoring of the short- and long-term stability of X-ray mirror coatings requires periodic, systematic, and nondestructive assessment of the coating performance, making XRR as an excellent technique for this purpose (Ferreira et al. 2018; Henriksen et al. 2021) (Fig. 20).

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Fig. 18 Example of time evolution of Cr/Ir/B4 C trilayer (Ferreira et al. 2018) and time stability of Ir/SiC bilayer (Svendsen et al. 2019)

Stress in Single and Multilayer Coatings The control of film stress is a leading technological challenge in the development of the next generation of high resolution, large collecting area, lightweight Xray spaceborne telescopes. The X-ray telescope’s grazing incidence, focusing mirror assembly, consists of a large number of concentrically nested, thin shells, whose thickness is on the order of a few hundred microns. This is done to maximize the telescope’s collecting area within prescribed weight and volume launch constraints. The thin film coatings, which are commonly deposited by the process of magnetron sputtering, are applied to enhance the X-ray reflective

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Fig. 19 Ir single-layer coated mirror appears to be robust to the effect of annealing. No reflectance degradation is observed on XRR (Svendsen et al. 2021)

spectral response of the mirrors prior to assembly and alignment. Despite the film’s nanometer-scale thickness, the in-plane forces caused by the residual stress in these coatings can distort the mirror’s precise figure and severely degrade imaging resolution. Therefore, the stress, σ , in the thin film coatings applied to enhance X-ray reflectivity must be reduced to near-zero values in order to preserve the substrate’s precise figure, particularly for the next generation of X-ray telescopes where sub arcsecond resolution imaging is sought. Single-layer thin films, such as Ir, are often used as a reflective coating for grazing incidence, total reflection, X-ray optics due to the large critical angle (L. Note that by construction, the limiting blocking angles for obstructed rays are Φ=

∗ R0 − RM + α0 , ∗ L1

(1)

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R0 − R0∗ , L1

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Σ=

∗ R0 − Rm − 3α0 . ∗ L2

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For focal length f >L1,2 , and L1 = L2 , Φ ≈ Ψ ≈ Σ. Further note that incidence angles vary with azimuthal position φ for sources at off-axis angular position θ : α1 (φ) = α0 − θ cos φ

α2 (φ) = α0 + θ cos φ

(4)

The limiting blocking angle Φ imposes a constraint on the FoV (θFoV ) since for θ > θFoV the geometric area of the shells exposed to the source decreases rapidly due to the rays being blocked. The expression for the available geometric area (Spiga 2011) is    A(θ ) 2θ Φ − α0 =1− 1+S A(θ = 0) π α0 θ

(5)

for off-axis angles Φ − α0 √ < θ < Φ/2 and α0 < Φ < 2α0 , and where 1 S(x) = x cos−1 (w) dw = 1 − x 2 − x cos−1 (x). Notice that A(θ ) decreases monotonically with θ , illustrating a direct relation between the FoV and the shell spacing. A useful measure of the extent of the FoV can be set by considering that off-axis angle where A(θ = θFoV ) drops to, say, A(θ = 0)/2. Note that the actual effective area will be smaller, due to increased vignetting due to both figure and scattering, and energy dependence of reflectivity. From Eq. (5), this sets a constraint on Φ, which in turn fixes the spacing between the shells for any given combination of shell radius and length. This defines a theoretical lower limit to the shell separations; considerations of shell thicknesses and engineering limitations in manufacturing, assembly, alignment, and mechanical support often result in the final designs having larger shell spacings. Nested shell configurations have several benefits. They allow compact designs that can be fit inside a small volume and yet have high effective areas. Critically, these designs are highly customizable and can be adapted to suit a variety of science cases (see section “Mission Concepts Using Miniature X-Ray Optics”). Variations in the coating allow for different energy bands to be better represented: e.g., Fig. 4 compares the effective areas achieved by an iridium (Ir) and an iridium-carbon (IrC) coating for the same shell configuration; the IrC coating, which is a layer of iridium with a carbon overcoating, used to mitigate photoabsorption in the metal layer, smooths out the sharpness of the Ir edge, but at the cost of reduced lowenergy effective area. Furthermore, despite the volume and mass constraints that MiXO designs operate under, adjustments to shell numbers, sizes, and positions allow versatile designs that may be tuned to specific science cases. For instance, missions such as SEEJ are targeted toward observing isolated point sources, so the half-power diameter (HPD) of the on-axis PSF can be optimized at the cost of offaxis performance (see Fig. 5). In contrast, missions like LuXIS that seek to map the

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Fig. 4 Effect of coating on effective area. Effective areas are computed using SAORT at a variety of energies for a SEEJ-like MiXO, for sources located at different off-axis positions. All parameters are held the same except for the coating, which uses iridium (left) and iridium-carbon (right). Including Carbon in the coating reduces the sharpness of the edge structure at 2 keV

Fig. 5 Effect of placing a source at different off-axis angles, simulated for a SEEJ-like configuration. The off-axis position is marked in arcminutes along the upper scale, while the half-power diameter (HPD) is listed in arcseconds below each source. The color table is designed to highlight the scattering wings of the PSF

lunar terrain require a stable imaging performance across a wide field of view, which is achieved with a combination of gradually varying focus offsets and shell lengths (see Fig. 6).

Ray Tracing Ray trace codes are a crucial component of designing telescope optics. They allow detailed explorations of the design in realistic configurations and experimentation of various parameters including shell sizes, lengths, spacings, and focus offsets. They also allow implementation of scattering effects due to micro-roughness as well as

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Fig. 6 As in Fig. 5, but for a LuXIS-like shell configuration that optimizes for stable HPD across the FoV (see Kashyap et al. 2020). An azimuthal distortion of the PSF is apparent at θ20′ , but the HPD is remarkably constant

large-scale variations in the figures of the mirrors, which is crucial to understand the actual performance. There are several ray trace codes that have been developed for specific use cases: e.g., SAOtrace (https://cxc.cfa.harvard.edu/cal/Hrma/SAOTrace.html) for X-ray tracing of Chandra mirrors, XISSIM for X-ray event simulator of Suzaku-XRT (Ishisaki et al. 2007), and generic Wolter Type I reflection gratings ray traces constructed by Rasmussen et al. (2004). The nested shell configuration specifically has been implemented in SAORT (Sethares et al. 2021), and we use this code to compute example ray traces shown here. As an example, we adopt a configuration similar to that used in SEEJ (see Table 1). Scattering due to mirror roughness is included for realistic behaviors. Ray traces are carried out at various energies 0.1–7 keV, for sources at various off-axis positions from 0 arcmin (i.e., on-axis) to 20 arcmin. The PSF degrades rapidly with off-axis (see Fig. 5), and the HPD goes from 20 arcsec on-axis to >2.5 arcmin at 20 arcmin off-axis. This broad disparity can be alleviated by allowing individual shells to come to focus at different offsets, as is done for LuXIS (Fig. 6; adapted from Figure 6 of Kashyap et al. 2020).

ENR and Metal-Ceramic Hybrid MiXO Two different MiXO optics configurations were fabricated using the ENR technique. One of the configurations has 62 mm diameter, 180 mm long, and 1 m focal length, while the other configuration has a 0.7 m focal length with 100 mm diameter × 90 mm length and 80 mm diameter × 80 mm length. Several mirrors were fabricated from each of the configurations and the performance of these optics is discussed in section “Performance of ENR MiXO”. One drawback, however, with the fullshell nickel optics is the high density of nickel, which necessitates thin shells

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Table 1 Key optics parameters of MiXO-based mission concepts: note these may change as each mission concept matures MIXS-Ta Fraser et al. (2010); Bunce et al. (2020) Science discipline Planetary

LuXIS Stupl et al. (2018); Hong et al. (2021a) Planetary

Tel. modules Shellsb Optics massb Ang. Res. (HPD) FoV (Dia.) Focal length Optics ODb On-axis effective areab @ 1 keV Energy range Main requirements

1 N/A 800. If the aperture to image distance is set equal to the focal length of a telescope, the Fresnel number, calculated using Equation 10, is the product of the f -number = D/F , the reciprocal of the diffraction-limited angular resolution, D/λ and the constant 1/4. It constitutes a dimensionless figure of merit for the diffraction-limited focusing power which can be used to provide a comparison of telescopes operating in different wave (energy) bands. For example, the JWST mirror imaging in the near-infrared at a wavelength of 5 microns has diameter of D = 6.5 m and focal length of F = 131.4 m giving NF = 1.6 × 104 . An X-ray mirror imaging at 1 keV (wavelength 1.2 × 10−9 m) with D = 1 m and F = 10,000 m gives NF = 2 × 104 , very close to the JWST value. However, the diffraction-limited angular resolution of JWST is 0.15 arc seconds compared to 0.00026 arc seconds for the X-ray telescope because the X-ray wavelength is so small. The depth of focus of a conventional telescope is determined by the f -number. If the focal plane is displaced by ±dF, then the width of the PSF will increase by ∼dF.D/F . In order to maintain the diffraction-limited angular resolution, we require dF.D/F < F λ/D, dF < F 2 λ/D 2 . Using the focal length of 800 m from above, the depth of focus is dF < 0.77 mm. That is, the imaging detector must be placed at a distance of 800 m from the aperture to an accuracy better than ±1 mm to achieve diffraction-limited imaging. However, the depth of focus of an interferometric system is larger. When the detector is displaced by dF, the fringes seen from the two-slit aperture persist because they exist over a much larger volume above and below the focal plane. The size of this volume depends on the total number of fringes that are visible, determined by the width of the slits (W = 0.025D in the example illustrated in Fig. 2) and the coherence length of the radiation. If the width of the slits is W and the distance between the outer edges of the slits is D, the number of bright fringes visible in the PSF, either side of the central peak, is Nvis ∼ D/W . These fringes will remain visible providing dF < Nvis .F 2 λ/D 2 , a displacement Nvis times greater than the the depth of focus for diffractionlimited imaging. All the diffraction-limited analysis presented so far has assumed monochromatic light, one wavelength, infinite coherence length. All astrophysical X-ray sources are broadband and incoherent, and the coherence length will be set by the spectral resolution of the imaging detector and the quality of the X-ray

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optics. The coherence length can be expressed as the number of fringes visible, Ncl ∼ E/∆E = λ/∆λ. ∆E depends on the type of detector employed. When a single X-ray photon is absorbed in a detector, a cloud of ion pairs is created in the detector material, and the amount of charge released is proportional to the X-ray energy. But the amount of charge fluctuates because of the statistical nature of the ionization process and the fluctuations are characterized by Fano noise (Fano 1947). Currently, Fano limited silicon detectors like CCDs give, at best, ∆E = 65 eV at 1 keV. Alternatively, the energy released when the photon is absorbed can be measured directly using cryogenic detectors like TESs (transition edge sensors) which give ∆E = 2.5 eV. Therefore, the maximum number of fringes produced by interference at 1 keV will be in the range 15 < Ncl < 400 depending on the detector system used. In any diffraction-limited X-ray telescope system, the number of fringes visible will depend on both the limitation set by the bandwidth and the geometry of the optical system.

Diffraction-Limited X-Ray Optics The response of X-ray optics is governed by the complex refractive index for X-rays in materials given by: n = (1 − δ) − iβ

(11)

where both δ and β are positive and small. The linear photoelectric absorption coefficient is: µ = 4πβ/λ

(12)

where λ is the wavelength and therefore the photoelectric mass absorption coefficient is: µ/ρ = 4πβ/(λρ)

(13)

where ρ is the mass density of the material. Figure 4 shows the real (δ) and imaginary (β) decrements as a function of energy, 0.1–10 keV, for iridium, silicon, and beryllium. For energies higher than the absorption edges of the material, both the real and imaginary decrements decay as power laws, δ ∼ E −2 and β ∼ E −4 . There is slight curvature, but these indices give a close match to the broadband decay profile. As a consequence, at high energies, the linear photoelectric absorption falls away as µ ∼ E −3 . Above 10 keV, the attenuation from Compton scattering starts to dominate over photoelectric absorption, and above 1022 keV, pair production will be significant, and these factors must be included when calculating the total linear absorption for hard X-rays and gamma-rays. The real part of n is a slightly less than unity, and therefore the phase velocity of X-rays in materials is a little higher than the velocity of light in vacuum, and likewise

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Fig. 4 The refractive index decrements, δ and β, for iridium, silicon, and beryllium over the energy range 0.1–10 keV

the wavelength in materials is greater than the wavelength in vacuum. Therefore, when X-rays pass from vacuum into a material, the refraction angle (measured from the normal within the material) is greater than the incidence angle, and at a critical grazing angle: cos θt = 1 − δ,

(14)

Total external reflection occurs, analogous to total internal reflection of visible light at a glass-vacuum boundary. Because of the absorption associated with the imaginary part of the refractive index, β, the reflection is not total, but for small √ grazing angles 30 eV), the refractive index can be predicted accurately. In the vicinity of absorption edges, the calculations are limited by the details of the electronic energy structure included in the theory and by extended X-ray absorption fine structure, EXAFS, which is a correction introduced by a second scattering of the outgoing primary scattered wave by nearby atoms in the surface. Tabulations of the refractive index decrements for all atomic types over the entire X-ray energy band are available, and therefore the Fresnel reflectivity of X-rays from mirror surfaces can be calculated in a straightforward manner. The canonical wavelength range defining the X-ray band is 0.1 to 100 Å; therefore, roughness and imperfections in the surface chemistry and geometry on the atomic scale are expected to strongly influence the X-ray reflectivity. Roughness or chemical contamination introduces small phase and amplitude changes in the reflected X-ray wave fronts, and some of the radiation is scattered (or diffracted) away from the specular direction. A complete theory of scattering of electromagnetic radiation from surface roughness was originally developed to describe scattering of radar from land and sea, but the results apply equally well to the much shorter wavelength regime of X-rays. Following the same Fourier optics analysis used in the Introduction section, surface roughness is modeled as a two-dimensional aperiodic diffraction grating, and each Fourier component of the surface height profile, period d, produces diffraction orders m at angles given by the grating equation: sin θs − sin θ =

mλ d

(15)

where θ is the angle of incidence and θs is the angle of scatter measured with respect to the surface normal. The detailed shape of the scattering wings generated by the surface roughness and figure errors will depend on the Fourier spatial frequency power spectrum of the aperiodic diffraction grating, but we can calculate the total integrated scatter (TIS), the fraction of the incident intensity which is scattered out of the specular beam. If the surface is reasonably smooth, first order scattering dominates, and there is no explicit shadowing (which must be the case to approach the diffraction-limited performance), and then: TIS = Rτ (θ, λ)



4π σ cos θ λ

2

(16)

where Rτ is the Fresnel reflectivity for polarization τ and σ is the root mean square of the surface height fluctuations. Typically, working in the energy band 0.1–10 keV σ must be ≤5 Å rms to keep the TIS at an acceptable level. Surface contamination which is distributed unevenly over the surface can be modeled in a similar way and acts like a phase grating. Any particulate or dust contamination will further block or scatter the X-rays. Surface contamination by hydrocarbons or similar compounds often forms a smooth layer or layers. A Fresnel reflection will result from each interface, and

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W

W

Fig. 5 Wave front distortion in optic. Left: grazing incidence reflection. Right: refraction through a thin wedge

the total reflection must be calculated by summing the component wave amplitudes taking into account the phase difference introduced by the thickness of the layers. The contamination acts in the same way as a multilayer coating on a conventional lens. A single monolayer of hydrocarbon contamination can severely compromise or indeed enhance the X-ray reflectivity of a grazing incidence mirror. Figure 5 illustrates the distortion of the X-ray wave fronts as they reflect at grazing incidence or refract through a thin dielectric wedge. If the surfaces are flat, plane wave fronts are reflected or refracted as plane wave fronts. If there is a very small curvature of the surface figure, the reflected or refracted wave fronts will be cylindrical or spherical and will converge or diverge to a very distant line or point. For grazing incidence reflection, the X-ray beam is deflected through twice the grazing angle 2θg , and surface figure errors and surface roughness height variations h(x, y) introduce small phase shifts: ∆φ =

2π h sin θg λ

(17)

and the length scale of the in-plane height variations is compressed by a factor of sin(θg ). So the profile of the gradient errors in the reflecting surface is imprinted on the wave fronts, but the length scale of the fluctuations is compressed and the amplitude diminished. The TIS for grazing incidence reflection described above is

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set by σ sin(θg ) where σ is the root mean square of the height variations, h(x, y), across the entire reflecting surface. In grazing incidence systems, the variation in θg along the surface is very small, so the amplitude of the reflected wave front is constant over the full width of the aperture. For refraction at near-normal incidence, the phase shifts are controlled by the real decrement in the refractive index, δ, such that: ∆φ =

−2π δh λ

(18)

and on transmission through a wedge, both the entrance and exit faces contribute to the wave front distortion. For this case, the TIS is set by δσ where σ is the quadratic sum of the rms fluctuations across both the entrance and exit surfaces. In refractiontransmission optics, the thickness of the optic (wedge in Fig. 5) is a significant factor because of absorption. The thickness and thickness variations across the aperture reduce the wave amplitude and determine the efficiency of the aperture and hence the effective area. Phase errors modify the PSF, shifting flux from the focal spot to elsewhere. Where that flux goes and how the size of the focal spot is changed depend on how the errors are distributed across the aperture. To keep both the HPD and FWHM of the PSF close to the diffraction limit values, the phase shift errors must be ∆φ ≪ 2π for all scale lengths up to the beam width W in both reflection and transmission optics. In some circumstances, the phase errors can be significantly larger than this while maintaining the narrow FWHM, but the HPD will be much broader. In transmission optics, the absorbed fraction is a function of thickness: Fabs = 1 − exp(−µt),

(19)

and the efficiency across the aperture will depend on the thickness profile. For lenses, the profile is parabolic (see section “Transmitting Optics”). The left-hand panel of Fig. 6 is the aperture efficiency as a function of absorbed fraction for both a simple concave lens and a Fresnel lens with maximum thickness variation ∆tmax . If Fabs (∆tmax ) = 0.5 and the minimum thickness is 0, then the aperture efficiency is 72%. If the minimum thickness is t0 > 0, then the absorption will increase across the whole aperture, and the aperture efficiency will be lower than this value. The right-hand panel shows the variation in HPD of the diffractionlimited PSF calculated using Fourier optics analysis including the variation in wave amplitude imposed by the lens thickness. For a simple concave lens (plotted in black), as the absorption increases and Fabs (∆tmax ) < 0.5, the HPD decreases because the absorption profile reduces the step in transmission at the edge of the aperture which in turn suppresses the side lobes in the PSF (a Fourier filtering process called apodization (Mills and Thompson 1986)), but as Fabs increases further, the absorption limits the effective width of the aperture and the HPD increases. For a Fresnel lens with 20 rings and the same ∆tmax , the apodization is reduced and the HPD increases monotonically with increasing Fabs (∆tmax ).

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Fig. 6 Left-hand panel: the aperture efficiency as a function of fraction absorbed at ∆tmax for a concave lens or for a Fresnel lens of the same maximum thickness. Right-hand panel: the HPD of the PSF as a function of fraction absorbed at ∆tmax for a concave lens (black) and Fresnel lens with 20 rings (red)

In order to achieve high aperture efficiency, greater than 50% at thickness ∆tmax , in a transmitting X-ray optic, we require exp(−µ∆tmax ) > 0.5. Under this constraint, the diffraction-limited HPD will be very close to the value imposed by aperture width in the absence of absorption. Figure 7 shows the limiting value of ∆tmax for Be, Si, and Ni as a function of energy. When the change in thickness ∆t across the transmitting wedge is: t1 = λ/δ

(20)

the wedge spans a full period zone within the aperture (corresponding to a phase shift of 2π in transmission). This thickness, proportional to photon energy, t1 ∝ E, is plotted as dashed lines in Fig. 7 for Be, Si, and Ni. It represents the minimum thickness required to produce a Fresnel lens (see subsequent section below). In practice, the thickness of a transmitting focusing optic with high efficiency must be between the solid and dashed lines. For low-Z materials like Be, the entire energy range is accessible, and for Si the energy must be greater than ∼8 keV and for Ni greater than ∼12 keV. Below 10 keV, the optics must be very thin, ∼10 microns and above 100 keV ∼1 mm.

Reflecting Optics Wolter optical systems (Wolter 1952) utilize two grazing incidence reflections to produce a coma-free image. The mirrors are surfaces of revolution about the optical axis, the primary generated by a parabola and the secondary by a hyperbola. Two configurations can be used for X-ray telescopes, Type I and Type II, as illustrated in Fig. 8. The surface generators, parabola and hyperbola, are shown as dotted lines.

303

1e−03

∆tmax cm

1e−01

1e+01

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Berylium Silicon

1e−05

Nickel

1

10

100

1000

10000

keV

Fig. 7 The thickness variation limit for high aperture efficiency, ∆tmax , across the aperture as a function of photon energy for Be, Si, and Ni. The dashed lines represent the full period zone thickness, t1 , as a function of energy for each material

The principal plane of an optic is defined by locus of the intersection between rays incident on the aperture and focused rays converging to the focal plane. For the Wolter geometry, this is the same as the join plane between the surface generators. For Type I, the reflecting surfaces lie either side of the join plane at a distance F , the focal length, from the focal plane. For Type II, the join plane is in front of the mirrors, so the reflecting surfaces are at a distance 800, and the diffraction-limited performance can only be approached using an off-axis sector aperture covering a small angle around the azimuth of the shell annulus. In order to provide good aperture coverage over a sector which is approximately square (azimuthal width the same as the radial width), many shells must be nested and there will be a path difference between successive shells in the nest: ∆L = (r22 − r12 )/(2F )

(21)

where r1 and r2 are the radii of the shells at the join plane. This path difference is always much greater than the coherence length of the astronomical X-rays, so we can calculate the diffraction-limited PSF of the complete aperture by summing the PSFs of the individual shells. The PSF of a nested, square, Wolter sector is illustrated in Fig. 9. The angular resolution in the azimuthal direction (around the shells) is ∆θ ∼ λ/D, but in the radial direction, it is ∆θ ∼ Nnest λ/D where Nnest is the number of shells. The Wolter Type II configuration offers a rather different prospect for diffractionlimited performance. For Type II, the grazing angles are no longer determined by the f -number, so, in principle, complete Type II primary and secondary surfaces of revolution could be used. But nesting is not possible, so the aperture would be a single annulus as illustrated in the top panels of Fig. 2, and the HPD would be determined by the ratio D0 /D. The width of the annular aperture, W = D − D0 ,

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Fig. 9 Left panel: Wolter nest sector aperture size D. Right panel: diffraction-limited PSF

is determined by the axial length, L, of the primary surface. W = L tan θg so for a typical grazing angle of 1 degree W = 0.02L and the diffraction-limited angular resolution set by the HPD performance are determined by the width of the annulus, ∆θ ∼ λ/W , and not the diameter of the primary shell, D. Aside from the performance limitation of the Wolter geometry considered above, the manufacture of Wolter optics that approach a diffraction-limited angular resolution is a formidable task. Currently there is no technology or metrology available which could meet the surface figure requirement of σ sin(θg )/λ ≪ 1 where σ is the rms figure error over the entire reflecting surfaces of the primary and secondary.

Transmitting Optics The radial thickness profile of a simple refracting convex lens is given by the lens maker’s equation and can be expressed as a parabola: t (r) = t0 −

r2 1 2 F (n − 1)

(22)

where t0 is the thickness at the center, F is the focal length, and n is the refractive index. Working in the X-ray band n − 1 = −δ so a converging lens must be concave with profile: t (r) = t0 +

1 r2 2 Fδ

(23)

As the thickness increases toward the edge of the lens, absorption will dominate in the X-ray band because of the relatively large ratio of the decrements in the

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Fig. 10 Top: simple concave lens. Bottom: Fresnel lens with six rings

refractive index, β/δ. Therefore, it’s pertinent to consider using a Fresnel lens as an alternative. In this case, the aperture is split into Nring annular rings with a constant step in thickness of: tring =

1 D2 8 F δNring

(24)

where D is the diameter of the lens. The profile of the Fresnel lens is the same as the simple lens but offset within each ring to keep the thickness below tring + t0 . Figure 10 shows the profiles of a simple concave lens and the equivalent Fresnel lens with six rings. The diffraction-limited PSF of the simple lens is the Airy function as illustrated in Fig. 1 giving the angular resolution FZR = 1.22λ/D. The diffraction-limited PSF of the Fresnel lens is modified by diffraction from the edges of the rings. There is a phase shift of (2π/λ)tring δ at each edge. If the optical path difference corresponding to this phase shift is greater than the coherence length, tring δ > λ2 /∆λ = (E/∆E)λ, then there will be no correlation in phase between rings, and we can calculate the diffraction-limited PSF by performing the summation of amplitude and phase over each ring aperture, squaring to give the intensity, and then summing the intensities over all the rings to yield the combined PSF. Figure 11 illustrates the surface brightness profile of a Fresnel lens calculated in this way compared to the Airy function for the same aperture. The right-hand panel shows the HPD as a function of the number of rings which is approximately HPD = 1.3Nring λ/D. If the step between the rings represents an integer number of wavelengths, m: tring δ = mλ

(25)

and m ≪ E/∆E, then the wave fronts in successive rings will be in phase and the PSF will return to the Airy function. Therefore, the PSF of the Fresnel lens depends critically on photon energy, E, (wavelength, λ) and the bandwidth, ∆E. There are two function forms of diffraction-limited PSF, the narrow Airy function that occurs at specific wavelengths and the wider broadband PSF for which the HPD depends on the number of rings in the Fresnel lens. To reach the diffraction limit of the aperture,

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Fig. 11 Left: broadband PSF surface brightness profile of a Fresnel lens with ten rings (red) compared to Airy function (black). Right: the broadband HPD of a Fresnel lens as a function of the number of rings in the lens

∆θ ≈ λ/D, we require tring δ = mλ where m is an integer, and the bandwidth, ∆E, must be small enough (and hence the correlation length large enough) so that wave fronts from the innermost ring interfere with wave fronts from the outermost ring, E/∆E > m(Nring − 1).

X-Ray Lens Design and Performance To achieve diffraction-limited performance with high efficiency in the Xray/gamma-ray energy band, the thickness of a transmitting optic must lie between t1 and ∆tmax , as plotted in Fig. 7. In the soft band, we require low Z materials with thickness of ∼10 microns. Manufacture of such lenses with aperture D ∼ 1 m is challenging but might be possible by adapting the technology currently used for the production of transmission diffraction gratings. For energies >30 keV, a thin lens with ∆t > 1 mm is a viable proposition and will be much easier to manufacture. At 100 keV, a Fresnel lens made from Si (or similar material) with a thickness of t = 2.5 mm will satisfy the constraints. The real decrement of the refractive index −2 for Si is δ = 4.4 × 10−4 EkeV and at 100 keV λ = 1.24 × 10−11 m so δt = 8.9λ. Setting ∆φ = 2π/10 in Equation 18 gives the sum in quadrature of the rms figure errors on the entrance and exit surfaces as h = 28 microns, so the rms figure error on each surface of the lens must be σ = 20 microns to achieve a phase error equivalent to figure quality of λ/10. This is a modest requirement well within the capabilities of currently available optical figuring techniques. The focal length and diffraction-limited angular resolution will be determined by the number of rings, and the focal length is very large because δ is so small. Using Equation 24 with tring = 2.5 mm, D = 1 m, and δ for Si from above gives F = 1.1 × 109 /Nring m when EkeV = 100. The broadband PSF will have the profile plotted in red on

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Fig. 11 with ∆θ = 2.6Nring micro-arc seconds, and the HPD of the focused spot will be 14 mm on the detector. At a wavelength λ = δt/m, where m = 9 or any nearby integer, and providing the bandwidth is small, E/∆E > 9(Nring − 1), there will be a much narrower PSF, ∆θ = 2.6 micro-arc seconds, with the form of the Airy function and a focused spot with HPD of 14/Nring mm on the detector. The radius  of the nth ring of a Fresnel lens with a total of Nring rings is rn = (D/2) n/Nring so the radial width of the outer (narrowest) ring is ∆rmin ≈ D/(4Nring ). The minimum radial width of the rings and hence the maximum number of rings that can be accommodated will depend on the manufacturing process used to make the lens, Nring = D/(4∆rmin ). The Fresnel number of the lens, calculated by substituting the focal length from Equation 24 for the aperture-image distance, l = F , in Equation 10 is NF = 2Nring (tring δ/λ). Substituting for Nring in terms of rmin from above gives NF = (D/(2∆rmin ))(tring δ/λ). If rmin ∼ 1 mm, then the Fresnel lens described above has Nring = 250 and NF = 4500. Unless some manufacturing process can be developed to produce a Fresnel lens with rmin ≪ 1 mm, the Fresnel number of such a lens and hence the diffraction-limited focusing power will be very modest in comparison with the largest diffraction limited optical or infrared telescopes – the Fresnel number for the JWST mirror was estimated above as NF = 2 × 104 . For a given thickness (t = 2.5 mm above), the broadband focus on the detector is independent of the number of rings, and when Nring = 1, we have a simple lens and the HPD corresponds to the aperture diffraction limit. As the number of rings increases, the focal length and HPD of the narrowband PSF shrink as 1/Nring . To achieve the greatest focusing advantage, the maximum number of rings will be limited by by the energy resolution of the detector: Nmax = E/(m.∆E) + 1

(26)

where m = tδ/λ. The parabolic (spherical) lenses described above produce the optimum diffraction limited PSF (Airy function), on-axis, in the focal plane. If the lens profile is modified, then the off-axis PSF and/or the out-of-focus PSF (depth of focus) can be optimized in a trade-off against the on-axis performance. For example, so-called axilenses use exponential profiles with thickness: t (r) = t0 + a × r b

(27)

where the exponent 0.5 < b < 3.5 controls the aspheric response. When b = 2, we get a parabolic lens. If b < 2 or b > 2, the depth of focus increases but the on-axis PSF is degraded. Such axilens profiles can be applied to full period zones in a Fresnel-type lens although the radii of the zones will depend on the exponent value, b. Further details about the design of axilenses can be found in the literature, e.g., Davidson et al. (1991). Using aspheric profiles may be of use in the final optimization of Fresnel lens design for application in the X-ray and gamma-ray regime.

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Further details about the application of Fresnel lenses in gamma-ray astronomy including construction, the focal length problem, effective area, and chromatic aberration are given by Skinner et al., ⊲ Chap. 49, “Laue and Fresnel Lenses”, Volume 2. Laue lenses are also used to provide focusing of flux in the gamma-ray energy band. They utilize Bragg reflections in transmission, from an array of crystals, to concentrate the flux. The angular resolution is determined by the size and internal structure of the crystals, but the geometry does not give access to diffraction-limited imaging.

Zone Plates If the change in path length across each ring in a Fresnel lens is one wavelength, λ, then m = 1 and the rings are full period zones within the aperture. We can split each ring into two half period zones and replace the refracting rings of the Fresnel lens by alternate open and blocked annuli to form a zone plate. In this case, the open area of the plate is half the area of the full aperture. Or we can introduce a thickness of dielectric in alternate half period zones, tzone = λ/(2δ), to produce a phase shift of π between the adjacent half period zones in which case the open area of the zone plate covers the full aperture. The PSF of the zone plate is then just the diffraction pattern of the aperture, and the complex amplitude at the focal plane is given by the Fresnel integral: exp(ikz) E(x, y, z) = iλz

 

′ 2 ′ 2 ik E(x , y ) exp (x − x ) + (y − y ) + φ dx′ dy′ 2z (28) where x, y are positions in the focal plane at axial position z and x ′ , y ′ are positions in the aperture (axial position z = 0) and φ is the phase change introduced √ by the dielectric. The radius of the nth half period zone of the zone plate is rn = nλz. Therefore, if the aperture diameter is D and there are n half period zones within the aperture, the focal length of the zone plate is z = D 2 /(4λn). The intensity of the PSF is given by the modulus of the complex amplitude squared. Figure 12 shows the PSF of a zone plate calculated using the Fresnel integral. When φ = π or 0 in alternate zones, the PSF is the sum of two components, the Airy function plotted in blue and a very broad residual function plotted in red which is the circular aperture blurred by diffraction. The radius of the first zero of the Airy function is given by the product of the angle 1.22λ/D and the focal length, 1.22(λ/D)(D 2 /(4nλ)) = 1.22D/(4n), while the mean level of the residual remains constant and extends well beyond the radius of the geometric shadow, D/2. The right-hand panel of Fig. 12 shows the encircled energy function for zone plates with 10, 20, 30, 40, and 50 full period zones. The half power radius is ≈0.44D independent of the number of √ half period zones and is always greater than radius D/(2 2) which is the half area radius of the aperture. If the phase term is set to: 

′

′

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Fig. 12 Left: PSF surface brightness profile of a zone plate with 40 half period zones. The dashed line indicates the profile of the geometric shadow. The Airy function component is plotted in blue and the residual in red. The vertical green line indicates the half power radius. Right: the encircled energy function of zone plates with 10, 20, 30, 40, and 50 full period zones (black). Airy function for Fresnel lens with 50 rings (full period zones) in blue

φ = modulo[(r/D)2 4n, 2]π

(29)

2 where r = x ′2 + y ′ , the radius within the aperture, the wave fronts passing through the zone plate are refracted toward the optical axis, and the Fresnel integral gives the PSF of a Fresnel lens, which is identical to the Airy function, and the residual function disappears. The encircled energy function of a Fresnel lens with 50 full period zones is plotted in blue on the right-hand panel. The energy fraction within the radius of the first zero of the Airy function is 84%. For a zone plate PSF, the energy fraction within the Airy component is reduced by a factor 4/π 2 , and the energy fraction within the first zero is 0.84 × 4/π 2 ≈ 0.34. For the Fresnel lens, all wavelet amplitudes at the focal point are in phase, and the integration of the complex amplitudes in the complex plane forms a straight line. For the zone plate, the phase of the wavelets change progressively across a half period zone, and the integration follows the circumference of a semicircle, and the resultant amplitude is reduced by factor 2/π . The refraction of the wave fronts in the Fresnel lens focuses all the flux into the Airy function component with angular half power diameter HPD = 1.06λ/D, while in a zone plate diffraction alone pushes only ∼34% of the flux into the central focused spot (radius to first zero), and the angular half power diameter of the full PSF is HPD = 3.52nλ/D where n is the number of half period zones within the aperture. Although zone plates have much lower efficiency in focusing the incident flux into the central focused spot compared to lenses, simple zone plates with alternate open and blocked half period zones are not subject to low efficiency imposed by the thickness of dielectric and can be used in the soft X-ray band.

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Interferometers When the aperture of an imaging system is reduced to two slits with separation D, as illustrated in Fig. 2, the PSF is dominated by cosine interference fringes with period ∆θ = λ/D. The amplitude and phase of the fringes provide a measurement of the flux and position of sources in the field of view at the spatial frequency corresponding to ∆θ in the direction set by the line of separation of the slits. By measuring the amplitude and phase of fringes with different separations, D, and different position angles of the slits, we can build up an image in the Fourier domain by a process of aperture synthesis. Provided there is adequate coverage in ∆θ and position angle across the Fourier plane, we can achieve diffraction-limited imaging equivalent to an aperture with diameter equal to the maximum value of separation Dmax . Interferometry is the primary method of imaging in radio astronomy and is now providing high angular resolution in the optical band (Baldwin et al. 1996; Monnier 2003). When operating in the long wavelength radio band, very high angular resolution can only be achieved by using very long baseline separations Dmax . However, the wavelengths in the X-ray band are extremely small, so high angular resolutions should be possible using modest baselines providing an X-ray interferometer can be built with sufficient precision to resolve the fringes. In 2000, Cash et al. (2000) reported the detection of X-ray fringes using a simple grazing incidence interferometer utilizing four flat mirrors. Their prototype instrument had a baseline of just one millimeter and gave fringes at 1.25 keV (wavelength 10 Å) equivalent to an angular resolution at source of ∼0.1 arc seconds. More recently the spatial coherence of X-rays from a synchrotron source, wavelength 1 Å, has been measured by Suzuki (2004) using a two-beam interferometer with prism optics. The angular resolution obtained was 0.02 arc seconds using an effective baseline of 0.3 mm. It is tempting to assume that the precision required for interferometry with very high angular resolution is beyond the reach of modern technology, but Cash et al. (2000) have demonstrated this is not the case. Generating a simple two-source fringe pattern is possible using currently available flat mirrors, and increasing the baseline does not require a pro rata increase in mirror precision. The challenge is to build an X-ray interferometer with a collecting area large enough to provide good statistics in the detected fringes while at the same time making the instrument compact and reasonably straightforward to construct. Ideally the dimensions of the instrument should be driven by the upper limit set for the baseline separation rather than being dictated by the geometry required for the mirrors and detectors. If ∆θ is 100 µ arc seconds at 2 keV, then λ = 6.2 Å and D ≈ 1.3 m, a modest aperture about twice the diameter of a single XMM-Newton module (Jansen et al. 2001) (D = 0.7 m) or slightly larger than the largest shell in the Chandra telescope (Weisskopf et al. 2000) (D = 1.2 m). Assuming a detector resolution of ∆y = 10 µm in the focal plane, the focal length must be F ≈ 40 km to give this

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Fig. 13 The geometry of two overlapping beams generating two-source fringes

angular resolution, and the cone angle of rays from the outer edge of the aperture would be 2R/F = 2φ ≈ 7 arc seconds corresponding to an f -number of ∼30,000. In order to achieve diffraction-limited imaging, all the optical paths from the aperture to the focus must be equal in length. As discussed above, for a thin lens operating in the hard X-ray regime, this is accomplished by advancing the wave fronts near the edge of the aperture using a thickness of dielectric. In Xray mirror systems, also discussed above, two grazing incidence reflections in the Wolter Type I or II configuration can provide equal path lengths over a small annular aperture and can, in principle, provide diffraction-limited imaging over a small field of view. Nesting of the Wolter Type I surfaces such as employed in Chandra or XMM-Newton can increase the effective area but cannot provide diffraction-limited imaging over the full aperture covered because the path difference between adjacent shells in the nest is much larger than the coherence length of the radiation. Figure 13 shows the basic geometry needed to generate two-source interference fringes in a wave front splitting interferometer. Parallel beams from two samples of the incident wave fronts enter from the right and converge until they overlap to the left creating a volume containing the interference fringes. Regardless of how the beams are manipulated to the right, a length L, as shown, is required to combine the beams and generate the fringes. If the angle between the beams is θb and the wavelength is λ, then the fringe spacing along the y-axis is: ∆y =

λ θb

(30)

If the beam width is W and the distance along the x-axis from the position where the beams are separate to where the beams fully overlap is L, then: θb =

W L

(31)

The number of fringes seen across the overlapping beams is given by: Nf =

W ∆y

(32)

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Eliminating θb from equations 30, 31 and 32, the fringe separation and beam width are given by:

∆y = W =

λL Nf

 λLNf

(33)

(34)

If we take L = 10 m, λ = 10 Å, and Nf = 10, then ∆y = 30 µm and W = 300 µm. The beam width W is very small, and in order to achieve a large collecting area, the depth of the beams along the Z axis (normal to the X − Y plane shown in Fig. 13) must be large, and/or many identical systems must be operated in parallel. The fringe spacing is small but can be resolved by currently available X-ray imaging detectors. The situation can be improved by increasing L, but we have already chosen a reasonably large distance of 10 m, and because both W and √ ∆y depend on L, a rather large increase is required to make a significant impact. The angle between the beams is small, θb = 6.2 arc seconds.

An X-Ray Interferometer Four flat mirrors can be used to take two samples of width W and separation D = 2R from the aperture and produce overlapping beams as illustrated in Fig. 14. All four mirrors are set at grazing incidence to provide high reflectivity. Operating in the soft X-ray band 0.1–2.0 keV, the grazing angles need to be θg ≈ 2◦ . If M1 and M3 are set at θg with respect to the x-axis, then M2 and M4 must be set at a slightly smaller angle θg − θb /4, where θb is the angle between the beams defined by Equation 31, so that the beams overlap to form fringes. Since θb is very small compared to θg , M2 is almost parallel to M1 and the same is true for M4 and M3 . The effective focal length F is much larger than L and is given by φ = θb /2 = tan−1 (R/F ). The fringe spacing is then ∆y = F δθ = F λ/D where ∆θ is the diffraction-limited angular resolution for the baseline separation D operating at wavelength λ.

Fig. 14 The four flat mirror configuration. The diagram is not drawn to scale. The axial distance between M2 and M3 is much less than the distance L, and F is much larger than L. The vertical scale is exaggerated so that the beam widths are visible

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The arrangement is similar to that used by Cash et al. (2000), but the front of M2 is placed at distance L from the maximum overlap of the beams, whereas in the Cash configuration, this mirror is at a distance 2L from the maximum overlap. The present configuration reduces the overall length required by a useful factor of 2. The physical length of the system is much smaller than the focal length, and the basic geometry is reminiscent of the Wolter Type II telescope in Fig. 8. If W = 300 µm (see above), then the axial length of the mirrors is only 8.6 mm if θg = 2◦ . The axial distance covered by the combination of M1 and M4 needs only be ∼25 mm. The axial distance between M1 and M2 (or M3 and M4 ) is D/(4 tan θg ) ≈ 7D.

A Slatted Mirror The collecting area afforded by a single four mirror arrangement as illustrated in Fig. 14 is going to be small for any sensible depth of mirror (along the z-axis into the plane of the paper). Furthermore, the mirrors required would be incredibly long and thin because the axial length utilized is so small (8.6 mm; see above). A major advantage of the four mirror configuration proposed here and illustrated in Fig. 14 is that a series of parallel systems can be stacked together. The mirror M2 must be split into a slatted mirror, comprising a series of parallel slats, as proposed by Willingale (2004) and Willingale et al. (2005). The axial lengths of mirrors M1 , M3 , and M4 must be increased to cover the full aperture width of all the slats in the slatted mirror. The beam geometry of the slatted mirror is shown in Fig. 15.

Fig. 15 The beam paths using a slatted mirror

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Fig. 16 The layout of an X-ray interferometer using a slatted mirror with 30 elements. Note that the vertical scale is expanded so that the geometry of the beams is easier to discern

Each slat is a long thin mirror facet extending into the plane of the paper. The axial width of a slat is the same as for the mirrors in Fig. 14. The slats are spaced so that the beam from mirror M4 , to the right, is broken into a series of beams of width W . Each slat mirror reflects a fraction of the beam from mirror M1 creating a second set of beams. Each pair of beams overlaps to form interference fringes. Providing there is not too much blocking from support structure needed to hold the slatted mirror together and provided the thickness of the mirror slats is the same order as the beam width W , then about one-third of the flux collected by the apertures of M1 and M3 will form fringes. A slatted mirror with ∼30 slats will provide an effective aperture width of ∼1 cm. The axial length for each slat-gap pair will be ∼26 mm. Figure 16 is a schematic diagram of the layout using a slatted mirror with 30 elements. The length ∆L is the axial separation of M1 and M4 , and the baseline separation D is the same for all the slat-gap pairs. Such a slatted mirror is like a macroscopic transmission grating with mirror facets on each line. It is likely that an optical element of this form could be manufactured using similar techniques to those currently employed in the fabrication of X-ray transmission or reflection gratings. A slatted mirror with dimensions 500 × 500 mm combined with three plane mirrors of the same size would provide a total collecting area of ∼50 cm2 (The final effective collecting area would depend on the X-ray reflectivity of the mirrors and the efficiency of the detectors.). If the mirrors in each arm are set parallel, the path length from the aperture plane at M3 to the detector plane is:

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 P0 = L + ∆L +

D 2 sin(2θg )



1 cos θ

(35)

where θ is the off-axis angle of the source. This is the same for both arms M1 M2 and M3 -M4 and for all positions across the detector. The angle between the incoming wave fronts and the aperture plane introduces a path difference, and when M2 and M4 are tilted by θb /4 to produce an overlap between the beams, we get an extra path contribution. The extra path lengths of the two arms are:  D 1 − 1 + y sin(θb /2) − sin θ =L cos(θb /2) 2

(36)

 D 1 = (L + ∆L) − 1 − y sin(θb /2) + sin θ cos(θb /2) 2

(37)

P12

P34





where y is the position across the detector plane. The path difference between the arms is:   1 ∆ = P12 − P34 = −∆L − 1 + 2y sin(θb /2) + D sin θ (38) cos(θb /2) It is this path difference which gives rise to the fringes. The first term is fixed and of no consequence since it can be eliminated by a small change in the position of M1 or M3 . Ignoring this small correction, the coincidence point of the interferometer (∆ = 0) is given by: y=

−D sin θ ≈ −F θ 2 sin(θb /2)

(39)

Here we have taken the small angle approximation and substituted for the focal length F = R/ tan(θb /2) ≈ D/θb . The interferometer behaves like an imaging telescope of focal length F with the coincidence point (center of the fringe pattern) at the expected position of a point source with off-axis angle θ . The negative sign represents the expected lateral inversion in the focal plane.

The Fringe Pattern If we move away from the coincidence point, the path difference ∆ increases linearly with y ′ = y + F θ , and we expect to observe cosine fringes. Because the wave fronts of the two beams are broken up by the slatted mirror, we must use the Fresnel diffraction formula to calculate the exact form of the fringe pattern. If plane waves of wavelength λ are incident on a slit of width W and we are looking at the fringes at a distance L from the slit, the dimensionless variable used in the Fresnel integrals is given by:

8 Diffraction-Limited Optics and Techniques

u=y

317

′



2 λL

(40)

 Substituting for y ′ = W from Equation 34, we have u0 = 2Nf . Since Nf > 1, the scaled width of the slit u0 is also > 1 and we must use the near field approximation (Fresnel diffraction) rather than the far field limit (Fraunhofer diffraction). We define limits u1 = u − u0 /2 and u2 = u + u0 /2. The complex amplitude at a scaled displacement u from the center of the beam is given by: (41)

A = C(u2 ) − C(u1 ) + i(S(u2 ) − S(u1 )) where C(u) and S(u) are the Fresnel integrals: u

C(u) =



S(u) =



0 u 0

cos(π w 2 /2)dw

(42)

sin(π w 2 /2)dw

(43)

The intensity expected is then given by I = AA∗ . Using the beam parameters from above, u0 = 4.5, and the intensity has the profile shown in the left-hand panel of Fig. 17. The geometric shadow of the edges of the slit (a mirror slat or gap between slats) without diffraction are expected at u = ±2.25. If the mirror slats and gaps are the same size, they will produce identical intensity profiles, but because they are tilted by θb with respect to each other, there is a phase difference between the beams which is a linear function of u, δ = π u0 u, and the complex amplitude in the overlap region is then given by: A2 = A(1 + exp(iπ u0 u))

–4

–2

(44)

3

12

2.5

10

2

8

1.5

6

1

4

0.5

2

0

2

4 u

–4

–2

0

2

4 u

Fig. 17 Left panel: the Fresnel diffraction profile of a single beam. Right panel: the fringe pattern from one slat-gap pair

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Again we can calculate the intensity profile in the same way giving the fringe pattern plotted in right-hand panel of Fig. 17. The intensity of the bright fringes is modulated by the Fresnel diffraction profile shown in the left-hand panel of Fig. 17. The expected Nf = 10 fringes are visible across the center of the beam. The edges of the beam spread into the geometric shadow due to diffraction, but there will be negligible interference between adjacent slat-gap pairs. As the path difference ∆ becomes comparable to the coherence length of the X-rays, the visibility of the fringes will decrease. If E/∆E = N , then we expect to see ∼N fringes across the entire pattern. If N ≫ Nf , then a continuation of the Nf fringes from the slat corresponding to the coincidence position will be visible from slat-gap pairs adjacent to this position, but in the gap between adjacent pairs, the fringes will be much reduced in intensity. These missing fringes can be recovered by splitting the slatted mirror into two halves, reversing the slat and gap positions in the second half. The pattern of slats required is shown in Fig. 18. Combining the fringe patterns from the two halves provides complete coverage of all N fringes. Figure 19 shows the fringe pattern expected from two sources at ±5 milli arc seconds with Nf ∼ 4 and N ∼ 10. The slats introduce a residual modulation, but this can be completely removed during analysis of the interferograms.

Fig. 18 A slatted mirror with complementary halves

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Fig. 19 The fringe pattern expected from two sources at ±5 milli arc seconds. The fringes from the two halves of the slatted mirror are plotted as dashed and dashed-dotted lines

Working at an X-ray wavelength of 10 Å and using L = 10 m, the fringe spacing for Nf = 10 is 30 µm. Such fringes could be resolved using a CCD detector with the smaller pixel sizes currently available. However, the fringes exist through a very long volume in which the two beams overlap. All ten fringes should be visible over an axial depth of ∼L/10. If the detector is set at a grazing angle θd to the beam, the fringe spacing will be increased to: ∆y ′ =

∆y sin θd

(45)

If θd = 5.7◦ , then the magnification factor will be 10, and the fringes will easily be resolved by current detector technology. Unfortunately, a detector operating at such a low grazing angle will have a low efficiency. In order to take advantage of the magnification, a detector with high quantum efficiency operating at small grazing angles would have to be developed. When observing astronomical objects, the X-ray flux will be broadband, and a detector with a moderate energy resolution will be required to detect fringes. We require an energy resolution E/∆E ≥ Nf to resolve the fringes at energy E in a bandwidth ∆E. A CCD typically has E/∆E ≈ 10 at 0.6 keV increasing to ∼15 at 1 keV and ∼50 at 7 keV. This is just adequate for our purpose. However, the imaging and spectral response of a CCD is not well matched to the requirement. High spatial resolution is only needed in 1D (across the fringes), and the sensitivity would be greatly improved if E/∆E > 100.

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Simulation of One-Dimensional Imaging

0

80 60 40 20 0

0

20

40

60

80

The interferometer illustrated in Fig. 14 has been simulated using the slatted mirror layout shown in Fig. 15 and the energy response of the XMM-Newton EPIC-MOS CCDs (Turner et al. 2001). In order to get good coverage in spatial frequency, four parallel systems were used with D-spacings of 35, 105, 315, and 945 mm. The corresponding effective focal lengths are 1.2, 3.7, 11.1, and 33.4 km. Each system has a collecting area of ∼20 cm2 in the energy band of 0.58–2.1 keV (using the reflectivity of gold and the MOS detector efficiency). The E/∆E of the detector provides 21 energy channels across this band. A total source flux equivalent to 1 Crab gives 460,000 counts in a 1000 second exposure. With 4 D-spacings and 21 energy channels, a total of 84 interferograms were recorded in a single exposure. The source distribution assumed was a binary system consisting of an extended source and a point-like companion. Even with ∼460,000 counts, the count per fringe is very small, and it is impossible to see the fringes in the raw simulated data. However, for each interferogram (one energy channel and one D-spacing), the fringe spacing and expected number of fringes are known. It is therefore possible to set up a Fourier filter that picks out the fringe pattern from each interferogram. Figure 20 shows the Fourier power spectra of the 84 interferograms and the Fourier filter constructed to pick out the

1

2 3 frequency moa–1

4

0

1

2 3 frequency moa–1

4

Fig. 20 The left-hand panel shows the Fourier power spectra of 84 interferograms. Each block of 21 corresponds to a given D-spacing. The right-hand panel is the Fourier filter used to pick out the fringes

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Fig. 21 The reconstructed source distribution. The inset shows an expanded detail of the significant peaks. The binary consists of a resolved component with a point source companion

fringes. The 4 blocks of 21 interferograms arise from the 4 D-spacings used. Two peaks are visible in each power spectrum. The vertical white lines to the left at low frequency are the peaks from the modulation caused by the slats. These are completely removed by the filtering. The white patches to the right are the fringes. The visibility of the fringes varies as the frequency increases because of the structure of the binary source under observation. A top-hat profile matched to the E/∆E for each interferogram was used to construct the filter. There is some overlap in the frequency coverage between the four D-spacings. In a practical setup, the overlap regions could provide a means of eliminating phase errors between the four parallel optical systems. Figure 21 shows the reconstruction of the source distribution. The intensity is plotted as counts per 0.058 milli arc second sample, and there are 1800 samples across the field of view. The rms noise level is 2.16 counts per sample, and all the significant samples are detected at >12σ . The total estimated count from the significant samples is 430,000 compared with the actual detected count of 462,000, so 93% of the original count has been successfully imaged. In this simulation and reconstruction, the source distribution was assumed to be independent of energy, and therefore all the detector energy channels could be summed to produce the final image. In reality, this would not always be the case, and more D-spacings would be required to reconstruct a source with a complex spatialenergy structure. To extend the imaging to 2D, more exposures would be required at different roll angles about the pointing axis to give a reasonable coverage in the (u,v) plane. If this were achieved by running several (five to ten) identical systems

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simultaneously at different roll angles not only would 2D imaging be provided, but there would also be a pro rata increase in the total collecting area. The system performs in a similar way to a shadow mask camera (Sims et al. 1980), but a fringe pattern is detected instead of a shadow mask pattern. Each pixel at the detector is multiplexed to many sky elements within the field of view, and therefore the sensitivity of the interferometer is dependent on the source distribution or the number of significantly bright point sources in the field of view. If the energy resolution of the detector were improved, the number of fringes N ≈ E/∆E across the pattern would increase, and the number of pixels multiplexed to a given sky position would be larger. The total area of the Fourier plane covered by the filter (Fig. 20) is ∝ 1/N, and if there √are Nx significant unresolved sources in the field of view, the signal-to-noise is ∝ (N)/Nx .

Tolerances, Alignment, and Adjustment Because the wavelength of X-rays is so small, the tolerances and alignment requirements for an interferometer are very tight, and we must consider figure errors and surface roughness in the flat mirror surfaces, alignment and positional placement of the mirrors, control of the difference between the path lengths in the two beams, and pointing accuracy and stability of the complete system. The mirrors must be flat enough so that incident plane wave fronts are reflected with the minimum perturbation and remain plane as described in sections above. Figure errors will introduce distortions in the wave fronts, and shorter scale surface roughness features will scatter some of the incident light into scattering wings which will reduce the contrast of the fringes. Fortunately, because the mirrors are operating at grazing incidence, the effect of figure errors and surface roughness in the mirror surfaces is reduced by a factor sin θg . A surface height error h introduces a wave front shift of 2h sin θg . To produce clean fringes, the wave fronts must not be perturbed by greater than ∼ λ/10. So we have: h≤

λ 20 sin θg

(46)

If λ = 10 Å and θg = 3◦ , then we require h < 1 nm. A high-quality optical flat has a specification of λ/20 (where λ = 633 nm), so even with the advantage of grazing incidence, we need very high-quality mirrors to obtain clean fringes. The surface height error of 1 nm is equivalent to an axial gradient error over the width of one slat of ∼0.03 arc seconds. Gradient errors over distances larger than the slat width will destroy the register between the overlapping beams produced by a single slat-gap pair and may introduce confusion between adjacent slat-gap pairs. The angular width of the fringe separation is ∆y/L ≈ 3 × 10−6 equivalent

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to 0.6 arc seconds as seen from the mirrors. Therefore, gradient errors between the slats and over the full faces of the other mirrors must be kept to this level. First order perturbation theory gives the total integrated scatter (TIS) after two reflections as: 4π σ sin θg TIS = 2 λ 

2

(47)

where σ is the rms surface roughness. To get TIS < 0.1, we require σ < 3.5 Å integrated over correlation lengths 5σ in 500 seconds. The system can provide imaging in 2D by making exposures at different roll angles. About 40 units (possibly packed into the same tube) running simultaneously with different D-spacings and roll angles could provide good coverage of the (u,v) plane, and because of the tenfold increase in collecting area, the same sensitivity would be achieved in ∼150 seconds using CCDs or detectors with a similar performance. If the detector energy resolution could be improved by a factor of 10 while retaining a spatial resolution of ∼10 µ m in 1D, then the same 2D imaging sensitivity could be achieved in ∼50 seconds. The slatted mirror system is similar to the MAXIM periscope configuration, the tolerances of which are described in detail by Shipley et al. (2003). The introduction of a slatted mirror dramatically reduces the total distance required between the primary mirrors that define the baseline separation and the detector system, and 0.1 mas imaging can be achieved without the requirement for two free-flying spacecraft. Each unit of four mirrors detects two-source fringes, and the combination of several such units provides imaging by aperture synthesis in the same way as conventional interferometers used in the radio and optical bands. This is rather different from the all-up MAXIM approach in which many mirror segments are used to produce a complex interferogram which looks much more like a conventional image.

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All the published proposed designs to date utilize flat mirrors. If technology to introduce a very small cylindrical curvature in the primary optics can be developed, then designs incorporating 1D focusing can be implemented, and the flux sensitivity limit of the X-ray interferometer will be significantly reduced.

Cross-References ⊲ Laue and Fresnel Lenses

References C.S. Adams, I.G. Hughes, Optics f2f from Fourier to Fresnel (Oxford University Press, Oxford, 2019) B.K. Agarwal, X-Ray Spectroscopy: An Introduction (Springer-Verlag, Berlin, Heidelberg, New York, 2013) J.E. Baldwin et al., Astron. Astrophys. 306, L13–L16 (1996) M. Born, E. Wolf, A.B. Bhatia, P.C. Clemmow, D. Gabor, A.R. Stokes, A.M. Taylor, P.A. Wayman, W.L. Wilcock, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 7th edn. (Cambridge University Press, Cambridge, 1999) W. Cash, A. Shipley, S. Osterman, J. Marshall, Nature 407, 160 (2000) N. Davidson, A.A. Friesem, E. Hasman, Opt. Lett. 16, 523–525 (1991) U. Fano, Physical review. APS 72(1), 26–29 (1947) K.C. Gendreau, W.C. Cash, A.F. Shipley, N. White, SPIE 4851, 353–363 (2003) F. Jansen et al., A&A 365, L1 (2001) M. Lieber, D. Gallagher, W. Cash, A. Shipley, SPIE 4851, 557–567 (2003) J.P. Mills, B.J. Thompson, J. Opt. Soc. Am. A 3, 694–703 (1986) J.D. Monnier, Rep. Prog. Phys. 66, 789–857 (2003) H.J. Pain, The Physics of Vibrations and Waves, 6th edn. (John Wiley & Sons Ltd, Chichester, New York, Brisbane, Toronto, Singapore, 2005) A. Shipley, W.C. Cash, K. Gendreau, D. Gallagher, SPIE 4851, 568–576 (2003) M.R. Sims, M.J.L. Turner, R. Willingale, Nucl. Instrum. Methods Phys. Res. 228, 512 (1980) Y. Suzuki, Rev. Sci. Instrum. 75(4), 1026–1029 (2004) M.J.L. Turner et al., A&A 365, L27–L35 (2001) M.C. Weisskopf, H.D. Tananbaum, L.P. Van Speybroeck, S.L. O’Dell, SPIE Proceedings, vol. 4012 (2000) R. Willingale, SPIE 5488, 581–592 (2004) R. Willingale, G. Butcher, T.J. Stevenson, SPIE 5900, 432–437 (2005). Advanced X-ray Astrophysics Facility (AXAF): an overview. Proc. Soc. Photo-Opt. Eng. 2805, 2–7 H. Wolter, Ann. Phys. 10, 94 and 286 (1952)

9

Collimators for X-ray Astronomical Optics Hideyuki Mori and Peter Friedrich

Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Stray Light and Baffle Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Classification of the Stray Light . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Design of the Stray-Light Baffle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . XMM-Newton . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Suzaku and Hitomi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Suzaku Pre-collimator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Optical Tuning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . On-Ground and In-Orbit X-Ray Calibrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Hitomi Pre-collimator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . eROSITA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Future Missions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

328 331 331 346 349 353 353 357 358 358 361 367 368 369

Abstract

An X-ray collimator, or baffle, can be installed in the X-ray optics of an X-ray telescope. This component is placed in front of an X-ray mirror to protect the mirror from severe in-orbit thermal environment or to limit the mirror’s field of view. Although the latter may be a disadvantage in the viewpoint of observational performance, the collimation of incident X-rays allows us to block X-rays with H. Mori () Japan Aerospace Exploration Agency/Institute of Space and Astronautical Science, Sagamihara, Kanagawa, Japan e-mail: [email protected] P. Friedrich Max-Planck-Institut für extraterrestrische Physik, Garching, Germany e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2024 C. Bambi, A. Santangelo (eds.), Handbook of X-ray and Gamma-ray Astrophysics, https://doi.org/10.1007/978-981-19-6960-7_10

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large off-axis angles. Thus, the mount of the X-ray collimator results in the reduction of an extended ghost image in the detector field of view that is created by the X-rays, called stray light, with abnormal paths inside the X-ray mirror. The contamination of the stray light hampers both imaging and spectroscopic observations of dim X-ray emission from a spatially extended source or a faint point source. The improvement of the angular resolution and the effective area is intensively pursued for the next-generation X-ray optics. In parallel, it is a vital issue to reduce the stray light as low as possible to fully achieve the expected performance of these future X-ray optics. Keywords

X-ray baffle · Thermal pre-collimator · Stray light · Ghost image · Single reflection · Backside reflection · Alignment process

Introduction We describe an X-ray collimator or baffle mounted on an X-ray mirror in this chapter. Here a collimator (or baffle) is defined to be a component structure as a part of the X-ray astronomical optics, which has some features that enhance the performance of the X-ray mirror. We hereafter use the terms of “collimator” and “baffle” as synonyms. We note that, basically, the collimator is not used for focusing X-rays from celestial sources. Figure 1a shows a schematic drawing of the X-ray mirror and collimator, together with definitions of some terms used in the chapter. The first X-ray mirror was equipped in the Einstein satellite (Giacconi et al. 1979). Even for the X-ray mirror in the Einstein satellite, an X-ray collimator was installed, called forward thermal pre-collimator (see Fig. 1b for its geometrical configuration). This thermal pre-collimator allows us to isolate the X-ray mirror thermally from a space environment and then to reduce heater power required for the thermal control of the mirror. Such a thermal pre-collimator was also introduced in the X-ray mirrors of ROSAT (Truemper 1982; Benz et al. 1983; Aschenbach 1988) and Chandra (Weisskopf et al. 2000; Gaetz and Jerius 2005; Schwartz 2014). Compared with a thermal shield that is mounted on the entrance of the X-ray mirror, another component to isolate the mirror thermally, one of the advantages of the thermal pre-collimator is that it does not block normal X-ray paths. As shown in Fig. 1b, on-axis X-rays reach on a detector plane without any interactions except for the X-ray mirror. Figure 1c indicates the geometrical configuration of the thermal shield. The thermal shield usually consists of an extremely thin film and its support structure. An aluminized polyethylene-terephthalate (PET) film with a thickness of sub-micrometers is utilized for radiation decoupling; thermal radiation is reflected back to the X-ray mirror. Although the aluminized PET film is quite effective to reflect optical/infrared lights completely, X-rays with a relatively low energy (below 0.5 keV) are also absorbed by the film, which prevents the telescope from their detection. For example, the transmission of the thermal shield for the

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Fig. 1 (a) A schematic drawing of a cross-sectional view of an X-ray mirror and collimator. The terms used in this chapter are also indicated. (b) A geometrical configuration of a thermal precollimator. (c) Same as (b), except for a thermal shield

Suzaku XRT was ∼0.7 at 0.5 keV (Serlemitsos et al. 2007). The thickness of the thermal shield was just 0.24 µm. While the thermal shield achieves a lightweight component without additional heater power, careful handling is requested for the extremely thin film not to be torn down. In addition, because the PET film contains carbon (C), severe absorption around the C-K edges (0.28 keV) precludes a clear detection of low-energy X-rays. No absorption of the low-energy X-rays is the advantage of the thermal precollimator because high effective areas of the X-ray mirrors are sustained even in the low-energy band. Moreover, we can avoid uncertainties of observational results caused by the X-ray Absorption Fine Structure (XAFS) of the elements used in the thermal shield. However, the thermal pre-collimator does not isolate the mirror from the space environment completely. Paraboloid shells (and a part of hyperboloid shells that depends on the mirror nesting density) of the X-ray mirror can still see the space directly, which causes radiative cooling. Of course, the cooling is mitigated by the thermal pre-collimator since the solid angle of the space is limited to some extent, depending on the internal structure of the thermal pre-collimator. Furthermore, the thermal coupling by radiation between the mirror shells and the thermal pre-collimator also contributes to thermal stabilization of the X-ray mirror. To keep the thermal environment constant, the temperature of the thermal precollimator is usually controlled by a heater. Hence, compared with the thermal shield, which is a passive component, power consumption is required to operate a thermal collimator.

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Another purpose to install the collimator on the entrance of the X-ray mirror is to reduce incident X-rays with abnormal paths that create a ghost image on a detector plane. These X-rays are called stray light. The stray light itself is a common problem in the design of the optics. For example, a star tracker camera that determines the aspect of the satellite has a baffle in front of the camera lens. Since light paths to the lens are restricted by the baffle, it allows us to reduce a ghost noise by the stray light. Similarly, the collimator installed on the X-ray mirror is expected to reduce the Xray stray light as much efficiently as possible. At the same time, this structure makes the field of view of the X-ray mirror narrower. Hence, the design of the collimator should be determined so as to optimize the total performance of the X-ray optics. So far, a variety of the X-ray collimators has been achieved to reduce the X-ray stray light for the X-ray mirrors on board XMM-Newton (Jansen 1999), Suzaku (Mitsuda et al. 2007), Hitomi (Takahashi et al. 2018), and eROSITA (Predehl et al. 2021). We summarize the missions equipped with the X-ray collimators for stray-light reduction as well as the thermal control in Table 1. Thanks to the X-ray collimators, dim X-ray emission is now able to be detected clearly without contaminations due to the stray light. Especially, new findings were achieved from complicated X-ray structures shown in outskirts of some clusters of galaxies or the regions of the galactic center, where the X-ray contamination from bright X-ray sources hampered accurate X-ray studies of spatially extended dim emission. Since the effectiveness of the X-ray collimators was verified from the in-orbit observations, the collimator with the same concept is an indispensable component even for the X-ray optics in some planned future missions. As the angular resolutions and the effective areas of the X-ray mirrors are improved to detect distant X-ray objects and to investigate fine structures of X-ray sources with extremely low surface brightness, the importance of reducing the X-ray stray light is increased. Indeed, the intensive study of the X-ray collimator design has been carried out for the future

Table 1 Summary of X-ray collimators installed in X-ray imaging optics Mission Einstein ROSAT XMMNewton Chandra

Collimator (or baffle) Thermal precollimator Thermal precollimator X-ray baffle

Swift Suzaku AstroSat Hitomi

Thermal precollimator Thermal baffle Pre-collimator Thermal baffle Pre-collimator

eROSITA

X-ray baffle

Reference Giacconi et al. (1979) Truemper (1982); Benz et al. (1983); Aschenbach (1988) Aschenbach et al. (2000); de Chambure et al. (1996, 1999a,b) Weisskopf et al. (2000); Gaetz and Jerius (2005); Schwartz (2014) Burrows et al. (2003) Serlemitsos et al. (2007); Mori et al. (2005) Singh et al. (2017) Okajima et al. (2016); Awaki et al. (2014); Iizuka et al. (2018); Mori et al. (2018) Predehl et al. (2021); Friedrich et al. (2012, 2014)

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X-ray large missions such as Athena (Bavdaz et al. 2021) and Lynx (Gaskin et al. 2019) (Lynx is also equipped with thermal pre- and post-collimators). We focus on the X-ray collimator for stray-light reduction hereafter because the thermal pre-collimator is a simple component to sustain thermal environment for the X-ray optics as described above. The structure of thermal pre-collimator is related to the thermal design of the X-ray optics, which reenters the domain of thermal engineering. Neither we discuss a simple collimator that only limits the field of view of the X-ray optics such as coded masks, which is beyond our scope. We first describe the classification of the stray light and then give detailed explanations for each component of the stray light. We also mention a basic design to reduce the stray light on the detector plane of the X-ray mirror. The detailed designs of the X-ray collimators are different among the missions, which reflects the requirement for each telescope. Thus, we describe the X-ray collimators separately for XMMNewton, Suzaku, Hitomi, and eROSITA. We also mention briefly the current status of the future collimator design at the end of this chapter.

Stray Light and Baffle Design Classification of the Stray Light In the Wolter-I type optics, X-ray photons are focused on a detector plane by nominal double reflection (see also Fig. 1a). However, since the Wolter-I type mirror is a grazing incident optics, some off-axis X-rays, which form a shallow angle with the common optical axis of the X-ray mirrors, can also arrive at the detector plane. If the off-axis angle becomes large enough, the nominal double reflection no longer occurs for these X-rays. They so create a de-focused and extended ghost image of the corresponding celestial object. However, the image is quite distorted and then does not store correct information on the spatial extent of the object. Such X-rays are called stray light. Figure 2 shows the stray-light image of the Crab Nebula taken by the ASCA GIS. Although the Crab Nebula was located 60′ away from the aim point, i.e., the center of the GIS, and then a source-free region was observed, the stray light was extended in the entire field of view. In this way, a part of the stray light comes into the detector field of view and then comes to represent an important source of X-ray backgrounds for observing targets we are interested in. Especially, for the observation of the source with low surface brightness, the stray light causes an imaging and spectroscopic contamination that makes severe problems to extract correct scientific results. For example, an outskirt of a cluster of galaxies is affected by the stray light from its bright core. Another example of the stray-light contamination is a mapping observation of the galactic diffuse emission in the galactic center where many bright X-ray sources are crowded. As the impact of the stray light on the observations was recognized, countermeasures were studied. The first telescope to be equipped with a stray-light baffle was XMM-Newton. After XMM-Newton, Suzaku (Astro-E2) and Hitomi (ASTRO-H) were equipped with a pre-collimator to reduce the stray light. Before discussing a

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Fig. 2 Stray-light image taken by the ASCA GIS with a circular field of view. The source of the stray light is the Crab Nebula located 60′ away from the aim point. The bright emission shown in the lower left part corresponds to the stray light by the secondary-only reflection, while the upper right part does correspond to the stray light by the backside reflection (This image is adapted from Mori et al. 2005)

structural design suitable for that task, we need to find out the paths of the stray light in the X-ray mirror. A ray-tracing simulation of the X-ray mirror is a powerful tool to understand what occurs inside the X-ray mirror assembly (e.g., Madsen et al. 2017; Saha et al. 2017). X-rays incident onto the mirror assembly are generated as an input file of the Monte Carlo simulation. According to properties of a given X-ray source, an initial direction and an energy are set for each ray. A three-dimensional mirror structure is accurately reconstructed in the computer. Interactions between the X-ray photons and mirror are given by probability functions that represent absorption, reflection, and scattering. We can trace an internal path for each X-ray that allows us to identify the positions at which the reflection occurs. Most X-rays are focused to the detector plane by the nominal double reflection; the ray is reflected in sequence by the primary and secondary mirrors. All the X-rays undergoing a single reflection (on either a primary or a secondary mirror) are not focused and contribute to the stray light. Furthermore, based on the ray path through the mirrors, we can divide the stray light into four types, designated as below: 1. 2. 3. 4.

No reflection or direct component Primary-only reflection or primary component Secondary-only reflection or secondary component Backside reflection or backside component

Figures 3 and 4 show schematic drawings of the paths inside the mirror assembly for the stray light, as well as that for the nominal double reflection. The significant contribution to the stray-light image is created by X-rays with single reflection,

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Fig. 3 X-ray paths inside the X-ray mirror for the (a) nominal double reflection and (b) no reflection. The terms and parameters are also indicated

especially that by the secondary-only reflection (see also Fig. 2). For the nested mirrors, the primary-only reflection has small contribution compared with the secondary-only reflection. Due to dense nesting of mirror shells to enhance the effective area, the majority of the primary-only reflection hits the backside surface of the inner primary or secondary shell, and it is then absorbed inside the mirror shell. The backside surface of the mirror shells is usually very rough compared with the frontside surface to which reflective coating is applied. Hence, the X-ray reflectivity for the backside surface is relatively low, depending on the surface condition. The low reflectivity implies that the flux of the backside reflection is dim. However, the geometrical area on the mirror aperture where the backside reflection occurs is large; therefore the contribution to stray light can be non-negligible. We discuss a simple analytical expression for each stray-light component that represents a relation between basic parameters such as a focal length of the mirror, an off-axis angle of the stray light, and its radial coordinate on the mirror aperture or the detector plane. The relation is useful for understanding the characteristics of each component and for a rough estimation of a collimator’s height explained later. Figure 3a shows a schematic cross-sectional view of the nominal double reflection. For a geometrical calculation, we also define some key parameters with

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Fig. 4 X-ray paths inside the X-ray mirror for the (a) primary-only reflection, (b) secondary-only reflection, and (c) backside reflection

symbols: an off-axis angle (θ ), a focal length (F ), and a tilt angle of a primary mirror shell (τ ). Here, we apply a conical approximation to the mirror shells that allows us to simplify the calculation. Thus, a cross section of each mirror shell is indicated by a straight line, instead of a parabolic or hyperbolic curve. h represents an axial

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height of a mirror shell. According to the mirror design, the axial height is usually different for each mirror shell. However, we assume here that the axial heights of all the primary and secondary mirrors are the same. R is a half size of the detector field of view. We assume that the detector has a square shape. If the detector field of view is a circle, R represents its radius. We designate the radii for the top of the primary mirror and the bottom of the secondary mirror as rp and rs , respectively. The radii for the bottom of the primary mirror and the top of the secondary mirror are slightly different in general since there is a gap between the primary and secondary mirrors produced by a mirrorsupport structure. However, we consider here that both are the same; this radius is designated as rf . We note that the thicknesses of the mirror shells are assumed to be zero to minimize the number of the parameters used in the calculation. Thus, radii of frontside and backside surfaces for a mirror shell are the same. We can easily replace these radii with those of the actual backside surfaces by adding the thickness of the mirror shell. rt represents a radius of an incident X-ray measured at the mirror entrance. There is also a gap between the mirror entrance and the top of the primary mirrors. Hence, strictly speaking, rt for an off-axis X-ray is different from the radius measured in the plane corresponding to the top of the primary mirrors. However, we assume that the gap is negligible hereafter and then compare rt with rp directly. Given a tilt angle of a primary mirror measured from an optical axis, designated as τ , that of the corresponding secondary mirror is set to 3τ so that the incident angle of the reflected X-rays on the primary mirror becomes τ on the secondary mirror (see Fig. 3a). Consequently, the on-axis X-rays (θ = 0) are bent at an angle of 4τ by the nominal double reflection. Hence, rf is given by rf = F tan 4τ . In general, the radii (rf ) for each pair of the primary and secondary mirrors are optimized to enhance the effective area. And then, the tilt angle of the corresponding primary r mirror is set by τ = 14 tan−1 Ff .

No Reflection The direct component is a simple stray light that goes though without any interactions with the mirror shells and their housing. The X-ray performance of the Wolter-I type optics, especially for the effective area, is determined by the focal length and the innermost/outermost radii of the mirror aperture. To enhance the effective area of the grazing incidence optics, the X-ray mirror shells are densely packed, covering a ring-shaped collecting area. Thus, a circular aperture remains clear in the center of the mirror module. Usually, other optical components are equipped in this space, for example, a retroreflector collimator (Chandra) and an alignment cube (Hitomi) that is used for the alignment of the X-ray optical axis. These components allow us to block a part of the direct component. In addition, we can easily seal this central space if necessary, using high-Z metals such as lead to block the direct X-rays. Hence, we ignore the direct component through the central space of the X-ray mirror hereafter. There is the other direct X-ray component that goes through a space between the innermost mirror shells and the inner wall of the mirror housing (see Fig. 3b). This direct component sometimes creates a dim X-ray arc in the detector field of view.

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One countermeasure to block this direct component is to make the space narrower by attaching a roof on the inner wall. However, it may be difficult to align the roof’s position accurately not to intercept the innermost primary shell for on-axis X-rays. Consequently, we need to accept a slight contribution from the direct component. There may be other spaces that the direct component can occur. For example, a space between the outermost mirrors and the outer wall of the housing also contributes to the direct X-ray component. Moreover, if the nesting density of the mirror is low (a sparse nesting), off-axis X-rays can go through a space between the mirror shells. However, since the direct component is not focused and the radial coordinate of these off-axis X-rays (rt ) is significantly larger than the detector size in general, they will rarely contaminate the detector field of view. As shown in Fig. 3b, the direct component for a given off-axis  angle  of θ can reach the detector field of view under a condition of ri ≦ rt ≦ F + h tan θ + rd . Here, rd and ri represent the radial coordinate on the detector plane and the radius of the inner wall, respectively. We note that the discussion below is based on the cross-sectional view limited only in the off-axis plane. An azimuthal effect on the off-axis X-rays is not considered hereafter. Another condition required at the mirror exits, which is given by ri ≦ rt − 2h tan θ ≦ rs . Thus, the condition for rt can be summarized to   ri + 2h tan θ ≦ rt ≦ min (F + h) tan θ + rd , rs + 2h tan θ ,

(1)

which indicates that an allowable radial range for the direct component is quite narrow. Since 2h tan θ is small enough, the blocking of the mirror aperture only with a radial range of ≦ rs provides an effective reduction of the direct component. However, as already mentioned, the alignment of the blocking component is a challenge because nested mirror shells are always affected by alignment errors that make the alignment of a blocking shell a critical step.

Primary-Only Reflection Since the primary and secondary components cause the reflection on the mirror shell, the analytical calculation using the cross-sectional view is a little complicated. Compared with the nominal double reflection, the primary-only reflection is deviated at an angle of τ + (τ − θ ) = 2τ − θ by the single reflection on the primary shell. Note that the condition for the off-axis angle in which the reflection occurs on the primary shell is θ ≦ τ ; if the off-axis angle becomes larger than the tilt angle, the X-rays would come to hit first the frontside of the secondary shell. However, a stronger restriction for the off-axis angle is imposed by the condition that the X-ray reflected on the primary shell should not hit the secondary shell. Since this condition also depends on the hit position on the primary shell, we express here the restriction of the off-axis angle as 2τ − θ  3τ . This restriction of θ  −τ implies that the tilt direction of the primary-only reflection is opposite to that of the primary shell, as shown in Fig. 4a. The tightly nested mirrors seldom meet the condition because of the existence of the inner primary shell. To meet the condition that the reflected X-rays do not hit the

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backside surface of the inner primary shell, another restriction of θ ≧ −τ is required for the off-axis angle as shown in Fig. 5a. For the tightly nested mirrors, the tilt angle of the inner primary shell is almost the same as that of the currently considering primary shell. And then, the radius of the top of the inner primary shell is set to the same as that of the bottom of the primary shell to improve the aperture efficiency. Thus, the minimum off-axis angle for the primary-only reflection is realized when the X-rays are reflected on the middle of the primary shell. Figure 5a shows that τ = ∆r/ h using a small-angle approximation, where ∆r represents the difference in radii between the top and bottom of   shell. This panel also indicates  the primary that the angle of the reflected X-ray is 23 ∆r / h2 = 3 ∆r h = 3τ , which should equal to 2τ − θ . Thus, the minimum off-axis angle is calculated to θ = −τ . Therefore, the off-axis angle for the primary-only reflection is allowable just around −τ . We also show the case of θ > −τ where the reflected X-ray does not hit the secondary shell in Fig. 5a. In summary, the primary-only reflection occurs only at a quite limited radial range of the primary shells for the tightly nested mirrors, except for the innermost primary shell. A correlation plot between the radial coordinates on the mirror aperture and the detector plane is useful to visualize the contribution of the stray-light components and their X-ray paths inside the X-ray mirror. Figures 6 and 7 show the correlation plots obtained from the ray-tracing simulations of the Suzaku XRTs (Shibata et al. 2003). Model lines described below are also indicated in this figure. Here, two segments of the X-ray mirror were considered so that the cross-sectional treatment was applicable. The off-axis angles were set to θ = ±30′ . To make the plot clear, we increased the flux of the stray light by assuming the X-ray energy of 1.49 keV, aluminum Kα X-rays, since we measured the reflectivity and the reflected beam profile at 1.49 keV for aluminum substrates used in the Suzaku XRTs. The direction

Fig. 5 (a) Supplemental drawing of the primary-only reflection in a tightly nested mirror. An offaxis X-ray is hit at the middle of a primary shell. Then, the reflected X-ray passes just behind the inner secondary shell. A blue line shows the case of the primary-only reflection with θ > −τ . (b) Same as (a), except for the secondary-only reflection

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Fig. 6 Correlation plots between the radial coordinates of the mirror aperture and the focal plane for X-ray photons with an off-axis angle of θ = −30′ . The results of the ray-tracing simulations

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of the reflected X-ray was slightly deviated from that of the specular reflection because of the X-ray scattering incorporated into the ray-tracing simulation, which results in the line spread (see the lower panels of Figs. 6 and 7). Moreover, the lines corresponding to multiple reflection, which includes the backside reflection on the inner shells, were removed in the simulation results since the multiple reflection rarely happens in reality. We also run other simulations under the condition that the reflectivity of both frontside and backside surfaces is unity and that only the specular reflection occurs. The results are shown in the upper panels of Figs. 6 and 7, which represent the model lines. The correlation plots clearly show linear relations between the radial coordinates on the mirror aperture and the detector plane although the real relations have scattering to some extent. We note that the nominal double reflection shows a horizontal line regardless of the radial coordinates of the incoming X-rays, according to the principle of the Wolter-I optics. The radial coordinate in the detector plane is F tan θ , if θ is small enough. The labels appended to the model lines represent a tracking path which shows the reflections on the mirror shells. The primary-only reflection corresponds to the label of “1,” implying that the contribution to the stray light in the detector field of view was quite small. In the case of the Suzaku XRTs, the primary-only reflection occurred at the radial coordinates on the mirror aperture of ∼60 mm, consistent with the above statement. There were two other paths of the stray light similar to the primary-only reflection that contaminates the detector field of view. However, these paths include the backside reflection which decreases the flux contribution. Indeed, the corresponding lines were dim in the correlation plots derived from the simulation. We can derive an analytical expression of the relation as described below. According to the sketch shown in Fig. 5a, the radial coordinate on the detector plane (rd ) is calculated by the geometrical optics as follows: rd = rt − (h − l) × tan θ − (F + l) × tan(2τ − θ ). Here, l is a distance from the top of the primary shell to the hit position, which is measured along the optical axis. Since l ≪ F and h ≪ F , the above equation can be reduced to

rd = rt − F tan(2τ − θ ).

(2)

◭ Fig. 6 (continued) for the Suzaku XRT are indicated in the upper panel. Hatched areas show the detector field of view (a width of 25.4 mm). The reflectivity of the frontside and backside surfaces of the mirror shells is set to unity. And then, no scattering of the reflected X-rays is assumed. Model lines estimated from the geometrical calculation are superposed with dashed lines. Labels of the lines represent the X-ray paths, where “1” and “2” represent the reflection on the primary and secondary shells, respectively. A suffix of “B” means the backside reflection. The reflectivity and the reflected beam profile at 1.49 keV measured for the mirrors and the aluminum substrates are used in the lower panel (This figure is adapted from Shibata et al. 2003)

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Fig. 7 Same as Fig. 6, except for a given off-axis angle of θ = +30′

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We already conjectured that the relation of the radial coordinates is expressed by a linear function. Using the addition theorem of tangent and the small-angle approximation of tan 2τ tan θ ≃ 0, we can further reduce it to a simple relation given by rd = rt − F tan 2τ + F tan θ . To evaluate a term of rt − F tan 2τ , let us consider the focusing condition of the nominal double reflection: rf = F tan 4τ . Since rt − rf = h tan θ ≃ 0, we can replace the condition with rt = F tan 4τ . Because 2τ is small angle, F tan 2τ can be also reduced to 2F τ = 21 4F τ ≃ 12 rt . Finally, substituting it to the term of rt − F tan 2τ , we can derive the simple expression of the relation as follows: rd = 0.5rt + F tan θ.

(3)

We again note that the sign of θ is negative, different from that for the secondaryonly and backside reflections.

Secondary-Only Reflection The secondary component is deviated at an angle of 3τ + (3τ − θ ) = 6τ − θ by the reflection on the secondary shell. For the tightly nested mirrors, while offaxis X-rays with θ < τ hit the frontside surface of the primary shell before the reflection on the secondary shell, those with θ > 2τ hit the backside surface of the inner primary shell. Hence, an angle condition for the secondary shells where the secondary component occurs is given by τ < θ < 2τ (see also Fig. 4b). The condition implies that the secondary component also occurs in a limited radial range of the mirror aperture, depending on a given off-axis angle. The condition for the tilt angle also tells us that the secondary component is bent by 4τ –5τ , larger than the bending angle for the nominal double reflection (4τ ). It indicates that the radial coordinates on the mirror aperture and the detector plane of the secondary component are in the opposite directions against the optical axis. Hence, for a given off-axis angle θ , the secondary component appears on only one side of the detector plane. The relation between the radial coordinates on the mirror aperture and the detector plane for the secondary component is shown in Fig. 7. This figure indicates that the area on the mirror aperture where the secondary component occurs is on the opposite side of that for the primary component. Similarly, the relation for the secondary component can be derived. The radial coordinate on the detector plane is given by rd = rt − (h + l) × tan θ − (F − l) × tan(6τ − θ ), as is shown in Fig. 5b. The relation can be reduced to rd = rt − F tan(6τ − θ ),

(4)

by using the approximation of h ≪ F and l ≪ F . We can expand F tan(6τ − θ ) to F tan 6τ − F tan θ . By using the small-angle approximation, the term of F tan 6τ is reduced to 6F τ = 23 4F τ ≃ 32 rt . Therefore, we obtain the relation for the secondary component as follows:

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rd = −0.5rt + F tan θ.

(5)

This expression is a powerful tool for the collimator design in which the secondary component should be blocked. The reduced relations for the primary and secondary components are indicated in the upper panels of Figs. 6 and 7, designated as “primary line” and “secondary line,” respectively. The result of the ray-tracing simulations is consistent with the relations. Since the reflectivity of the backside surface is low, some lines which correspond to the paths of multiple reflection are dim or eliminated. However, the relations allow us to perform a simple geometrical calculation for the collimator design. We note again that the secondary component is the main contribution to the stray light on the detector plane. Since the reflection occurs only once in the mirror, the flux of the secondary component is still large even for soft X-rays. If the incident angle to the secondary shell of 3τ − θ exceeds a critical angle of the reflective material, the contribution becomes rapidly decreased. Hence, the X-ray spectrum of the stray light no longer keeps information on the correct energy spectrum of the source. For the Suzaku XRTs, the effective area of the secondary component is ∼1/100 of the on-axis effective area. Figure 8 shows an angular dependence of the effective areas of the secondary component. One remarkable feature is that the flux of the secondary component is almost independent of the off-axis angle. As the off-axis angle is large, the radial coordinates of the secondary component on the mirror aperture become large, leading to the increase in the tilt angles of the secondary shells. Hence, the incident angle on the secondary shell does not change significantly, which causes slow decrease in the flux of the secondary component. At an off-axis angle of >70′ , the secondary component disappears since there are no primary shells that meet the angle condition (τ > θ/2). A similar trend is shown in the ray-tracing simulations for the eROSITA telescope (see Fig. 9), implying that the fraction of the effective area for the stray light is a common feature of the Wolter-I type optics.

Backside Reflection The backside component is a bit complicated to an analytical treatment. The first hit point is the backside surface of the primary shell. Because of a rough surface of the shell substrates, the reflected X-rays are widely scattered; a large scattering angle makes it difficult to predict the precise direction after the backside reflection. As the number of the backside reflections increases, the probability that the incident X-rays survive without absorption in the mirror becomes quite small. Multiple reflection components including the backside reflection can be found by the raytracing simulation (see Figs. 6 and 7). However, their actual contribution to the stray-light image is negligible so that we focus on here the backside component that causes the backside reflection only once. The dominant X-ray path of the backside component is (1) backside reflection on the substrate of the primary shell → frontside reflection on the primary shell → frontside reflection on the secondary shell or (2) backside reflection on the substrate of the primary shell → frontside reflection on the secondary shell (see Fig. 4c). We

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Fig. 8 Angular dependence of the effective areas of the secondary component. Red-filled circles are the effective areas measured at off-axis angles of 20′ , 30′ , 45′ , and 60′ for the Suzaku XRT before the pre-collimator’s installation. Those measured after the installation are shown by redfilled triangles. The effective areas at 1.49 (red), 4.51 (green), and 8.04 (blue) keV obtained from the ray-tracing simulations are also superposed with dashed and solid curves (This figure is adapted from Mori et al. 2005)

note that, for the second path, the incident angle to the secondary shell amounts to ∼3τ , implying that the reflection probability is relatively small. In addition, if the X-ray is reflected on the secondary shell, the bending angle of the reflected X-ray becomes ∼6τ . Thus, a part of the reflected X-rays are possibly hit on the backside surface of the inner secondary shell although it depends on the hit position of the frontside surface of the secondary shell. For the first X-ray path, we also note that the frontside reflection on the primary shell followed by the backside reflection plays a role of cancelling the reflection. A tilt angle of a primary shell and a tilt angle of its inner one are almost the same, implying that the incident and reflection angles on the backside and frontside surfaces of these two primary shells are all θ − τ . The deviation angle is then (θ − τ ) + τ = θ at the bottom of the primary shell. Hence, this backside component can be considered to be similar to the secondary component. Thus, the reflected X-rays are deviated at an angle of 6τ − θ . This is indeed indicated in Fig. 7, which represents that both the secondary component and the first path of the backside component are on the same line. The angle condition of the backside component which follows the first X-ray path is given by 2τ < θ < 3τ under the assumption that the scatter by the

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Fig. 9 Ray-tracing simulations for the eROSITA telescope, single reflection rejection of the X-ray baffle (for mirrors without profile error or roughness)

backside reflection is negligible. The condition is determined by the requirement that both the backside and the frontside reflections occur on the primary shell. The survived X-rays which escape from the mirror without absorption have a bending angle of 3τ –4τ calculated directly from the deviation angle of 6τ − θ and the angle condition of 2τ < θ < 3τ . Therefore, the stray-light image of the backside component appears on the opposite side of that for the secondary component (see also Fig. 2). Different from the primary and secondary components, the condition described above in which the backside component occurs is not exact. Since the X-ray scattering on the backside surface makes the direction of the reflected X-rays spread, there may be the cases where the shells that do not meet the condition contribute to the stray-light image on the detector plane. Therefore, the aperture area which brings about the backside component is larger than that for the secondary component. From the reflectivity viewpoint, the flux of the backside component created from a given shell is small. Moreover, the reflectivity of the backside reflection has a strong energy dependence. The backside component rapidly disappears above ∼2 keV, which is indicated in Fig. 2 by the difference in the surface brightnesses. However, the large aperture area accumulates the backside component which makes non-negligible contribution to the stray-light image. We note that effective methods to block the backside component have not been developed so far. One reason is a

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technical difficulty in blocking the X-ray path of the backside reflection without affecting the X-ray focusing performance. Because of the large scattering, there seems to be no simple structure to block the backside-reflected X-rays efficiently. The modelling of the X-ray scattering is another difficult issue. So far, many theoretical treatments of the X-ray scattering have been developed: the models invoking a plane-wave Born approximation (Sinha et al. 1988) or bidirectional reflectivity distribution function (Kunieda et al. 1986). However, the surface condition of the shell substrate usually does not meet the requirements for which these theoretical models can be applied. For example, the roughness of the backside surface for the aluminum thin foils, which were used for the Suzaku X-ray mirror, was an order of micrometers (σ = 1–2 µm), much larger than that of the frontside surface (σ = 4 Å). The rough surface of the aluminum foils was created by rolling an aluminum plate, which makes a thin sheet with a thickness of 150 µm. Thus, the roughness had a dependence of the rolling direction. Since the surface condition of the substrates used for the X-ray mirror shells is different from mission to mission, it is almost impossible to establish a unified X-ray scattering model that can be applied to the backside reflection. One method we can mitigate the backside component is that we should select substrates with the X-ray reflectivity as low as possible. In order to the future precise prediction of the backside component, the X-ray scattering theory applied to micrometer-scale surfaces should be examined as well.

Advanced Analytical Treatment The treatment of the stay-light components described above is a simple one where we employed a geometrical optical calculation for a cross section of the X-ray mirror only in the off-axis plane. In addition, we assumed the conical approximation of the Wolter-I type optics and used several approximations to simplify the analytical treatment. In reality, however, the stray X-ray light has an azimuthal dependence. Thus, we usually use a ray-tracing simulator to investigate the stray light for a given optics. Recently, Spiga (2016) developed analytical formalism for the effective areas of the nominal double reflection, the primary component, and the secondary component (see also Spiga 2015). A vignetting coefficient was introduced to take into account the geometrical area of the mirror shells responsible for each component, which gives us a unified treatment for off-axis X-rays. The effective area was easily calculated by performing an integral in the formalism. Although the integrand in the formalism includes reflectivity terms, a numerical integration can be performed to obtain the effective area. Here, we would emphasize that the required resource for the numerical integration is much smaller than that for the ray-tracing simulations. Spiga (2016) also carried out the comparison between the analytical calculation and the ray-tracing results; the ray-tracing simulation was well reproduced by the calculation. In other words, this analytical treatment makes a good estimation of the effective areas for the primary and secondary components without writing a complicated ray-tracing code. Hence, it has the advantage of enabling a quick assessment of the stray light for a given Wolter-I type optics.

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Design of the Stray-Light Baffle As already mentioned, the secondary component is a main source of the straylight image contaminated in the detector field of view. We now discuss a collimator design that focuses on the blocking of the secondary component only. The effective area of the secondary component is about two orders of magnitudes smaller than the on-axis effective area. The secondary component creates a part of a distorted radial pattern on the detector plane. The X-ray path of the secondary component is simple; the incident X-rays go through above the top of the primary shell when entering into the X-ray mirror (see again Fig. 4b). Thus, a structure aligned onto each primary shell can easily block the secondary component. At least, the structure is required not to affect the on-axis X-rays. The simple structure for the reduction of the secondary component is a thin cylindrical shell that is radially aligned with the corresponding primary shell. If the thickness of the cylindrical shell is smaller than that of the primary shell, the on-axis effective area and angular resolution are unaffected. The next problem is what the optimized design parameters for the structure should be to maximize the performance of the X-ray collimator, without degrading the one of the X-ray optics. Hence, the key parameters are the height and thickness of the cylindrical shell. We designate the cylindrical shell as a blade hereafter. Let us consider an X-ray with an off-axis angle of θ and some pairs of the primary and secondary shells inside the X-ray mirror. Similar to the previous subsections, we represent the tilt angle of the primary shell by τ . The angle condition of τ < θ < 2τ for the secondary component indicates that the primary shells with a range of the tilt angle of θ/2–θ contribute to this component. Thus, as is indicated in Fig. 10, a higher blade is required for the outer shell to block the X-ray path of the secondary component. Since the primary shell with a tilt angle of θ is parallel to the incident X-rays, the solid angle subtended to the secondary-shell surface becomes maximum. In other words, the maximum height for a given off-axis angle of θ can be calculated from the case of the primary shell with the tilt angle of θ . We can calculate the blade height, H , required to block this X-ray path completely as below. Again, we define the focal length of the X-ray mirror to be F . The height of the mirror shell is represented by h. We assume here that the radius of the frontside surface of the blade is the same as that of the primary shell, i.e., rp . The case of τ = θ in Fig. 10 shows that the requirement for the blade height is given by rp − (H + h) tan θ ≤ rb ,

(6)

where rb represents the radius of the bottom of the backside surface of the inner primary shell (rb < rp ). This equation can be reduced to H ≥

rp − rb − h. tan θ

(7)

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Fig. 10 Schematic drawing of the blade heights to block the secondary component at an off-axis angle of θ. The larger the tilt angle of the mirror shell becomes, the higher the blade is required (This figure is adapted from Mori et al. 2005)

We then estimate the maximum gap of rp − rb . As is noted in the previous subsection, only a part of the stray-light image created by the secondary component contaminates the detector field of view. The relation between the radial coordinate on the detector plane (rd ) and rt is given by rd = −0.5rt +F tan θ . Hence, if we assume the half size of the detector field of view to be R, only the shells within a radial range between rp,min and rp,min + 2R contribute to the stray-light contamination in the detector field of view. The secondary component occurred at the primary shell with a tilt angle of τ = θ/2 reaches at the center of the detector field of view. Thus, rp,min ∼ F tan 4τ = F tan 2θ . Using a smallangle approximation, the relation can be reduced to rp,min = 2F θ . The maximum radius of the primary shell is thus estimated to be rp,max = 2F θ + 2R. Considering that rp ∼ F tan 4τ = 4F τ , the tilt angle of this primary shell (τmax ) is given by R . We can approximate the gap of rp − rb as 2h tan τ ≃ 2hτ . Thus, τmax = θ2 + 2F the maximum gap is given by 2hτmax = hθ + hR F . Then, the maximum height of the blade can be obtained from

Hmax =

hθ + hR F −h tan θ

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Fig. 11 Radial dependence of the blade height required to block the secondary component. The curve is calculated based on the design of the Suzaku XRTs. Distributions of the blade heights are also indicated by vertical lines. The off-axis angles of the secondary component are assumed to be 20′ , 30′ , 40′ , 50′ , and 60′ . The constant blade height of 30 mm actually adopted for the Suzaku pre-collimator is shown with a dashed line (This figure is adapted from Mori et al. 2005)

≃

hR , Fθ

(8)

where we use a small-angle approximation of tan θ to derive the second equation. This result indicates that the required height can be easily estimated from the basic parameters only. An ideal curve required for the blade heights is an envelope of the maximum heights obtained by changing the off-axis angle θ . Figure 11 shows an example of the calculation carried out for the pre-collimator design for the Suzaku XRTs. Since the maximum height of the blade is proportional to 1/ tan θ and the angle condition of the secondary component is given by τ < θ < τmax , the height of the inner blade becomes larger than that of the outer blade. We note that a radial dependence of the required blade height makes an issue of the mass production of the blades, especially for the thin-nested foil mirrors. The mount of the X-ray collimator on the mirror entrance makes the field of view of the X-ray mirror narrower. Here, the field of view of the mirror is normally defined by the full-width half maximum of the vignetting function of the X-ray optics: the angular response of the effective area. We should determine the optimum design of the X-ray collimator in terms of the reduction rate of the stray light, the field of view of the X-ray mirror, the production, and the structure with enough

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mechanical strength that stands for the launch environment. We show an example of the trade-off study between the stray light and the mirror’s field of view in the section of the Suzaku’s pre-collimator. Another attention induced by the collimator’s mount is that the collimator itself becomes a cause of the stray light. New X-ray paths in which the reflection occurs on the blades in turn become a cause of stray light. If the blade surface is rough, similar to that of the backside surface of the mirror shells, the stray light created by the blade is probably mitigated. However, it is difficult to measure accurately the contribution of the stray light created by the X-ray collimator. For the Suzaku XRTs, the pre-collimator’s blades had line-like marks made by the rolling. To make the X-ray reflectivity as low as possible and to spread the X-ray scattering angles, the marks were arranged normal to the direction of incident X-rays. Similar to the backside reflection, the understanding of the X-ray reflection on rough surfaces is necessary for the suppression of the stray light newly added by the mount of the X-ray collimator.

XMM-Newton The XMM-Newton spaceborne X-ray observatory, an ESA cornerstone mission, was launched in December 1999 and is still operational after 22 years. It consists of three telescopes with identical 7.5 m focal length Wolter optics (Aschenbach et al. 2000; Burger et al. 2000). While the optical and mechanical design of the XMM mirror modules was already fixed in 1995 and demonstration models were built and tested, the X-ray baffle was still under design (de Chambure et al. 1996), since it had been recognized that single reflections from one or more of the hyperboloid surfaces would introduce a high level of confusing stray flux in the field of view of the detectors, created by Xray sources close to, but outside, the field of view from a cone angle of 15 arcmin (de Chambure et al. 1999a). An early conception provided an almost perfect X-ray baffle consisting of a set of cylinders, one for each mirror shell, placed in the shadow zones in front of the mirror shells (see Fig. 12) and each with an individually optimized height (Aschenbach et al. 2000). This, however, was given up because a realization seemed not feasible. de Chambure et al. (1999b) give a detailed description of the design and development of the XMM-Newton X-ray baffle and the following passage, which describes the design trade-offs, quoting his paper: “The only rays, which come to the sensitive area of the focal plane are rays, which can be blocked by an annular concentric cylinder in front of every mirror shell.” Their principle of elimination of singly hyperboloid reflected rays is sketched in Fig. 13. The cylinders have individual lengths between 25 and 160 mm according to the field of view of the associated mirror shell. The baffle cylinders had to be equipped with light traps to prevent additional stray light from their large surfaces. For this purpose, the cylinders should be divided into a stack of “sieve plates,” which both allows a smaller wall thickness than that of the mirror shells and minimizes the areas where

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Fig. 12 Functionality of an X-ray baffle: the single reflections (red) should be blocked, while the double reflections (green) should all pass; an effective way to cut away the single reflections is blades (gray) on top of each mirror shell (yellow); the light gray areas between the mirror shells can be potentially also used for a baffle

light could be scattered toward the mirrors. The tapered edges of the cylindrical rings further reduce the stray light. Due to the limited space in front of the mirror module, which is partly occupied by the “spider” that holds the mirror shells, finally a system of only two sieve plates was adopted. This system cannot fully eliminate the single reflections, but it is able to reduce them by a factor of 5 to 10 depending on the location on the detector. According to de Chambure et al. (1996, 1999a,b), the precise manufacturing of the finely structured sieve plates with 59 × 16 tiny strips was a challenge. It was finally achieved by using wire electrical discharge (WED) machining to cut out material from a massive Invar plate, which, however, led to machining times of 400 to 500 h for each of the two sieve plates. As the final metrology with a coordinate measuring machine (CMM) revealed, the WED technique allowed to limit average radial error to about 25 µm. The requirement on the accuracy of the radial position of the edges of the vane strips of the sieves with respect to the position of the mirrors was to be better than 100 µm, including manufacturing, assembly and integration errors, and displacement due to thermal conditions. As a consequence, the co-centering of all mirror shells (better than 50 µm) became more stringent. To avoid optical stray light from the X-ray baffle directly in front of the optic, the lateral surfaces of the strips were chamfered by 5◦ , and the edges of the strips were made very sharp (radius smaller than 20 µm). All the baffle surfaces (including the edges of the vane strips) facing the mirrors were blackened. The accurate positioning of the X-ray baffle with respect to the optic was achieved by taking both the optic’s and the X-ray baffle’s centers as references, which are defined by two reference points on the mirror module structure and by two

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Fig. 13 Sketch of the opto-mechanical principle of the XMM-Newton X-ray baffle (after de Chambure et al. 1999a): X-rays are coming from the top progressing to the focal plane. Ray #2 is reflected slightly before the end of the hyperboloid is reached and travels to the focus of the telescope. Ray #1 has an inclination against the optical axis which is lower by the radius of the field of view (δε ) and to the edge of the field of view in the focal plane. Any singly hyperboloid reflected ray to be blocked is contained in the bundle bounded by the angles ε0 and εi

reference points on the X-ray baffle structure, respectively. These reference points were used to perform the corresponding alignment of the both parts (de Chambure et al. 1999b). Figure 14 shows the sieve plate baffles mounted in front of the three XMM-Newton mirror modules. The performance verification for all f ive mirror modules (three FM, two FS) was done at the Centre Spatial de Liége (CSL) in Belgium using a parallel EUV beam. The testing included a verification that the imaging performance in terms of on-axis point spread function (PSF) and on-axis effective area did not degrade after the mounting of the X-ray baffle. To demonstrate the stray-light rejection ability of the X-ray baffle, images for effective area measurements were taken from −80 arcmin off-axis to +80 arcmin off-axis in steps of 5 arcmin. In conclusion, the

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Fig. 14 The lower module of the XMM Flight Model during preparation for a 10-day thermal vacuum testing at ESTEC in January 1999; the X-ray baffles are mounted in front of all three X-ray optics (Photograph courtesy of ESA)

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Fig. 15 XMM-Newton data: bright point source (Sco X-1) outside field of view, 40 arcmin offaxis (left) and bright extended sources (Crab) outside field of view, 45 arcmin off-axis (right), data analyses by Michael Freyberg, MPE

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CSL tests confirmed that there was no on-axis performance degradation and that the stray-light rejection rate was 80%, which was close to the predictions. Figure 15 shows the remaining stray light from extremely bright sources, a point-like and an extended one, when they are slightly outside the field of view.

Suzaku and Hitomi Suzaku Pre-collimator Suzaku, the fifth Japanese-US collaborative mission, was equipped with a nested thin-foil X-ray mirror, called X-ray telescope (XRT) (Serlemitsos et al. 2007). The foils used in the X-ray mirror were produced by a replication technique; a reflective gold surface is replicated from a glass mandrel to a thin aluminum foil. Since the thickness of the aluminum foil is 180 µm, a lightweight X-ray optics with a large effective area was achieved. Since the problematic stray light was already recognized for the same nested thin-foil mirrors adopted in ASCA, a collimator to reduce the stray light, called pre-collimator, was planned to be mounted on the Suzaku’s X-ray mirror (see Fig. 16). The detail in the design of the pre-collimator, especially its height to determine the reduction efficiency, is already described. The basic structure of the precollimator is that a thin aluminum blade is arranged onto each mirror foil to block the stray-light path of the secondary-only reflection. As is explained above, the ideal distribution of the pre-collimator heights is proportional to 1/ tan θ , where θ is an off-axis angle of the stray light. However, the different heights of the blades caused a difficulty in the mass production of the blades by heat forming. Alternatively,

Fig. 16 Picture of a pre-collimator quadrant (This figure is adapted from Mori et al. 2005)

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we chose a constant height of the blades. After a trade-off study mentioned below between the field of view and the reduction efficiency by changing the blade height, we decided that the blade height should be 30 mm, roughly 1/3 of the X-ray mirror foil (4 inch = 101.6 mm). A blade with a height of h makes shadows on the mirror aperture for the X-rays with an off-axis angle of θ as is shown in Fig. 17. We first estimated the geometrical areas of the shadows created on the aperture in a radial range of rout –rin by a simple analytical calculation. Here, rin and rout represent the radii of the frontside surface of the top of the primary foil and the backside surface of the top of the inner primary foil, respectively. The blade makes two crescent-shape shadows (S1 , S2 ) on the opposite sides of  the mirror aperture. The angle of AO ′ O is given by  h tan θ/2 θ

AO ′ O = cos−1 ≃ π2 − h2rtan . Thus, the geometrical area of the shadow rout out (S1 ) is calculated by  2π − AOA′

AO ′ A′  − 2π 2π   ′ 2 AO O 2 1− = π rout π = hrout tan θ.

2 S1 = π rout

(9)

Similarly, another area (S2 ) is given by S2 = hrin tan θ . These results imply that the shadow area is radially dependent. While the analytical treatment to estimate the reduction rate of the field of view of the X-ray mirror was difficult, the ray-tracing

Fig. 17 Schematic drawing of shadows on a mirror aperture caused by the pre-collimator mount. Parameters used for the calculation of the geometrical areas (S1 , S2 ) of the shadows are also indicated

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Fig. 18 Trade-off study of the field of view and reduction rate of the secondary component by changing the blade heights

simulation was an easy way to obtain robust results. In addition, the simulation can also estimate the reduction rate of the effective areas of the secondary component in the ideal case of the pre-collimator mount. Thus, we prepared photon files in which incident photons do not go through the shadow area; we performed ray-tracing simulations using these photon files. One advantage of this method is that we do not need to construct the detailed structure of the pre-collimator. This method did not consider full interactions between the X-ray mirrors and the incident photons. However, the result was almost consistent with those by the full simulations, which verifies the method using the blade shadows. We show the relation between the reduction rates of the mirror’s field of view and the effective areas of the secondary component when changing the blade height in Fig. 18. As the blade height becomes large, the reduction rates of the field of view and the effective area increase. The relation shows that the curves have a kink at which the best performance for the X-ray optics is obtained. In the case of the Suzaku pre-collimator, the optimized blade height was 30 mm. If we choose the blade height of >30 mm, the reduction rate of the effective area changes a little. However, the mirror field of view rapidly decreases, which concludes that the height over 30 mm has little benefits. We note that there was a gap between the top of the primary foil and the bottom of the blade since both the foils and the blades were supported separately by structures explained later. Hence, we finally determined that the blade height and length were set to 30 and 22 mm, respectively.

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The blades are made of bare 1000-series aluminum with a thickness of 120 µm. The difference between the blades and foils is that the blades have no reflective coating such as gold, iridium, or multilayer and that the blades have a cylindrical shape. This is why we employed the same procedure for the mass production of the pre-collimator blades as that for the foils (Mori et al. 2005, 2012). Aluminum sheets are cut into a strip shape by electro-discharge machining (EDM) which enables us to obtain the precise height of 22.0 mm. A sparkle generated by the EDM creates tiny thorns with a few micrometers on the edge of the aluminum strip. Since the aluminum strips are stacked on a mandrel, the remaining thorns become a cause of figure errors. Thus, we removed the thorns by shaving the edges using a grinder. After the shaving, each aluminum strip is rolled to add a given curvature. The rolled strips are stacked on a mandrel. The mandrel is a precision-machined aluminum cylinder that has a smooth surface with a sub-micrometer roughness. The stacked strips are surrounded by a silicon sheet with a spacing of ∼1 mm. A Kapton film is attached on the top of the stacked strips and the silicon sheet. The aluminum mandrel has a hole connected to a pump to evacuate air remaining in the space. When the pump is turned on, the Kapton film presses the stacked strips onto the mandrel’s surface by atmospheric pressure. The mandrel with the strips pressed is placed in an oven and then is heated up to 160–180 ◦ C for ∼10 h, which releases internal stress induced by the rolling. This is a heat-forming method that is applied to the foil production. Using a laser profiler, the axial figures of the strips are measured to confirm that the figure errors are small enough for the blades to be inserted into grooves of a supporting structure. Since a length in the azimuthal direction is different for each blade, we cut the extra length of the corresponding strip by a cutter. To hold the blades with a cylindrical shape, we introduced an alignment plate as is shown in Fig. 19. The alignment plate had an open window with grooves carved in the top/bottom sides of the window. The grooves were made by the EDM at Ohishi Co., Ltd. The shape of the groove was a rectangle joined with a trapezoid that was designed for easy insertion. The width of the groove at its bottom was set to 140 µm, which is between the blade thickness and the foil thickness. Thus,

Fig. 19 Picture of an alignment plate used for the Suzaku pre-collimator (This figure is adapted from Mori et al. 2005)

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the accuracy of the radial position of each blade is mechanically limited to 20 µm in vicinity of the alignment plates. The relative uncertainty of the radial positions of the grooves was investigated by an NH series laser profiler, a three-dimensional measuring instrument produced by Mitaka Kohki Co., Ltd. The precise EDM cut for the grooves resulted in the relative uncertainty of 5 µm. Hence, the alignment plates enabled us to give a position determination of an order of ±10 µm, much smaller than an alignment margin of ∼30 µm. The width of the alignment plate was 1 mm, which was narrower than that of the alignment bars, which supported the foils, not to interfere with the mirror aperture. Another important issue of the pre-collimator design was that there was a gap between the primary foils and the pre-collimator blades since the X-ray mirror and pre-collimator were fabricated separately. Carrying out ray-tracing simulations for a trade-off study, we found that the gap should be less than 8 mm to block the stray light going through this gap. Since the blade height is 30 mm and the thicknesses of the foils and the blades are 180 and the stray light with an  120 µm, respectively,  incident angle of θ  64′ = tan−1 (0.18 + 0.12)/2/8 is hit on the top surface of the primary foils. The gap between the top of the primary foils and the top surface of the mirror housing was 5 mm. Hence, an allowable gap between the pre-collimator’s bottom surface and the bottom of the blades is 3 mm. However, the thickness of the bottom frame was designed to be 5 mm to maintain the mechanical strength of the pre-collimator housing. We then determined that the alignment plates were once lifted up by 2 mm for the blade insertion into the grooves and then returned to the original position.

Optical Tuning It was a tough challenge to mount the pre-collimator housing on the X-ray mirror so as to match each blade position to that of the corresponding primary foil. The alignment was a key issue not only to block the stray light as was expected but also not to reduce the on-axis effective area of the X-ray mirror. Since the blades were already inserted into the grooves of the alignment plates, an independent position alignment for each blade cannot be performed. We could only move the alignment plates in the radial direction to adjust the radial position of the whole blades. The alignment margin was ∼30 µm as described above. We performed a tuning of the alignment plates that maximizes the optical throughput. We first measured the optical throughput of the X-ray mirror before and after the pre-collimator mount. A parallel optical beam was illuminated to the mirror and then the throughput was measured by a photo sensor diode. After the pre-collimator mount, the optical throughput was decreased. Next, we placed a mask that limits the aperture only in vicinity of the alignment plate to be tuned. We measured the change of the limited optical throughput while moving the alignment plate radially with a step of several micrometers. The maximum throughput was obtained where the blade positions were best aligned with those of the primary foils. Because of the alignment margin, the profile of the optical throughput had

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a trapezoid-like shape; the position of the maximum throughput was obtained from the center of the flat top. We tuned the radial positions of all the alignment plates one by one in the same manner. Finally, we again measured the optical throughput and then confirmed that the throughput was recovered to that before the pre-collimator mount.

On-Ground and In-Orbit X-Ray Calibrations The X-ray performance of the pre-collimator was measured at the ISAS 30 m beamline facility (Kunieda et al. 1993; Shibata et al. 2001; Hayashi et al. 2014). The key characteristics related to the pre-collimator were the effective area of the stray light, the reduction rate of the on-axis effective area by the pre-collimator mount, and the field of view of the XRTs. The results are shown in the literature (Mori et al. 2005). The ISAS 30 m beamline facility can illuminate an X-ray beam with high parallelism of 15′′ × 15′′ . The X-ray mirror and the detector (a CCD camera or a proportional counter) were separately placed on two three-axis movable stages. These stages were moved synchronously, which enables us to illuminate the parallel X-ray beam to the 1/4 aperture of the X-ray mirror. We measured the stray-light images in the detector field of view (see Fig. 20) and effective areas of the straylight components (secondary-only and backside) by the proportional counter and then confirmed that the pre-collimator blocks the stray light as was expected (see red triangles in Fig. 8). While the stray light was effectively blocked, the on-axis effective area was reduced only by ∼0.5%, implying that the optical tuning method was successfully verified. The results of the in-orbit calibration of the Suzaku XRTs were summarized in Serlemitsos et al. (2007). The in-orbit calibration of the Suzaku pre-collimator was carried out for given off-axis and azimuthal angles because of the limitation of the observational times. The protection of the stray light allowed us to carry out many successful observations such as the galactic center and the outskirts of the cluster of galaxies (Simionescu et al. 2011). At the same time, we found that the reduction of the stray light has a dependence on a roll angle of the satellite. The detailed measurement of the roll-angle dependence is shown in the literature (Takei et al. 2012). This dependence would be caused by a slight difference in curvatures between the foils and the blades. Since the blades were supported by the alignment plates and the alignment plates were moved at the optical tuning, the blade curvature was not perfect compared with the ideal cylindrical design. Although the tuning was a tough problem, we consider that we did the best as much as possible to achieve the effective stray-light reduction for the tightly nested thin-foil mirrors.

Hitomi Pre-collimator Hitomi, the next Japanese-US collaborative mission after Suzaku, was also equipped with four nested thin-foil X-ray mirrors. Two of which were SXTs (Okajima et al.

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Fig. 20 Stray-light images at 20′ , 30′ , 45′ , and 60′ off-axis taken by an X-ray CCD camera installed in the ISAS 30 m beamline. The images were taken without (left panels) and with (right panels) the pre-collimator. A white circle indicates a field of view of a proportional counter by which the effective areas of the secondary component were measured (This figure is adapted from Mori et al. 2005)

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2016) and the others are hard X-ray telescopes (Awaki et al. 2014). The HXT employs the reflective coating of Pt/C multilayers that allows us to perform imaging spectroscopy up to 80 keV. The SXTs were similar to the Suzaku XRTs. The SXTs were provided to a microcalorimeter and an X-ray CCD camera. Since the field of view of the microcalorimeter was small, the stray light was negligible even for the secondaryonly reflection. The X-ray CCD camera had a wide field of view of 50′ × 50′ . Since the similar performance for the stray-light reduction was required to the SXT for the CCD camera, the blade height of the pre-collimator was designed to be 65 mm. For a given off-axis angle of θ , the maximum radius of the primary shell that creates the secondary component is given by 2F tan θ + 2R. Since the focal length of the SXT becomes 5.8 m, larger than that of the Suzaku XRTs, it implies that a radial range for the Hitomi SXTs to be considered for the stray-light reduction was larger than that for the Suzaku XRTs. The thicknesses of the SXT substrates were 150, 200, and 220 µm, dependent of the radial position of the foils. The thicker foils allowed us to mitigate the limitation of the gap between the blades and foils. Hence, we did not need to lower the alignment plate down against the bottom frame of the pre-collimator’s housing. In addition to the change of the design parameters, the supporting method of the blades was slightly changed; the blades were adhered to the grooves of the alignment plates since environmental conditions were severe. The design parameters of the HXT pre-collimator were as follows: the height was 50 mm, the length was 35 mm, and the thickness is 150 µm (Mori et al. 2010). The secondary component emerged at the off-axis angles of 10′ –30′ , according to the mirror design. The aluminum blade was transparent for the X-rays above 10 keV. We examined another material for the blade, SUS304 with a thickness of 50 µm. For the X-rays at 30 keV, the reduction rates of the secondary component were comparable to each other. The difference has occurred at 50 keV. A part of the secondary component with the off-axis angle of 20′ –30′ remained in the detector field of view. However, the reduction rate was still ∼10%, compared with that without the pre-collimator. In addition, the detection limit of the HXT + detector system was determined by the non-X-ray background. Hence, we chose the aluminum blade for the HXT pre-collimator. We also carried out the ray-tracing simulations of two types of scientific cases, the observations of the cosmic X-ray backgrounds (CXB) and the galactic center region, to demonstrate the improvement of the HXT performance. The stray-light contamination from the CXB was reduced to be from 33% to 8.7% by mounting the pre-collimator. The simulated images of the mapping observations of the galactic center also indicated that the stray-light flux was reduced by half in the source-free region. For the HXT pre-collimator, there were two major differences from the SXT pre-collimator. Instead of the alignment plate, we used the alignment bars which had grooves on the both sides for the primary foils and blades. The positional accuracy was determined by the machining accuracy of the EDM. Since the top of the blade is supported by another alignment bar, however, the optical tuning was still required to keep the blade configuration as a cylinder. Since the top and bottom of the blade were supported by two alignment bars, we need to insert the blades

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from the top view of the X-ray mirror, similar to the foil insertion. We note again that we performed the optical tuning of the radial position of the alignment bars in which the optical throughput becomes maximum. The X-ray calibration of the stray-light reduction was carried out at ISAS 30 m beamline facility for the SXTs and SPring-8 for the HXTs. The results showed that the stray light was reduced as expected (Sato et al. 2016; Iizuka et al. 2018; Mori et al. 2018). Unfortunately, since the Hitomi’s in-orbit operation was short, the inorbit performance of the stray-light reduction was not investigated.

eROSITA eROSITA (extended ROentgen Survey with an Imaging Telescope Array) is the primary instrument on the Spectrum-Roentgen-Gamma (SRG) mission, which was successfully launched on July 13, 2019, from the Baikonur Cosmodrome. After the commissioning of the instrument and a subsequent calibration and performance verification phase, an all-sky survey started in December 2019 and shall last until the end of 2023 to be followed by a pointing phase (Predehl et al. 2021). eROSITA’s X-ray telescope consists of 7 identical and co-aligned mirror modules, each with 54 nested Wolter-I mirror shells (Burwitz et al. 2014; Friedrich et al. 2012, 2008). An X-ray baffle in front of each mirror entrance protects against X-ray stray light from single reflections from the Wolter mirrors. Similar to XMM-Newton, the eROSITA X-ray baffle was developed not as part of the mirror module. It has been designed as a separate mechanical piece to be connected and aligned later to the mirror module with a minimum of mechanical and thermal coupling (Friedrich et al. 2014). The need for baffling the eROSITA optic is obvious: The instrument has a large field of view with 61 arcmin diameter, which results in a high grasp during the 4-year all-sky survey. Unlike in pointed observations, the off-axis source detections over the entire field of view contribute essentially to the sensitivity of the survey. However, single reflections, mainly from the hyperbola part of the Wolter mirrors, are frequent at larger off-axis angles. They come from X-ray sources outside the field of view and would contribute an additional background component or, in the case of bright sources, create false sources in the field of view. According to Fig. 4b that illustrates the “θ ≈ 2τ rule,” the single reflections for the eROSITA optic originate from off-axis sources within a range from about 40 to 180 arcmin. This has been confirmed by ray-tracing simulations, which give a more detailed and quantitative picture. The range of contributing off-axis sources shrinks for photons with energies >2 keV, because the reflectivity of an increasing number of mirror shells, starting with the outer ones, drops to zero with increasing photon energy. Ray-tracing has also revealed that there is a minor contribution from single reflections at the parabola part of the innermost mirror shells, which becomes visible already for X-ray sources at an off-axis angle of 20 arcmin so that the X-ray source and its single reflections are both in the field of view. In total, the amount of stray light caused by single reflections at lower energies (calculated for 1 keV)

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Fig. 21 Sketch of a single baffle shell

adds up to 40% of the twice reflected photons resulting in a correspondingly large background contribution, if no baffling would be foreseen. For 4 and 7 keV, the possible background contribution would be 43% and 35%, respectively. The eROSITA X-ray baffle needed a special design adapted to the optical parameters of the mirror module: The aperture ratio of up to 4.5 and the large field of view require that the baffling of single reflections has to happen close to the mirror shells; the baffle has to reach inside the envelope of the mirror spider (see Figs. 21 and 22). Therefore, different from XMM, the X-ray baffle could not be realized as a stack of sieve plates. Instead, a system of co-aligned “baffle shells,” one for each mirror shell, was chosen. Since the mirror diameters range from 77 to 358 mm, the incidence angles vary by a factor 4.7 from the outermost to the innermost mirror shell. As a consequence, the ideal height of the baffle shells also varies by that factor, while it was only a factor of 2.3 for XMM-Newton. Thus, for eROSITA it would have been far from optimum to choose a design with a constant height over the entire baffle, which also speaks against a sieve plate design. The comparison between the eROSITA and XMM-Newton mirror modules, with the latter ones being roughly a factor of 2 bigger in all dimensions, demonstrates that downsizing doesn’t make all things necessarily easier. As the eROSITA mirror thickness ranges from 0.2 to 0.55 mm, which is also about a factor of 2 less than for XMM-Newton, the shadow zone in front of the mirror shells (see Fig. 12) is extremely small and is also relatively short due to the large field of view. It became clear that a 100% rejection of stray light would only work at the price of cutting into the incoming beam. Vice versa, restricting the baffle to the shadow zone would

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Fig. 22 Mechanical design of the eROSITA mirror assembly (vertical cut)

make the stray-light rejection inefficient. Therefore, there was a trade-off between efficient stray-light suppression and an unblocked path for the focused light. Finally, a design was chosen which can reduce the stray light by 95% at 1 keV while the impact on the off-axis area is acceptably low. This design restricts the length of the baffle shells to 60 mm for the outermost shell and 120 mm for the innermost shell resulting in the conical shape of its envelope (Friedrich et al. 2014). Actually, this design corresponds widely to the early baffle concept for XMM-Newton, except that the eROSITA X-ray baffle is not designed for 100% rejection of single reflections as an outcome of the above described trade-off. While the optical design of the X-ray baffle was almost fixed, the question arose how the manufacturing could be realized and which material would be the best choice. Several materials were considered in the beginning, e.g., electroformed nickel, CFRP, eroded aluminum, and Invar. Selection criteria were mass, thermal expansion (the baffle frontside sees the cold space and the rear side the warm mirrors), and manufacturing accuracy. After some prototyping, the decision was in favor of a mechanical design based on concentric Invar foils fixed by an own spider. The thickness of these foils should be on the one hand as low as possible for optical reasons, but on the other hand, mechanical stability could not be neglected. A thickness of 125 µm, which is still less than the thickness of the thinnest mirror shells, turned eventually out to be the best choice, although Invar foils with such thickness were not the lightest option; but they fulfill the other criteria very well. The place of the baffle spider was chosen to be at the entrance aperture because there the exact positions of the baffle shells are most important. Ray-tracing simulations showed that deformations of the baffle rings could be accepted up to ±100 µm when the minimum stray-light suppression factor of 90% is considered acceptable. To avoid mechanical stress in the mirror module, the X-ray baffle is attached to it with 16 “soft” triangular-shaped thermal spacers (see Fig. 23). A major development phase was needed to bring the Invar foils into a precise concentric shape within the allowed tolerances. A material with constant thickness and no other inhomogeneities is an indispensable requirement for the later bending

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Fig. 23 X-ray baffle, top and bottom view (left), and mirror assembly with X-ray baffle on top (right)

Fig. 24 Laser cut Invar foils (left) and welded foil on cylinder (right)

process. The manufacturing process was as follows: The Invar foils were first laser cut (see Fig. 24, left) and then bent by moving them between two rollers: a big one covered with a precisely constant radius-shaped rubber layer and a small one made from steel. The bending radius was controlled by adjusting the pressure of the steel roller onto the soft roller. Actually, two soft rollers with different rubber hardness and three steel rollers with different diameters were used in combination in order to achieve good results for the wide range of radii. The bent foils were fixed on aluminum cylinders with the precise diameter of the corresponding baffle shell and were checked for defects and curvature errors, in particular at the free-standing parts between the cutouts (see Fig. 21). Finally, the foils were welded while fixed on the aluminum cylinder (see Fig. 24, right).

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Fig. 25 Sequence of baffle shell integration, from left to right: inserting a baffle shell on cylinder into the grooves of the spider wheel, gluing and curing for 20 h, removing the cylinder, and measuring the surface with contactless distance sensors

The integration of the baffle shells into the spider was accomplished on an integration stand, which allowed the precisely concentric placement of the shells, the injection of glue into the spider grooves, and final metrology with a contactless optical distance sensor (plus reference sensor) resulting in a roundness map of the just integrated shell. The sequence is pictured in Fig. 25. The curing time of the glue triggered a scheme with one shell integrated per day; the in total eight X-ray baffles for eROSITA were manufactured on two integration stands in parallel. The analyses of the roundness mapping resulted in predicted single reflection efficiencies between 90.6% and 92.1%, while the average loss of on-axis effective area was calculated to 2.4%. Mounting and Alignment: Due to the “soft” mounting interface of the baffle, the unification of mirror module and X-ray baffle required an alignment procedure, in which the baffle could be adjusted in all degrees of freedom. A dedicated assembly and alignment stand (Fig. 26) had been built to mount each X-ray baffle to its mirror module. The granite base was adjusted horizontally with an accuracy of a few arc seconds. After the mirror module and the X-ray baffle were fixed on their platforms, a three-step alignment procedure started: 1. Visual pre-alignment in all degrees of freedom 2. Vertical alignment of mirror module and X-ray baffle with autocollimation on reference mirrors 3. Iterative fine adjustment with fine thread screws under optical monitoring with a telecentric lens and a high-resolution camera The telecentric lens allows a straight view onto the baffle and the mirror shells over its entire field of view. With its image scale of 1 : 10, the edges of the baffle rings appeared with a width of 12.5 µm in the camera corresponding to 7.5 pixels. The edges of the mirror shells appeared accordingly wider. An adjustable diffuse illumination from the top of the alignment stand and a ring of bright LEDs on top of the telecentric lens ensured enough brightness and contrast to distinguish the edges of mirror shells and baffle rings, thus giving a criterion for the correct lateral position of the baffle with respect to the mirror module. A lateral alignment accuracy

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Fig. 26 eROSITA mirror assembly in the baffle mounting and alignment stand (left) and image obtained with the optical monitoring system (right)

Fig. 27 Results from X-ray tests (eROSITA FM1) before and after the X-ray baffle was mounted: comparison of measured and simulated single reflection rate as a function of the off-axis angle (left), measurements at ±90 arcmin, where the inner circle of the PSPC detector corresponds to the eROSITA field of view, data analysis by Gisela Hartner, MPE

of 20 µm had been achieved. When the iterative alignment process was successfully completed, the X-ray baffle was glued to the mirror module with the 16 thermal spacers. The eROSITA FM1 mirror assembly served as a proto-flight model and was tested in much more detail than the following FMs. So, after the baffle mounting, the FM1 mirror assembly was X-ray tested in MPE’s Panter facility to study the efficiency of the baffle and its impact on the imaging performance. Figure 27, left, shows the results of single reflection measurements outside the field of view up to ±200 arcmin and the corresponding predictions for a perfect X-ray baffle. Figure 27,

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right, shows an example of stray-light suppression in the field of view (the inner circle) for a single off-axis angle. In addition, scans to characterize the off-axis PSF performance and to measure the vignetting curves at various photon energies were performed. As expected, the vignetting curves steepened a bit, because the X-ray baffle cuts a small fraction of off-axis rays.

Future Missions XRISM (Tashiro et al. 2020), the recovery mission of ASTRO-H, was equipped with two X-ray mirrors (Okajima et al. 2020) for an X-ray microcalorimeter (Resolve) and an X-ray CCD camera (Xtend). Each XMA has a pre-collimator similar to that of the ASTRO-H SXTs. However, to reduce the stray light with primary-only reflection, “No. 0” primary foil and “No. 0” blade are introduced for the X-ray mirror and pre-collimator, respectively. The “No. 0” primary foil is made by a bare aluminum sheet without a gold reflective surface to avoid X-ray reflection. The gap between the innermost radius of the aperture of the mirror housing and the inner radius of the bottom of the #1 primary foil is large enough for the direct and primary components to go though the inside of the mirror. By introducing the “No. 0” foil and blade, the contribution of the stray light can be reduced, compared with that for the SXT pre-collimator. The FORCE mission (Mori et al. 2016), a planned US-Japanese collaborative mission, aims to elucidate the nonthermal picture of the Universe by the X-ray telescopes covering a wide energy band of 0.5–80 keV. The foil production technique for this X-ray mirror has been extensively investigated to achieve the angular resolution below 15′′ even for the multilayer-coated silicon substrates (Zhang et al. 2019). One of the scientific goals of the FORCE mission is to resolve the cosmic X-ray background into discrete sources at 30 keV. Hence, the stray-light contamination should be reduced as much as possible. An X-ray pre-collimator, similar to those on board Suzaku, Hitomi, and XRISM, is planned to be installed. Athena, the fifth ESA M-class mission, is equipped with an X-ray mirror in which an X-ray silicon pore optics (SPO) is adopted (Bavdaz et al. 2021). The X-ray baffle or collimator that has been used so far has difficulty in mounting the silicon pore optics since the housing structure of the X-ray mirror is quite different from the traditional one. In addition, the alignment of the collimator to reduce the stray light is also severe because of the tight nesting of the silicon mirrors. Regardless of these difficulties, the Athena collaborators are investigating feasibility of a lightweight stray-light baffle (in private communication; see Fig. 28). They consider a meshtype collimator; many stainless-steel meshes with a width of 50 µm and a thickness of 0.7 mm are stacked on the primary structure of the SPO. It is not necessary that cylindrical blades are used to block the paths of the stray light. The mesh-type collimator is developed in terms of the easy production by a chemical etching and achievement of the lightweight module. To increase the structural stiffness, a thin glass spacer is inserted between two meshes. The production trial of the 14-stage stacked BBM is still ongoing.

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Fig. 28 Picture of a glass mesh (left) for a lightweight stray-light baffle and zoomed one taken from an angle (right), by courtesy of Dr. Yoshitomo Maeda and Japanese development team

Conclusion An X-ray collimator is mounted on an X-ray mirror to maintain its expected performance in the viewpoint of the thermal control and the stray-light reduction. The stray light often creates a spatially extended ghost image in the detector field of view, and then affects the observations as X-ray backgrounds. The stray light is mainly caused by off-axis X-rays that go through a single reflection in the Wolter-I type X-ray mirror, different from the nominal double reflection for on-axis X-rays. The stray light that occurs by the reflection on the backside surface of the X-ray mirror shells is also non-negligible. Hence, the X-ray background from the stray light shows an energy dependence that makes it difficult to be removed properly in the X-ray analysis. The single reflection on the secondary (hyperboloid) mirrors is a main contributor of the stray light in the detector field of view. Thus, a collimator, consisting of structures placed on the primary (paraboloid) mirrors to block this single-reflection path, is an effective countermeasure for the stray-light reduction. The field of view of the X-ray mirror becomes narrower by the mounting of the collimator. Therefore, the basic design of the collimator is different from mission to mission, and then needs a trade-off study under the performance requirements for the X-ray optics. Some relations between basic parameters of the X-ray mirror are provided for the collimator’s design. The demand for X-ray optics that achieve supreme angular resolution of a few (to sub) arcseconds and large (1 m2 ) effective areas simultaneously is increasing in recent years, which accelerates the development of the light-weight X-ray optics. To enhance the effective area, we cannot avoid to increase the focal length of the mirror and the mirror nesting. Hence, the detection limit for such highly nested mirror would suffer from stray-light contamination, if no X-ray collimator is installed for its reduction. The X-ray baffle of eROSITA is the state-of-the-art countermeasure of the stray light. However, as the nesting increases drastically, the alignment process between the X-ray mirror and collimator definitely becomes harder challenges. Not only a new fabrication technique such as the mesh-type collimator but also a new method of the fine tuning has been sought in various projects, institutes, and

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companies Ponsor (2017). Also, the use of other new technologies such as precise 3D printing could allow for new advanced designs having been not realized with the current manufacturing techniques.

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Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . X-Ray Mirror Fabrication: Fundamentals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Manufacturing Methodologies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . X-Ray Mirror Manufacture and Technology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Evaluating Optical Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Terminology: Basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Terminology: Optical Surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Section Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Subtractive . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Polishing: General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Polishing: Robotic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ion Beam Figuring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Subtractive: Silicon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Silicon Pore Optics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Monocrystalline Silicon Meta-shell X-Ray Optics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Formative . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Electroforming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Slumping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Differential Deposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Fabricative . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Active/Adjustable Optics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Additive . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Additive Manufacture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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C. Atkins () STFC UK Astronomy Technology Centre, Edinburgh, UK e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2024 C. Bambi, A. Santangelo (eds.), Handbook of X-ray and Gamma-ray Astrophysics, https://doi.org/10.1007/978-981-19-6960-7_11

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Abstract

X-ray mirror fabrication for astronomy is challenging; this is due to the Wolter I optical geometry and the tight tolerances on roughness and form error to enable accurate and efficient X-ray reflection. The performance of an X-ray mirror, and ultimately that of the telescope, is linked to the processes and technologies used to create it. The goal of this chapter is to provide the reader with an overview of the different technologies and processes used to create the mirrors for X-ray telescopes. The objective is to present this diverse field in the framework of the manufacturing methodologies (subtractive, formative, fabricative, & additive) and how these methodologies influence the telescope attributes (angular resolution and effective area). The emphasis is placed upon processes and technologies employed in recent X-ray space telescopes and those that are being actively investigated for future missions such as Athena and concepts such as Lynx. Speculative processes and technologies relating to Industry 4.0 are introduced to imagine how X-ray mirror fabrication may develop in the future. Keywords

X-ray mirrors · Mirror fabrication · Subtractive · Formative · Fabricative · Additive · Replication · Active control

Introduction The goal of a telescope is to provide the astronomers with photons to analyze, and the objective of a telescope is to deflect the photons from the field of view to the detector. The key component of a telescope is the primary mirror (or lens). The primary mirror must collect as many photons as possible and accurately deflect the photons to the focus or detector. A normal incidence telescope – e.g., Hubble Space Telescope, angle of incidence θi = 90◦ – achieves this by having a mirror as large as possible (2.4 m diameter) and polished as accurately as possible. The primary mirror for a grazing incidence telescope required for X-ray astronomy is based upon the Wolter I geometry, where photons hit the surface at very small angles of incidence (θi ≈ 1°, or less). Therefore to fill the telescope aperture, to collect as many photons as possible, multiple grazing incidence mirrors are nested and as such, the “primary mirror” is made up from many X-ray mirrors. The challenge then becomes how to make the individual X-ray mirrors. Normal incidence mirrors can be made thick (a ∼ 6:1 diameter-to-thickness ratio is often used) to ensure that the mirror surface is rigid; however, thick mirrors for an X-ray telescope reduce the telescope aperture (collecting area) because they are “seen” by the source edge-on and limit the number of mirrors that can be nested in

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the system. In contrast, thin mirrors block less of the telescope aperture and more mirrors can be nested, but the accuracy of the mirror surface is lower. There are multiple methods to create an X-ray mirror. The technology and process used depends upon the science objectives of the telescope/observatory – i.e., imaging, number of photons, or both, required by the telescope. This chapter will explore the plethora of technologies and processes used in X-ray mirror fabrication, both in use today and under development for the future. To limit the scope of the chapter, only the technologies and processes that deliver 1.8% at 6.4 keV 1.5 keV (at 5.9 keV) α. The RGA diffracts the X-rays to an array of nine MOS back-illuminated CCDs. Each has 1024 × 768 pixels, half exposed to the sky and half used as a storage area. During readout, 3 × 3 pixel on-chip binning is performed, leading to a bin size of (81 µm)2 , which is sufficient to fully sample the line spread function, reducing the readout time and the readout noise. In the dispersion direction, one bin corresponds to about 7, 10, and 14 mÅ in first order and about 4, 6, and 10 mÅ in second order for wavelengths of 5, 15, and 38 Å, respectively. The size of one bin projected onto the sky is about 2.5′′ in the cross-dispersion direction and roughly 3, 5, and 7′′ and 4, 6, and 9′′ in the dispersion direction at 5, 15, and 38 Å in first and second order, respectively. After the first week of operations, an electronic component in the clock driver of CCD4 in RGS2 failed, affecting the wavelength range from 20.0 to 24.1 Å. A similar problem occurred in early September 2000 with CCD7 of RGS1 covering 10.6 to 13.8 Å. The total effective area is thus reduced by a factor of two in these wavelength bands (see Fig. 14). In 2007, the readout method in RGS2 was changed from double-node, in which data from the two halves of the chips are retrieved separately, to single-node, in which data from the whole chip are read out through a single amplifier. Hence, RGS2 frame times are twice as long as those from RGS1. The standard mode of operation of the RGS instrument is called “Spectroscopy.” It consists of a two-dimensional readout of one or more CCDs over the full energy range. The accumulation time when reading the eight functional CCDs is 4.8 s for RGS1 and 9.6 s for RGS2. To mitigate the effects of pile-up, very bright sources can be observed in the RGS “Small Window” mode. In this mode, only the central 32 of the 128 CCD rows in the cross-dispersion direction are read. The CCD readout time is therefore decreased by

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Fig. 13 RGS data for an observation of Capella. The dispersion axis runs horizontally and increases to the right. The top panel shows the image of the dispersed light in the detector. The cross dispersion is along the vertical axis. The bottom panel shows the order selection plane, with the energy (PI), on the ordinate. This also illustrates the mechanism used for separation of first, second, and higher grating orders. Standard data extraction regions are indicated by the curves

a factor 4 compared to Spectroscopy mode. It can be further decreased by reading only a subset of the CCDs.

Scientific Performance A consequence of the diffraction equation (1) is that orders overlap on the CCD detectors of the RFC. Separation of the spectral orders is achieved by using the intrinsic energy resolution of the CCDs, which is about 160 eV FWHM at 2 keV. The dispersion of a spectrum on an RFC array is shown in the bottom panel of Fig. 13. First and second orders are very prominent and are clearly separated in the vertical direction (i.e., in CCD energy, or PI, space). Photons of higher orders are also visible for brighter sources. The calibration sources can also be seen in the bottom panel as short horizontal features (Fig. 13). A complete overview of the performance of the RGS, instrumental details, and calibration procedures can be found in de Vries et al. (2015) (Fig. 14). A summary of the RGSs’ performance is given in Table 2.

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Fig. 14 Example of the RGS effective area for a recent observation. Clearly visible are the gaps due to the non-working CCDs and, in RGS1, the prominent instrumental O edge near 23 Å

Table 2 RGS In-orbit Performance

Effective area (cm2 ) Resolution (km s−1 ) Wavelength range Wavelength accuracy

1st order 2nd order 1st order 2nd order 1st order 2nd order 1st order 2nd order

RGS1 RGS2 10 Å 15 Å 35 Å 10 Å 15 Å 51 61 21 53 68 29 15 – 31 19 1700 1200 600 1900 1400 1000 700 – 1200 800 5–38 Å (0.35–2.5 keV) 5–20 Å (0.62–2.5 keV) ±5 mÅ ±6 mÅ ±5 mÅ ±5 mÅ

35 Å 25 – 700 –

The calibration of the RGS effective area is based on a combination of ground measurements and in-flight observations (Fig. 14). Empirical corrections have been introduced along the years, the first one based on the assumed power law form of blazar spectra, followed by the recognition of wavelength-dependent sensitivity changes consistent with a buildup of hydrocarbon contamination on the CCD surface. There are indications of a continuous decrease in effective area over the last years, in both instruments and affecting most of the spectral range. This decrease cannot be explained by only contamination by hydrocarbons. Its origin is not understood. This calibration takes into account this effect, following an empirical

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algorithm. The first-order effective area peaks around 15 Å (0.83 keV) at about 120 cm2 for the two spectrometers. The wavelength scale is determined by the geometry of the various instrument components. The original pre-flight calibration kept the wavelength scale accuracy well within specification. Nevertheless, it has been improved by taking into account some systematic effects. With these corrections, the accuracy of the wavelength scale is now of order of 6 mÅ. The observed line shape is well represented by the model. The empirically determined width of strong emission lines is a slowly varying function of wavelength in both instruments, with a mean FWHM of about 70 mÅ in first order and 50 mÅ in second order, giving a spectral resolution that increases with wavelength. It is estimated that an observed line broadening of more than 10% of the FWHM can be considered to be significant for strong lines. The current status of the instruments and the calibration can be found in the “XMM-Newton Users Handbook” (Ebrero 2021) and in the document “Status of the RGS Calibration” (González-Riestra 2021), both available at the XMM-Newton website.

Optical Monitor (OM) The Optical Monitor (OM) provides simultaneous optical/UV coverage of sources in the EPIC field of view, extending the wavelength range of the mission and enhancing its scientific return. The photon-counting nature of the instrument and the low in-space background mean it is highly sensitive for the detection of faint sources, despite its small size, being able to reach about magnitude 22 (5σ detection) in the B filter in 5 ks of exposure (with maximum depth in the White filter). The provision of UV and optical grisms permits low-resolution spectroscopic analyses, while the fast mode timing options allow detailed studies of temporal variability.

The Instrument The OM is a 2 m-long, 30 cm diameter telescope of Ritchey-Chretien design, with a focal length of 3.8 m (f/12.7). After passing through the primary mirror hole, the light beam impinges on a rotatable 45◦ flat that deflects it to one of two redundant detector chains. Each chain comprises a filter wheel containing 11 apertures (V (500–600 nm), B (380–500 nm), U (300–400 nm), UVW1 (220–400 nm), UVM2 (200–280 nm), UVW2 (180–260 nm), and White-light (180–700 nm) broadband filters, visible (290–600 nm) and UV (180–360 nm) grisms for dispersive (resolving power (λ/∆λ) ∼ 180) spectroscopy, a magnifier (not available for use), and a mirror acting as a blocking filter). A schematic of the OM is shown in Fig. 15, while the photographs in Figs. 16 and 17 show the telescope and the filter wheel assembly, respectively.

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Detector

Baffle

Filter Wheel

Processing Electronics Telescope Power supply

Detector Power Supply Door

Digital Electronics Module(Prime)

Digital Electronics Module(Redundant)

Fig. 15 Schematic of the Optical Monitor Fig. 16 The Optical Monitor at Mullard Space Science Laboratory, UK

The detector, located behind the filter wheel in each chain, is a Micro Channel Plate (MCP)-intensified CCD (MIC), comprising a S20 photocathode, a pair of MCPs, a P-46 phosphor, a fiber taper, and a CCD. An electron liberated from the photocathode by an incident sky photon drifts to the upper MCP where a potential accelerates it along a pore, creating a cascade of electrons by collisions with the pore walls. On passing through the second MCP, this charge cloud is amplified to around 5 × 105 –106 electrons, and these impinge on the phosphor, resulting in a burst of photons. This photon burst, spatially localized by the MCP arrangement, then traverses the fiber taper, onto the CCD, which has 256 × 256 light-facing pixels (each 4 × 4 arcsecs on the sky). The footprint of the photon burst at the CCD covers about 3 × 3 CCD pixels. On readout, an onboard algorithm then centroids each footprint to 1/8 of a CCD pixel, creating an effective image of 2048 × 2048 image pixels (maximum resolution, 0.5 × 0.5 arcsec pixels on the sky). The CCD is read out about 90 times (frames)/s (for the full field). Thus, each sky photon incident on

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Fig. 17 One of the two filter wheels positioned in front of the OM’s CCD detectors

the photocathode that yields a footprint at the CCD within the frame is subject to onboard validation thresholds, recorded as an incident event by the onboard data processing system. The OM has two main modes of operation: Imaging mode, where events from each frame are accumulated into a single image covering the total exposure time, and Fast mode, where, for a small 11′′ ×11′′ window, each event is time-tagged, yielding an event stream. In Imaging mode, the observer has, subject to telemetry-related constraints, significant freedom to define window(s) for optimum sky coverage for their science goals. This may involve coverage of the whole field, at the expense of longer instrument overheads, or coverage of more localized areas of the field via up to five smaller windows. Grism data is taken either in a Full-field mode, potentially yielding spectra from all sufficiently bright objects in the field, or with a narrow, predefined window, designed to concentrate on a specific target observed at the boresight. In Fast mode only two Fast mode windows are allowed, though normally these can be used in conjunction with image mode windows. The highest time resolution in fast mode is 0.5 s. Three important consequences of the OM design on its output data are as follows: (1) When two or more photon bursts arrive at the CCD within the same readout frame and their footprints spatially overlap, the probability of which increases with source count rate and/or longer frame times, they may not be distinguished and so be recorded as a single event. This effect is referred to as coincidence loss and is similar to the pile-up effect in the EPIC cameras. (2) The instrument design, particularly the fiber taper, results in a distortion of the imaged field compared to the real sky. (3) For speed, the onboard algorithm exploits a lookup table to centroid the count distribution in each 3 × 3 CCD-pixel footprint, a simplification that results in a so-called “modulo-8” pattern appearing on a scale of 8 pixels in the 2048 × 2048 output image. These effects are generally corrected for through software tools in the XMM-Newton Science Analysis Software (SAS). Some OM observations also contain low-intensity, diffuse light features, arising from reflections from the back side of the detector entrance window and/or from a chamfer around it. The OM, being a photon-counting instrument, has high sensitivity, and, with the low background (dominated by zodiacal light), it can reach stars as faint as about V = 21 (for a 5σ detection of an A0 star in the B filter) in 1000 s. On the other

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hand, the photocathode can be damaged by high incident photon rates, and this places limits on the brightest sources that the OM can be exposed to. In practice, the limiting magnitude is around V = 7.3 for an A0 star. A more complete description of the OM instrument is given in Mason et al. (2001). For observations not performed in Full-Frame mode, the OM performs a short (20 s) field-acquisition exposure at the start of each observation (Talavera and Rodriguez 2011). This enables a number of pre-specified stars to be recognized in the exposure by the onboard software and the observed and predicted positions compared to measure shifts due to uncertainties in the spacecraft pointing. Consequently, the chosen OM science observation windows can be adjusted in position to ensure the sky coverage is optimal for the observer’s science. This is especially important for accurately positioning the small Fast mode windows, when used, to ensure the target is well centered in the window. In addition, the star positions are also monitored every 20 s, permitting the tracking of any spacecraft drift. This tracking information is used by the onboard software, to relocate events to the correct position in the accumulating image for Image mode data (referred to as “shift and add”). For Fast mode data, this tracking information is not applied onboard but is used for the same purpose in downstream data reduction performed by the SAS.

Scientific Performance The OM has proven to be a very stable instrument. Nevertheless, it has experienced some spatial and temporal changes in sensitivity over the long baseline of the XMMNewton mission, both expected and unexpected (Rosen 2020). Of particular note are the effective areas. These were determined soon after launch, for each photometric filter, based on measurements of spectrophotometric standard stars, alongside the conversions from count rate to absolute flux and the equivalent magnitude zero-point determinations. The effective area for each filter, initially modelled from pre-launch information of the optical components (e.g., mirror area, reflectivities, filter transmissions), and the quantum efficiency of the photocathode were subsequently adjusted, in-flight, to match the observed count rates of standard stars. It was found that all filters showed reduced sensitivity (from 16% to 56% residual throughput) compared to pre-launch expectations, with the UVM2 and especially UVW2 filters most affected. The reduction in sensitivity has been adequately modelled by absorption due to a molecular contaminant layer somewhere in the OM system (Kirsch et al. 2005). The effective areas of the photometric filters, essentially at launch, are shown in Fig. 18. Subsequently, anticipated aging of the detector and, likely, some further contaminant growth have resulted in a gradual decline in sensitivity since launch. This decline, known as the time-dependent sensitivity (TDS) degradation, is filter (wavelength) dependent. It is monitored and characterized via analysis of data from the OM Serendipitous UV Sky Survey (SUSS) catalogues (Page et al. 2012) and is routinely verified via observations of spectrophotometric standard stars. The most

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Fig. 18 The effective area curves for each of the OM photometric filters, essentially at the start of XMM-Newton mission operations (2000)

recent TDS trends for the narrowband filters are shown in Fig. 19. The decline in sensitivity ranges from around 7% in the B filter to about 22% in the UVW2 filter. These curves are used to correct the observed count rates of sources at any epoch within the mission baseline to the rate expected at the start of the mission. That rate can then be converted to absolute photometric values via the at-launch flux and zero-point conversions.

Organization of the XMM-Newton Ground Segment The Mission Operations Centre (MOC) at the European Space Operations Centre (ESOC), Darmstadt, Germany, controls the spacecraft 24 h per day, all year round, using, as main ground stations, Kourou (French Guiana) and Santiago (Chile) and various other additional stations in South America and Australia. The MOC is responsible for the maintenance and operations of the spacecraft and the required ground infrastructure. As XMM-Newton has no onboard data storage capacity, all data are immediately down-linked to the ground in real time. Since 2018 XMMNewton has been operated together with Gaia and INTEGRAL. The Science Operations Centre (SOC) at the European Space Astronomy Centre (ESAC), Villanueva de la Cañada, Madrid, Spain, is responsible for science operations and for supporting the scientific community. The SOC handles Announcements of Opportunity and proposals, including technical evaluation and

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Normalised count rate

Normalised count rate

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0.95 0.90 0.85 0.80

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0.90 0.85 0.80

UVW2

1.00 0.95 0.90 0.85 0.80 0.75

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Normalised count rate

Normalised count rate

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0.75 Normalised count rate

Normalised count rate

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UVW2

1.00 0.95 0.90 0.85 0.80 0.75

2000

4000 6000 MJD-50000.0

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4000 6000 MJD-50000.0

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Fig. 19 Normalized, observed count rates of constant sources in the OM SUSS4 catalogue, binned into 20 time bins (black error bars), for each OM filter. The solid red and dashed blue curves represent the most recent and previously fitted decline trends, respectively, highlighting the ubiquitous flattening of the decline

OTAC support as well as the subsequent planning of observations, including instrument handling, calibration observations, and Targets of Opportunity. Data from these observations are processed from raw telemetry to standard data products at the SOC, before being ingested into the XMM-Newton Science Archive (XSA) and distributed to the users. A Quick-Look Analysis of data and anomaly monitoring of the instruments are part of this process. The SOC also takes a leading role in the continuous calibration of the instruments and the provision of scientific analysis software (SAS) to the users together with experts from the XMM-Newton community. The Survey Science Centre (SSC) (Watson et al. 2001), a consortium of ten institutes in the ESA community, is responsible for the compilation of the XMMNewton Serendipitous Source Catalogue, the follow-up/identification program for the XMM-Newton serendipitous X-ray sky survey, support to pipeline processing at the SOC, and development of parts of the scientific analysis software. NASA provides a Guest Observer Facility (GOF) at the Goddard Space Flight Center (GSFC), Greenbelt, Maryland, USA. The GOF supports the usage of

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XMM-Newton by the scientific community in the USA. It distributes the XMMNewton data to US users and contributes to the SAS development. The GOF is responsible for the organization of the Guest Observer (GO) program funded by NASA.

Observing with XMM-Newton All the scientific instruments onboard XMM-Newton can be operated independently and can obtain science data simultaneously, if operational constraints permit. These constraints are imposed to preserve the safety of the instruments as well as to achieve the conditions for an optimal calibration of the data. The combination of the orbit of the spacecraft with limits in the instruments’ operational parameters (mostly temperatures but also radiation dose) results in observation constraints related to the orientation of the spacecraft with respect to the Sun, Earth, and Moon and to the position of the spacecraft in the Earth’s magnetosphere. XMM-Newton was launched in December 1999 into a highly elliptical orbit, with a high inclination with respect to the Equator and with an apogee height of 115,000 km in the Northern hemisphere and a perigee height of 6000 km in the Southern hemisphere. Due to several perturbations, the orbit of XMM-Newton evolves with time. An orbit correction maneuver was performed in February 2003 to ensure full ground station coverage during the entire science period. But the evolution of the orbit has changed the fraction of the sky visible to science instruments and the effective available science time per orbit along the mission lifetime. The spacecraft has no capacity for data or commanding storage onboard so it requires continuous contact with the ground for science operations. The operations are conducted from the MOC through ground stations in Kourou, Santiago de Chile, and Yatharagga (and in Perth and New Norcia during the early years of the mission and occasionally in Madrid). The EPIC and RGS CCD detectors are sensitive to both X-ray and optical radiation as well as particles. Electromagnetic radiation can affect the scientific analysis of the data collected, but protons striking the detectors can permanently damage the surface of the CCDs. In order to protect the EPIC cameras, their filter wheel is moved into the closed position during intervals of high particle radiation. The RGS spectrographs do not have a similar filter protection so the instruments are placed into a special configuration with minimal equipment switched on during high radiation intervals. Before launch, it was expected that the radiation environment above 46,000 km from the Earth was safe for the mission. This meant that ∼143 ks of the ∼173 ks (∼48-h) orbital period could be devoted to science operations at the beginning of the mission. However, strong fluctuations and variability of the particle background in the cameras were one of the main surprises and concerns following launch. An ad hoc model for radiation belts around the Earth was developed in order to predict the time window within every revolution when science observations could be safely

46 XMM-Newton Fig. 20 The evolution of the XMM-Newton orbit during the mission has changed the spacecraft velocity near perigee passage and the orientation with respect to Earth magnetosphere. As a result the fraction of time available to science has changed with a long-term trend superposed on a seasonal modulation

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0.8

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0.6 2000

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2010

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conducted (Casale and Fauste 2004); see Fig. 20. According to the model and the expected orbital evolution, the science window will be as short as ∼130 ks by 2025. Many parameters in the EPIC cameras and RGS spectrographs are strongly dependent on the temperatures at which the instruments are operated. In order to guarantee a consistent calibration for all observations, the operations are designed to maintain the temperatures of the science payload within a narrow range. Since the main source of heating is illumination by the Sun, strong constraints on temperatures are translated into a strong constraint on the orientation of the spacecraft with respect to the Sun. The solar aspect angle (angle between pointing direction and Sun direction) must be within 70◦ and 110◦ at all times to assure thermal stability and sufficient power from the solar array. This means that ∼65% of the sky is inhibited in every single XMM-Newton revolution. Other celestial constraints are unrelated to temperature or power stability, but to potential electromagnetic radiation damage of the OM. The main sources of dangerous light emission, away from the Sun, are the Earth and the Moon. The Earth limb avoidance angle is 42.5◦ , and the Moon limb avoidance angle is 22◦ , which is increased to 35◦ during eclipse seasons. As in the case of the radiation constraints, the evolution of the XMM-Newton orbit with respect to the ecliptic has had consequences on the fraction of the sky available at any time and on the evolution of the visibility in certain areas of the sky; see Fig. 21. The constraint outlined above apply to any type of observation, independent of the configuration of the instruments. There are a number of constraints that apply only to OM exposures, and some science exposures cannot be performed using the OM, but exposures with the X-ray instruments are permitted. These OM constraints refer to the presence of nearby bright celestial sources that may damage the detector. In addition, OM exposures are forbidden near the following solar system objects (Table 3).

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Fig. 21 The high inclination of the orbit and the high latitude of the perigee have made the South Ecliptic Pole the region of the sky with the best accessibility to XMM-Newton along its lifetime. By contrast, the visibility around the North Ecliptic Pole is constrained by the Earth in most of the revolutions. The image shows the fraction of visible orbits along 21 years (right) and the average maximum visibility in 21 year (left)

46 XMM-Newton Table 3 OM avoidance angles

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Avoidance angle 3.5◦ 4.5◦ 2◦ 0.25◦ 0.25◦

Scientific Data and Analysis XMM-Newton reformatted telemetry is organized in Observation/Slew Data Files (ODF/SDF). Most of the ODF/SDF components have a FITS format. An ASCII summary file provides the astronomers with general information on the observation and an index of the files contained in the ODF. The Science Analysis System (SAS) is the software established to reduce and analyze XMM-Newton science data. It consists of two main blocks: • reduction pipelines, which apply the calibrations to the ODF and the SDF science files and produce calibrated and concatenated event lists for the X-ray cameras, flat-fielded and calibrated OM sky images, source lists, and time series. • a set of file manipulation tools, which include the extraction of spectra, light curves, and (pseudo-)images and the generation of source lists, as well as the generation of auxiliary files such as appropriate instrument response matrices. The SAS reduction pipeline (PPS) is run on all XMM-Newton datasets. Each PPS dataset is manually screened to verify its scientific quality and identify potential processing problems. The PPS output (Rodríguez 2021) includes a wide range of top-level scientific products, such as X-ray camera event lists, source lists, multiband images, background-subtracted spectra, and light curves for sufficiently bright individual sources, as well as the results of a cross-correlation with a wide sample of source catalogues and with the matching ROSAT field. All the XMM-Newton calibration data are organized in a Current Calibration File (CCF). Summary documents, containing an overview of the current calibration status and associated systematic uncertainties, are available from the XMM-Newton Calibration Portal. The XMM-Newton Science Archive (XSA) content is regularly updated with all the newly generated ODF, SDF, and PPS products, with updated versions of the catalogues of EPIC sources, OM sources, and Slew Survey sources, and with ancillary info like associated proposal abstract and publications. On-the-fly data analysis and processing can be performed from the XSA using the SAS without the need of downloading data or software. With all the sources serendipitously detected in the EPIC FOV of XMM-Newton public observations, the SSC compiles and regularly updates the XMM-Newton EPIC source catalogue. At the time of writing, the SSC has created four catalogue

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generations, with 4XMM being the latest, with a few incremental versions for each of them, leading so far to a total of 11 catalogue data releases, 11DR. 4XMMDR11 (Webb et al. 2020) was released in August 2021 and contains 787,963 “clean” detections corresponding to 602,543 unique sources covering 1239 sq. deg. In addition, the 4XMM-DR11s catalogue of serendipitous sources detected from stacked data from overlapping XMM-Newton observations (Traulsen et al. 2020) contains 358,809 unique sources of which 275,440 were multiply observed covering 350 sq. deg. The data acquired during satellite slews are used to build the XMMNewton Slew Survey Catalogue, XMMSL2 (Saxton et al. 2008). The current version contains 55,969 clean detections covering an area of 650,000 sq. deg. The OM team, under the auspices of the SSC, produces and regularly updates a catalogue of sources detected by the Optical Monitor. The 5th version of the XMM-Newton OM Serendipitous Ultraviolet Source Survey Catalogue, XMM-SUSS5, (Page et al. 2012) contains 8,863,922 detections of 5,965,434 sources. Specific queries to all catalogues can be made using the XMM-Newton Science Archive. A database of Upper Limits across the FOV of all public XMM-Newton pointed and slew observations has been built with new observations being added as they become available (Ruiz et al. 2021). The database is searchable from the XSA interface.

Scientific Strategy and Impact

Fig. 22 The over-subscription factors, or requested versus available observing time, for the first 21 XMM-Newton Announcements of Opportunity (AOs) are shown in black. The two blue symbols show the over-subscription of the Multi-Year-Heritage programs

Oversubscrition Factor

XMM-Newton observing time is made available worldwide via Announcements of Opportunity (AOs). The AOs open in the second half of August each year, and the results are publicized in early December. All the AOs were highly over-subscribed, typically by a factor 6 to 7; see Fig. 22. The proposals are peer-reviewed by panels composed of scientists located worldwide. The XMM-Newton observing strategy was discussed with the community at large at two workshops: “XMM-Newton: The next Decade” in 2007 (Schartel 2008) and 2016 (Schartel 2017 and (Schartel et al. 2017)). The unique capabilities of the instruments and the long mean observing time (30 ks) in combination with the possibility of long uninterrupted observations foster XMM-Newton’s

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potential for transformative science. Here transformative science is understood to be scientific results which lead to radically restructuring the scientific understanding or as observational confirmation of central predictions of astrophysical and cosmological theory and modelling. Examples include: (1) the non-detection or weak detection of cooling flows in the galaxy clusters Abell 1835 (Peterson et al. 2001), Abell 1795 (Tamura et al. 2001) and Sérsic 159-03 (Kaastra et al. 2001) which led to the concept of the coupling of the cosmic evolution of supermassive black holes with that of galaxies and clusters of galaxies via feedback. This meant that two object classes which were considered to be completely independent before were from then on understood to undergo a strongly coupled evolution; (2) the detection of transitional millisecond pulsars (Papitto et al. 2013), which confirmed the transition of accretion-powered to rotationpowered emission modes in pulsars; (3) the detection of low magnetic field magnetars (Rea et al. 2010; Tiengo et al. 2013) which changed our understanding of the magnetic fields which cause the short X/gamma ray bursts in repeaters, (4) the identification of neutron stars within ultra-luminous X-ray sources (Fürst et al. 2016; Israel et al. 2017). This changed the understanding of the nature of this source class and allowed the study of super-Eddington accretion (Ciro et al. 2016), (5) the determination of the mass, spin, and X-ray corona size of supermassive black holes (Fabian et al. 2009; Risaliti et al. 2013; Parker et al. 2017; Alston et al. 2020; Wilkins et al. 2021) which quantitatively describe the inner geometry of AGNs, (6) the study of tidal disruption events (Reis et al. 2012; Miller et al. 2015; Kara et al. 2016; Lin et al. 2017, 2018; Pasham et al. 2019; Shu et al. 2020) which shed light on the details of the accretion process and jet launching, (7) the detection of the warm-hot intergalactic medium (Nicastro et al. 2018), which confirmed cosmic simulations by the detection of the missing baryons. Further examples of transformative science resulting from XMM-Newton and Chandra observations are given in two Nature review articles by Santos-Lleo et al. (2009) and by Wilkes et al. (2021). An analysis of the science results and the discussion of the 2017 workshop showed the increased importance of Target of Opportunity observations, large and very large programs, and observations joint with other facilities for transformative science. About 15% of submitted proposals request anticipated target of opportunity (TOO) observations. In addition there are about 45 requests for unanticipated TOOs and/or Director’s discretionary time observations each year, which in general are forwarded to an OTAC (Observing Time Allocation Committee) chairperson for a recommendation. XMM-Newton has not formally limited the time available for TOOs. However, the high amount of fixed-time observations and observations performed simultaneously with other missions limit the time which may be allocated to TOO observations. In the very late 2010s and very early 2020s, XMM-Newton typically performed 80 TOO observations per year. This rate is more than double the rate of TOO observations in the early days of the mission (e.g., 2005); see Figs. 23 and 25. Multi-wavelength and multi-messenger observations are a powerful tool to foster transformative science. With its suite of instruments, XMM-Newton already

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Fig. 23 Performed Target of Opportunity observations

Fig. 24 Observations performed coordinated or simultaneous with other facilities

provides multi-wavelength coverage from the optical to X-ray regimes. XMMNewton SOC staff investigated ways to further extend this approach to “multi”wavelength observations. These can be performed via joint programs. In 2021, XMM-Newton has joint programs with nine facilities. The joint programs allow the time allocation committees of each facility to allocate time on the other mission in connection with the allocation of time on the own facility. Therefore, with one proposal, in response to an XMM-Newton AO, observing time on up to 10 facilities can be requested. Table 4 shows the joint programs and the time exchanged per year. The XMM-Newton joint programs allow the spectral energy distribution of a source to be covered from the radio, optical, UV, and X-ray, Γ -ray all the way to the TeV range. About 30% of the performed high-priority observations (i.e., observations whose execution is guaranteed) are from a joint program, most of them simultaneous with one or more facilities; see Figs. 24 and 26.

46 XMM-Newton Table 4 Joint programs

1533 Facility NRAO VLT(I) HST Chandra Swift NuSTAR INTEGRAL MAGIC H.E.S.S.

Exchanged time 2 × 150 ks 2 × 290 ks 2 × 150 2 × 1 Ms 300 ks 2 × 1.5 Ms 2 × 300 ks 2 × 150 ks 2 × 150 ks

Fig. 25 Observing time performed for Target of Opportunity observations

Requests for observing time longer than 300 ks are submitted as large programs. About 40% of the high-priority observing time (execution guaranteed) is given to large programs, such that they have the same over-subscription as the normal programs. Examples of transforming science resulting from larger programs are given in Fabian et al. (2009), Alston et al. (2020), and Nicastro et al. (2018). To accomplish programs requiring more than 2 Ms, e.g., Pierre et al. (2017), the call for Multi-Year-Heritage (MYH) program was introduced in 2017. Here, up to 6 Ms of observing time are available for distribution, to be executed over a period of three AOs (3 years). The call for MYH programs in 2017 had an over-subscription of a factor 10. The call in 2020 suffered the pandemic constraints showing a lower over-subscription. The distribution of elapsed time between performed observations and publication peaks at 2 years (Ness et al. 2014). Most of the times, TOO observations lead to rapid publications with about 1 year elapsed time between observation and

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Fig. 26 Observing time performed coordinated or simultaneous with other facilities

publication (Ness et al. 2014). The predefined observing modes in combination with the provided support, e.g., pipeline products, calibration, archive, or catalogues, make XMM-Newton data highly comparable and therefore ideally suited for studies based on archival data. In fact 90% of the observing time has been used in at least one publication (Ness et al. 2014). XMM-Newton data also play an important role in education and in the development of new generations of researchers around the world. At the time of writing (November 2021), 406 Ph.D. theses had used XMM-Newton data or included results of research related to the development of the instruments. XMM-Newton is frequently used by young scientists who are starting their career in astrophysics. Since the 5th call for observing time proposals, in 2005, astronomers sending proposals the first time submit about 20% of the proposals of each call. The success rate of these first-time proposers is slightly below the average success rate of all proposers. Remarkably, in more than one third of the calls since 2005, the rate of requested to allocated observing time secured by first-time proposers was similar or even larger than the average rate of all proposers. About 380 articles are published in refereed journals each year making use of XMM-Newton data, describing the instruments, or using pipeline products or the catalogue. Figure 27 gives an analysis of all refereed articles listed in ADS, which mention XMM-Newton, demonstrating not only the usage of XMM-Newton data but also its impact via citations. Articles containing results based on XMM-Newton observations are about three times more cited than all astronomical papers. Figure 28 shows the number of articles making use of XMM-Newton data published in Nature or Science journal demonstrating the high amount of transforming science which typically is published in these two journals.

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Fig. 27 Classification of all refereed articles listed in ADS which contain “XMM” in a full text-search: (1) article makes use of XMM-Newton data or pipeline products; (2) catalogue based on XMM-Newton observations; (3) article makes quantitative predictions for XMM-Newton observations; (4) article describes XMM-Newton, its instruments, scientific impact, etc. (5) article makes use of the primary catalogues (6) article makes use of published XMM-Newton results (7) article refers to papers presenting XMM-Newton results (8) article refers to “XMM-Newton” in general (9) article uses expression derived from XMM-Newton, e.g., names of objects

Authors Contribution Norbert Schartel and Maria Santos-Lleó contributed the “Introduction”, “Scientific Data and Analysis,” and “Scientific Strategy and Impact” sections, Rosario González-Riestra contributed “The Reflection Grating Spectrometers (RGSs)” section, Peter Kretschmar contributed the “Organization of the XMM-Newton Ground Segment” section, Marcus Kirsch contributed “The Spacecraft” section, Pedro Rodríguez-Pascual contributed the “Observing with XMM-Newton” section, Simon Rosen contributed the “Optical Monitor (OM)” section, Michael Smith and Martin Stuhlinger contributed the “European Photon Imaging Camera (EPIC)” section, and Eva Verdugo Rodrigo contributed the “X-Ray Mirrors” section. Norbert Schartel prepared the chapter outline and compiled and homogenized the different contributions.

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Fig. 28 Articles in Nature and Science making use of XMM-Newton data are shown per year as an indicator of the amount of transformative science results

Acknowledgments The authors deeply thank Arvind Parmar for many useful suggestions and Lucia Ballo for help with the statistical numbers for joint programs. The authors also acknowledge the outstanding contribution of the Survey Science Centre to the mission success and the dedication and excellence of the rest of the team members of the XMM-Newton Mission Operations and Science Operations centers, where the authors of this paper feel as an honor to serve.

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Part V Optics and Detectors for Gamma-Ray Astrophysics Lorraine Hanlon, Vincent Tatischeff, and David Thompson

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Telescope Concepts in Gamma-Ray Astronomy Thomas Siegert, Deirdre Horan, and Gottfried Kanbach

Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Historical Perspective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The “MeV Sensitivity” Gap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Interactions of Light with Matter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Instrument Capabilities and Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Earth’s Atmosphere and Space Environment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Instrumental Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Background Suppression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Astrophysical Sources of Gamma Rays: Not One Fits All . . . . . . . . . . . . . . . . . . . . . . . . . . . Instrument Designs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . General Considerations: A Gamma-Ray Collimator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Temporal and Spatial Modulation Apertures, Geometry Optics: Coded Mask Telescopes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Quantum Optics in the MeV: Compton Telescopes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Quantum Optics for Higher Energies: Pair Tracking Telescopes . . . . . . . . . . . . . . . . . . . . Scattering Information: Gamma-Ray Polarimeters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Other Apertures: Combinations and Wave Optics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Gamma-Ray Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Understanding Gamma-Ray Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Calibrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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T. Siegert () Institut für Theoretische Physik und Astrophysik, Universität Würzburg, Würzburg, Germany e-mail: [email protected] D. Horan Laboratoire Leprince-Ringuet, CNRS/IN2P3, Institut Polytechnique de Paris, Palaiseau, France e-mail: [email protected] G. Kanbach Max Planck Institute for Extraterrestrial Physics, Garching, Germany e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2024 C. Bambi, A. Santangelo (eds.), Handbook of X-ray and Gamma-ray Astrophysics, https://doi.org/10.1007/978-981-19-6960-7_43

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Outlook and Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Abstract

This chapter outlines the general principles for the detection and characterization of high-energy γ -ray photons in the energy range from MeV to GeV. Applications of these fundamental photon-matter interaction processes to the construction of instruments for γ -ray astronomy are described, including a short review of past and present realizations of telescopes. The constraints encountered in operating telescopes on high-altitude balloon and satellite platforms are described in the context of the strong instrumental background from cosmic rays as well as astrophysical sources. The basic telescope concepts start from the general collimator aperture in the MeV range over its improvements through coded mask and Compton telescopes to pair-production telescopes in the GeV range. Other apertures as well as understanding the measurement principles of γ -ray astrophysics from simulations to calibrations are also provided. Keywords

Gamma-ray measurements · Collimator · Coded mask · Compton telescope · Pair creation telescope · Space environment · Instrumental background

Introduction Gamma rays (γ -rays) are traditionally defined as penetrating electromagnetic radiations that arise from the radioactive decay of an atomic nucleus, and, indeed, for γ -rays produced naturally on Earth, this is the case. Gamma rays constitute the electromagnetic radiation having energy of 100 keV and, therefore, have energies that traverse more than ten decades of the electromagnetic spectrum. In addition to those γ -rays coming from radioactive decays, the extra-terrestrial γ -rays incident on Earth are produced in a variety of different astrophysical scenarios. These include when extremely energetic charged particles accelerate in magnetic fields or upscatter ambient radiation to γ -ray energies, hadronic processes such as cosmic-ray (CR) interactions in the Galaxy, and, indeed, possibly in more exotic interactions, for example, the self-annihilation of dark matter particles (section “Astrophysical Sources of Gamma Rays: Not One Fits All”). In this chapter, an outline of the various techniques and instruments for the detection and characterization of γ -rays will be presented. The limitations and advantages of each particular detection technique, the backgrounds that must be overcome, and the environmental circumstances that must be considered will be reviewed. Only the direct detection of γ -rays will be discussed here, thus effectively

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limiting the upper energy range to approximately 100 GeV. For the detection techniques at the so-called very-high energy (VHE; Eγ  100 GeV), the reader is referred to chapters Introduction to groundbased Gamma-ray astrophysics. In order to detect γ -rays, we rely on one of their three interactions with matter, the photoelectric effect, Compton scattering, and pair production, whose respective cross sections depend on the energy of the γ -ray and on the material in which it interacts (section “Interactions of Light with Matter”). Since γ -rays cannot penetrate the Earth’s atmosphere, it having an equivalent thickness of approximately 0.9 m of lead, a detector needs to be placed above the atmosphere in order to detect γ -rays directly (section “Earth’s Atmosphere and Space Environment”). Like no other energy range, the γ -ray regime is dominated by an irreducible instrumental background (MeV energies) and limited by collection area (GeV energies) and telemetry (MeV and GeV energies; section “Instrumental Background”). Due to these factors and to the energy-dependent cross section of a γ -ray’s interaction with matter, the discussions in this chapter will be split according to the detection technique being employed, which is itself a function of the energy range of the γ rays being studied. Because of CR bombardment, MeV telescopes suffer from a high level of secondary γ radiation. This includes electron bremsstrahlung, spallation, nuclear excitation, delayed decay, and annihilation, all of which contribute to the instrumental background in the MeV range. This orders of magnitude enhanced rate of unwanted events leads to a worse instrument sensitivity – the “MeV sensitivity gap” – compared to neighboring photon energy bands (section “The “MeV Sensitivity” Gap”). The correct identification of background photons from celestial emission leads to an artificial split in the science cases (section “Astrophysical Sources of Gamma Rays: Not One Fits All”) because γ -ray instruments are built to observe either in the MeV or in the GeV. Even though astrophysical high-energy sources can span several decades in the electromagnetic spectrum, the MeV regime is often omitted because the sensitivities of current instruments rarely add much spectral information. In this chapter, we therefore handle MeV- and GeV-type instruments separately. We note, however, that leaving out information, even though it appears weak in the first place, leads to a biased view of the astrophysics to be understood. In the pair-production regime at tens of MeV to GeV energies, the spectra of γ -ray sources phenomenologically follow a power law such that the flux changes rapidly as a function of energy. With the exception of grazing incident mirrors used for hard X-rays in the energy range up to ∼100 keV (section “Other Apertures: Combinations and Wave Optics”), γ -rays cannot be focused and, therefore, in order to be detected, need to enter the detector and interact with it. So, unlike optical telescopes where a large effective area can be achieved by using a huge mirror to focus the optical photons onto a small detector, a large collection area can only be achieved at γ -ray energies by having a large detector volume. This requirement coupled with the constraints of launching a large mass high enough in the atmosphere that it can detect sufficient γ -rays (section “Atmospheric Effects”) limits the upper bound energy at which γ -rays can effectively be detected directly: for the direct detection of γ -rays, the physical volume of the detector is always

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larger than its effective detecting volume and hence the effective area photons see. The requirement to observe from space has the advantage of fewer constraints with respect to observing schedules (e.g., no day and night cycles); however, it limits the sensitive collecting areas of the telescopes because of the mass that can be transferred into an orbit. In this chapter, we will introduce the only 60-year-long history of γ -ray observations (section “Historical Perspective”); describe the least explored range of the electromagnetic spectrum, the MeV range (section “The “MeV Sensitivity” Gap”); and present the basic interactions of high-energy photons with matter that are used in all γ -ray telescopes (section “Interactions of Light with Matter”). Details about the instruments’ current capabilities and requirements to study high-energy sources are given in section “Instrument Capabilities and Requirements”, followed by an extensive discussion of instrumental background origins in section “Instrumental Background” and state-of-the-art suppression mechanisms (section “Background Suppression”). Based on the different science cases in the MeV and GeV range (section “Astrophysical Sources of Gamma Rays: Not One Fits All”), we detail principal instrument designs in section “Instrument Designs”. This includes the basic collimator (section “General Considerations: A Gamma-Ray Collimator”), coded mask telescopes (section “Temporal and Spatial Modulation Apertures, Geometry Optics: Coded Mask Telescopes”), Compton telescopes (section “Quantum Optics in the MeV: Compton Telescopes”), pair creation telescopes (section “Quantum Optics for Higher Energies: Pair Tracking Telescopes”), γ -ray polarimeters (section “Scattering Information: Gamma-Ray Polarimeters”), as well as other, alternative, but not necessarily yet realized instruments (section “Other Apertures: Combinations and Wave Optics”). Gamma-ray detectors are briefly explained in section “Gamma-Ray Detectors”, followed by how γ -ray measurements are to be understood, evaluated (section “Understanding Gamma-Ray Measurements”), and compared to simulations (section “Simulations”) and calibrations (section “Calibrations”). We close this chapter with an outlook about future and possible more advanced concepts in section “Outlook and Conclusion”.

Historical Perspective First Observations Gamma-ray astronomy, the highest-energy range of multi-wavelength astronomy, was already recognized in the 1950s as having the potential to provide direct insight into astrophysical processes with particles, fields, and dynamics of extreme conditions in the Universe (chapter “History of Gamma-Ray Astrophysics”). The principal source processes for high-energy γ radiation in space (beyond the energy range of radioactivity) were studied first. These include synchrotron radiation (Iwanenko and Pomeranchuk 1944), Compton scattering (Feenberg and Primakoff 1948), meson production and the decay of π 0 → 2γ (Hayakawa 1952), and bremsstrahlung (Hutchinson 2010).

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The status of particle physics, CR research, and radio astronomy in the 1950s raised widely debated questions such as: “Where do CRs come from and how are they produced?”, “What is the photon fraction in the CR beam?,” “What powers the strong Galactic radio emission?,” “Are there discrete γ -ray sources in the sky and what could be the nature of such sources?,” “Do the observed particle emissions from solar flares lead to γ -ray emissions (nuclear lines and continua)?,” and “Is there antimatter around?.” Estimates for the strength of cosmic γ -ray sources were mainly based on the contemporary knowledge of CRs, the distribution and density of the Galactic interstellar medium (HI radio emission), and the observations of radio emission from individual objects like the Crab Nebula or radio galaxies. Morrison (1958, Morrison 1958) estimated that the active Sun would emit 0.1–1 ph cm−2 s−1 between 10 and 100 MeV and 1–100 ph cm−2 s−1 in the neutron-proton capture line at 2.23 MeV. The Crab Nebula (the pulsar was unknown at the time) and typical radio galaxies should have intensities of 10−2 ph cm−2 s−1 . A thorough study of γ -ray production by CRs interacting with the interstellar medium in the Galaxy by Pollack and Fazio (1963) predicted a flux from the Galactic Center of ∼10−4 ph cm−2 s−1 sr−1 and half that intensity from the Anticenter. All of these flux estimates turned out to be much too high, but nevertheless many experiments were started to detect celestial γ -rays. Short exposures on balloons and a very strong environmental background prevented significant detection of γ -rays from the Milky Way or from discrete sources. The beginning of the space age in 1958 finally provided the facilities to operate γ -ray experiments above the atmosphere. The clear, unabsorbed view of the sky, the longer exposures, the absence of the atmospheric background, and the advanced instruments succeeded in establishing γ -ray astronomy as a new and promising branch of astrophysics. Gamma-ray astronomy is a discipline that depends on the technical resources of the space age. The ground level of Earth-bound observatories is shielded from cosmic γ radiation by the atmosphere (Fig. 1), with roughly 20 (resp. 60) mean free

Fig. 1 Absorption of cosmic electromagnetic radiation in Earth’s atmosphere

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path lengths of attenuation at 1 GeV (resp. 1 MeV) Furthermore, the charged fraction of cosmic radiation, which dominates primary γ -rays by roughly a factor of 104 , generates a high level of secondary γ -ray background in the atmosphere and in detector equipment. It is therefore essential to expose a γ -ray telescope in a low level of external background, i.e., above the atmosphere but below the Earth’s radiation belts, for long periods of observation to obtain the necessary detection statistics. For satellites, this is best achieved in a low Earth orbit (LEO) above the equator with an altitude of 400–500 km. Equally important is the design of the telescope so as to suppress the recording of unwanted charged particles (veto systems) and local γ radiation (material selections). Both requirements directly impact the sensitivity of a γ -ray telescope with detector exposure area A, detection efficiency ε, and angular resolution elements of size θ . Discrete cosmic sources with fluxes of Fγ embedded in a “quasi” continuous background intensity IB observed for an exposure time tobs are then detected with a statistical sensitivity of S:

S=

Fγ Aεtobs (IB Aεtobs π θ 2 )

1/2

=

Fγ θ



Aεtobs IB π

1/2

(1)

It is evident from Eq. (1) that high sensitivity is the result of a large effective area, Aeff = Aε, and long observation times, combined with small angular resolution and low background intensities. Of course this formulation is extremely simplified compared to more appropriate analysis tools using proper instrument response functions for effective detector area, angular and energy resolution, and detailed models for the background radiation, all as a function of primary energy and incidence direction.

Missions 1960–1990 The first successful satellite detectors for high-energy γ -radiation were small ˇ scintillation Cerenkov counter assemblies with anticoincidence shields. As depicted in Fig. 2, they had to fit on the satellites of the 1960s and could only transmit data with limited rates. The emission of >100 MeV photons from the inner Galaxy was, however, clearly established by the OSO-3 measurements (Kraushaar et al. 1972) and confirmed by a spark-chamber imaging balloon experiment (Fichtel et al. 1969). Here, it is interesting to note a performance comparison between the scintillator telescope and the pointed balloon instrument: both could achieve similar results on the Galactic emission with an effective area of 2–8 cm2 even though the former required ∼16 months of observation time, whereas the balloon flight only required several hours. Gamma-ray instruments for the low-energy range 50 MeV) was derived from ∼16 months of observations (Kraushaar et al. 1972), but the coarse angular resolution (15◦ ) prevented the detection of point sources

spectrometer, with its omni-directional response, a massive “well-type” collimator is placed around a central detector. Collimators can be either active radiation detectors, for example, made of BGO or CsI scintillators, or passive structures made of high-Z metals. Two examples of successful instruments are the γ -ray spectrometer (GRS) on the Solar Maximum Mission (SMM, 1981–1990; Fig. 3) and the Oriented Scintillation Spectrometer Experiment (OSSE) on the Compton Gamma-Ray Observatory (CGRO, 1991–2000). The advantage of an imaging telescope for astronomical observations was clearly established and led to the next generation of high-energy detectors, SAS2 and COS-B. Both high-energy satellite telescopes were based on digital readout spark chambers that allowed for the reconstruction of pair-creation events by tracking the electron-positron pairs. Around the central tracker, a charged particle anticoincidence shield made of plastic scintillator and, for COS-B, a calorimeter to measure the deposited pair energy were used. SAS-2 was developed on the basis of previous balloon detectors at NASA/GSFC, and the COS-B instrument was built by a European consortium of research institutes.

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Na I Spectrometer

Am 241

Na I Spectrometer X ray (2)

CsI Back Detector

Co60(3)

Front Plastic

CsI Annulus

Back Plastic

Fig. 3 SMM/GRS (1981–1990): an actively shielded multi-crystal scintillation spectrometer, sensitive to photons in the range 0.3–100 MeV (Forrest et al. 1980). SMM was continuously pointed at the Sun. The open acceptance angle of about (135◦ ) in the forward direction prevented the identification of individual sources, but allowed the instrument to monitor the temporal signatures of solar flares

The “MeV Sensitivity” Gap Figure 4 shows the sensitivities for past and current γ -ray instruments in the range between 10−2 and 105 MeV. While sensitivity should be defined case by case, i.e., depending on the source spectrum, its spatial distribution, and position in the instrument field of view, an order of magnitude estimate of the instrument performance can be given assuming a generic spectral shape at each photon energy. When provided with background estimates, the effective area, and a typical exposure time (here 1 Ms), the sensitivity can be calculated from Eq. (1) to the desired level (here 3σ). In general, the lower the sensitivity, the better the instrument performs. It is evident that the currently flying telescopes NuSTAR (0.03 GeV; chapter “Large Area Telescope”) shape a region in sensitivity space that peaks in the MeV. This several orders of magnitude worse sensitivity is called the “MeV sensitivity gap" and is the direct result of a small collection area (section “Instrument Designs”) combined with a high instrumental background (section “Instrumental Background”). Reducing this MeV gap is currently an active field of technological, methodological, and conceptual development, and attempts to alleviate the problems in the MeV range are described in sections “Other Apertures: Combinations and Wave Optics” and “Outlook and Conclusion”.

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Fig. 4 Continuum sensitivities of hard X-ray to high-energy γ -ray instruments. Shown is the 3σ sensitivity for an observation time of 1 Ms. The Crab’s spectral energy distribution from Meyer et al. (2010) is shown with respect to the sensitivities as it is the “standard candle” of high-energy sources. MilliCrab (mCrab) flux levels can only be seen with deep exposures in the 0.3–100 GeV range or below 100 keV. This defines the “MeV gap” of instrument sensitivities (red shaded area) – the least explored region in the electromagnetic spectrum

In addition to this MeV gap for continuum emission, there is also a similar problem for nuclear γ -ray lines. While COMPTEL on CGRO (⊲ Chap. 64, “The COMPTEL Experiment and Its In-Flight Performance”) could, for example, identify narrow line emission at 1.8 MeV, its spectral resolution was only 10% (FWHM) so that many lines blended together to form one broad feature. High spectral resolution in the MeV range can be achieved by the use of germanium detectors (section “Gamma-Ray Detectors”), such as in RHESSI or SPI. While increased spectral resolution helps to identify background features more easily, the small collecting area still prohibits the investigation of many potential astrophysical sources. As of now, only a dozen nuclear lines of astrophysical origin have been observed with HEAO-3, COMPTEL, RHESSI, and SPI (and NuSTAR). These include the positron annihilation line from the center of the Galaxy at 511 keV (e.g., Mahoney et al. 1994; Purcell et al. 1997; Jean et al. 2006; Churazov et al. 2011; Siegert et al. 2016, 2021); short- and long-lived ejecta from massive stars and their supernovae such as 44 Ti (e.g., Iyudin et al. 1997; Renaud et al. 2006; Grefenstette et al. 2014; Boggs et al. 2015; Siegert et al. 2015; Weinberger et al. 2020, at 68, 78, 1157 keV), 26 Al (e.g., Mahoney et al. 1984; Diehl et al. 2006; Kretschmer et al. 2013; Siegert and Diehl 2016; Pleintinger et al. 2019, at 1809 keV), and 60 Fe (e.g., Harris et al. 2005; Wang et al. 2007, 2020, at 1173 and 1332 keV); short-lived isotopes powering the early light curves of type Ia supernovae (e.g., Diehl et al. 2014, 2015; Churazov et al. 2014; Isern et al. 2016, with 56 Ni and 56 Co at 158, 812, and 847, 1238 keV, respectively); as well as nuclear excitation

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lines from solar flares (e.g., Gros et al. 2004; Kiener et al. 2006, with 511 keV from electron-positron annihilation, 2 H at 2223, 12 C at 4438, and 16 O at 6129 keV, among others). With a factor of 10 improvement in the line sensitivity, the number of detected lines, and therefore the science enabled by this, could increase by the same order of magnitude, eventually finding CR excitation of interstellar medium material, ejecta from classical novae, and multiple supernova lines (e.g., Timmes et al. 2019). The advantage of nuclear line studies is the possibility of finding an absolute measure of ejecta masses, CR fluxes, and kinematics, which may be biased by using observations at other wavelengths.

Interactions of Light with Matter While, for longer-wavelength light, most interactions with matter are either of refractive, reflective, or diffractive nature owing to the wave characteristic of light, higher-energy photons experience processes prone to particles instead of waves. These are used to determine the energy of the incoming light by measuring their partial or total deposits in the detecting material. While more processes can occur, the most relevant reactions for X- and γ -ray photons are photoelectric absorption (photo-effect), Compton scattering, and pair production. The photo effect (Einstein 1905) describes a photon undergoing an interaction with an atom in which the photon deposits its total energy and is removed completely. To conserve momentum and energy, a photoelectron is emitted by the absorbing atom. Since the interaction is with the atom as a whole, having bound electrons in its shells, the photo effect cannot occur on free electrons. The most probable electron to be ejected in photoelectric absorption is the one most tightly bound in the K-shell. The photoelectron has an energy of Ee = Eγ − Eb where Eb is the binding energy of the electron in the atom. The interaction probability for a γ -ray photon to undergo the photo effect is described by the cross section, typically as a function of energy, σPE =

16 √ Z5 2π re2 α 4 3.5 , 3 k

(2)

where re is the classical electron radius, α is the fine-structure constant, Z is the atomic charge number, and k = Eγ /(me c2 ) is the photon energy in units of electron rest masses (Fornalski 2018). Equation (2) is a valid approximation for k  0.9; for higher energies and for more precision over large photon energy ranges, the cross section from Davisson and Evans (1952) should be used. At photon energies of approximately between k = 0.1 and 1.0, depending on the material, the Compton effect (Compton 1923) becomes the dominant interaction process of light with matter. Compton scattering describes the process of a γ -ray undergoing scattering with an electron, assumed to be at rest. The photon changes

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its path as a result of this process and transfers some of its energy to the electron which then recoils. The deflection angle, also called the Compton scattering angle ϕ, is the fundamental property that determines the origin of the γ -rays in Compton telescopes (section “Quantum Optics in the MeV: Compton Telescopes”). Because, in principle, the range of scattering angles covers a full circle, the process of Compton scattering, i.e., the photon loses energy to enhance the kinetic energy of the electron, can also be inverted to inverse Compton scattering, i.e., the photon gains energy by scattering with fast electrons. In the range k = 0.2–20 (Fornalski 2018), the total cross section for Compton scattering is approximated by

σCE =

Z2π re2



   1 + k 2(1 + k) ln(1 + 2k) 1 + 3k ln(1 + 2k) . − − + 1 + 2k k 2k k2 (1 + 2k)2 (3)

Higher-order corrections can again be found in Davisson and Evans (1952). For k > 2, pair production (Blackett and Occhialini 1933), i.e., the conversion of a γ -ray into an electron-positron pair, becomes possible. While, formally, the production of pairs starts at twice the rest mass energy of an electron of 1.022 MeV, the interaction probability stays at a low level until the cross sections dominate, typically above k = 20. Pair production can occur in any electromagnetic field; for the detection of γ -rays, the Coulomb fields of nuclei are to be considered. The γ ray photon loses all of its energy in the process, is removed from the scheme, and is replaced by a pair that carries the total energy of the photon. The kinetic energy of the electron and positron, respectively, is symmetric about half the energy of the incident photon, minus the rest mass energy of the electron. The interaction cross section for pair production (Fornalski 2018; Davisson and Evans 1952) is σPP = Z 2 αre2



 28 218 ln 2k − + O(ln k/k 2 ) , 9 27

(4)

where higher-order terms span several lines of terms. The important feature to note here is that the cross section for pair production in the field of a nucleus increases with the charge number of the nucleus squared. In detail, the cross sections vary for different materials, compositions, and matter structures. In Fig. 5, the mass attenuation coefficients, nσ/ρ, with ρ being the density and n being the number density of the material, for γ -ray detector media that are typically used are shown. The shapes of photo effect, Compton scattering, and pair production are similar for the elements and compounds shown; however, the minuscule details change the behaviors and areas of use of the detectors. For example, plastic shows a much broader Compton scattering regime compared to other scintillating materials (e.g., BGO), making it the scattering material of choice of classic Compton telescopes (section “Quantum Optics in the MeV: Compton Telescopes”).

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Fig. 5 Mass attenuation coefficients for commonly used detector materials as a function of photon energy. The individual interaction processes are shown as colored lines. Left: Germanium (solid) and silicon (dashed). Compton scattering dominates in the energy range ∼200 keV to ∼10 MeV which makes these semiconductors efficient scattering detectors. Right: BGO (solid) and CZT (dashed). In these high-Z materials, absorption through photo effect or pair creation is more pronounced

Instrument Capabilities and Requirements In order to do γ -ray astronomy, the direction from which the γ -ray originated, its time of arrival, its energy, and its polarization would, ideally, be determined accurately. Depending upon the energy of the incident γ -ray and upon the nature of the source of interest, different types of γ -ray detectors are required for this task. As will be discussed in section “Astrophysical Sources of Gamma Rays: Not One Fits All”, some scientific objectives require highly accurate energy resolution, usually achieved at the expense of positional accuracy, i.e., angular resolution. Conversely, when high angular resolution is required, the spectral accuracy of the measurement usually has to be compromised. Gamma-ray polarimetry is an upcoming field, and individual chapters in this book are dedicated to this topic (⊲ Part XIX, “Polarimetry”); a brief overview of measuring the polarization of γ rays is provided later in this current chapter. A massive detector with limited positional but good energy resolution and deep enough to absorb most of the scattered photons can be used as calorimeter to measure spectra of incident γ radiation. Limited angular resolution can be achieved by fitting massive anticoincidence wells around the detectors leaving an “acceptance angle” free or by constraining the field of view with a passive or active collimator. A modern high-resolution Ge spectrometer is the MeV spectrometer SPI on the INTEGRAL mission (Winkler et al. 2003; Vedrenne et al. 2003), which in addition to a massive anticoincidence well encodes the incident γ -ray beam through a coded mask to enable imaging of radiation sources (section “Temporal and Spatial Modulation Apertures, Geometry Optics: Coded Mask Telescopes”). In order to detect a γ -ray via its pair-production interaction while extracting as much positional and energy information as possible, two main elements are

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required: Firstly, the γ -ray must be made to interact, i.e., pair produce, in the detector. In order to increase the probability of the γ -ray pair-producing, a high-Z material is required. For the Energetic Gamma Ray Experiment Telescope (EGRET) detector aboard CGRO, this comprised tantalum foils (Thompson et al. 1993), while for both the Large Area Telescope (LAT; ⊲ Chap. 68, “The Fermi Large Area Telescope”) on board the Fermi satellite and the Gamma-Ray Imaging Detector (GRID) on the Astro-rivelatore Gamma a Immagini LEggero (AGILE) satellite (⊲ Chap. 66, “The AGILE Mission and Its Scientific Results”), the high-Z converter material is provided by tungsten (Atwood et al. 2009; Tavani et al. 2009). The resulting electron-positron pair must then be tracked as accurately as possible so that the direction of the incident γ -ray can be reconstructed. This is done by measuring the passage of the electron/positron pair by the tracker. For EGRET, this was achieved by means of a multilevel spark chamber (Thompson et al. 1993). In both LAT and AGILE’s GRID, the trajectory of the charged particles is recorded by layers of silicon strip detectors (Atwood et al. 2009; Tavani et al. 2009) (section “Quantum Optics for Higher Energies: Pair Tracking Telescopes”). To determine the energy of a γ -ray, it is desirable to stop the electron-positron pair in the detector via a calorimeter, where the total energy deposit is measured. For EGRET, a large NaI Total Absorption Shower Counter was the principal energymeasuring device, while in LAT, the calorimeter comprises 16 modules, each of which is composed of 96 CsI(T1) crystals. The calorimeter on AGILE’s GRID is also composed of CsI(T1), in this case 30 bars arranged in 2 planes (Tavani et al. 2009). In addition to providing an energy measurement, a segmented calorimeter can also act as an anchor for the electromagnetic particle shower, providing further positional information to aid with pinpointing the direction of the incident γ -ray and to help with background discrimination (section “Tailored Data Selections”). The required elements of a γ -ray detector operating in the pair-production regime are, therefore, a tracker and a calorimeter. Not essential for the detection of the γ -ray but absolutely necessary so as to reject the overwhelming background of charged CRs that constantly bombard the instrument is an anticoincidence detector (ACD, section “Anticoincidence Shields”). This allows the detector to self-veto upon the entry of a charged particle, so it is essential that it has high detection efficiency for such particles. The ACD of EGRET comprised a large scintillator which surrounded the spark chamber. Backsplash, whereby a charged particle generated inside the detector traversed the ACD and thus caused a false veto, became a problem above 10 GeV (section “Background as a Function of Energy”). To avoid backsplash, the ACD of both the LAT and AGILE are segmented allowing only the segment adjacent to the incident photon candidate to be examined when searching for a veto. This drastically reduces the effects of backsplash allowing for a much more efficient background rejection by the ACD. All these considerations are summarized in the four basic parameters of any γ ray telescope, most importantly the effective area, as well as the energy, angular, and temporal resolution. An overview of current and past γ -ray instruments in the MeV– GeV range is provided in Fig. 6. It is clear that the effective area is the reason why

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Fig. 6 Characteristics of a selection of historic and current instruments as a function of photon energy. Top left: Effective area. Top right: Angular resolution. Bottom left: FWHM energy resolution. Bottom right: Timing accuracy

there is such a great loss in sensitivity in the MeV range (100 cm2 ) compared to the keV or GeV range (both 1000 cm2 ; section “The “MeV Sensitivity” Gap”). However, because of Ge detectors, for example, the spectral resolution of MeV instruments (FWHM/E ≈ 10−3 –10−2 ) can supersede those of GeV instruments by two orders of magnitude. The angular resolution of MeV telescopes can be similar to those of GeV telescopes, but only under specific circumstances, for example, when observing the Sun in the case of RHESSI with a temporal modulation aperture (section “Temporal and Spatial Modulation Apertures, Geometry Optics: Coded Mask Telescopes”). Normally, Compton telescopes suffer from their inherently poor angular resolution on the order of degrees, whereas coded mask telescopes could achieve arcminute resolutions or better (see section “Temporal and Spatial Modulation Apertures, Geometry Optics: Coded Mask Telescopes”). GeV telescopes can be considered almost direct imaging telescopes as the dispersion is only important for lower energies. Because of the trackers, angular resolutions below the 0.1◦ scale are possible. Finally, the scarcity of γ -rays from celestial sources as well as their intrinsic temporal variability adjusts the timing resolution to typical values around 100 µs.

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Earth’s Atmosphere and Space Environment Atmospheric Effects While at sea level the Earth’s atmosphere blocks almost all low- and high-energy γ -rays to the extent that ground-based observations are impossible, high-altitude observations are still worth the effort and reduce the cost. For instrument prototypes, in particular, balloon flights are often used to test new apertures and concepts. In Fig. 7, the transmissivity of the Earth’s atmosphere is shown for different photon energies, incidence angles (zenith), and altitudes above the surface (Hubbell and Gaithersburg 1996; Berger et al. 2017). The transmissivity is defined as the probability for a photon to reach a certain altitude without previous interaction and therefore to be unabsorbed. At aeroplane cruising altitudes (12 km), for example, the chance for a 1 MeV photon to pass through the upper layers of the atmosphere is 0.001% at most (i.e., at zenith). At this height, the transmissivity is maximized for 40 MeV photons at about 5%. Because of the exponential decrease in the density of the atmosphere, the stratosphere layers of the atmosphere (up to 50 km above ground) provide a useful environment for γ -ray telescopes. At typical balloon flight altitudes of around 30 km, the zenith transmissivity is already around 30% for photon energies of 50 keV. Up to 40 MeV, the transmissivity grows exponentially to about 85% and slightly declines afterward to flatten out at 80% for GeV energies. Clearly, with the beginning of the mesosphere at altitude of approximately 80 km, essentially all γ -ray photons are directly measurable, and only soft and hard X-ray photons remain absorbed. Beyond the von Karman line at around 100 km, which conventionally defines the border between the atmosphere and space, all photons are readily detected as the transmissivity is nearly 100% throughout the electromagnetic spectrum. Most important for γ -ray observations at balloon altitudes, however, is the zenith angle dependence. For the same photon energy and observation altitude, different zenith angles lead to vastly different transmissivities and therefore a much more drastic change in the effective area of the instrument (section “Instrument Designs”). While response functions for balloon experiments take into account the

Fig. 7 Transmissivity of Earth’s atmosphere as a function of incoming photon energy (left) and observation altitude above surface (right) for different zenith angles

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zenith dependence of their effective area, the simulations to provide a reasonable measure of the atmosphere effects require different setups depending on the balloon position around the Earth. This is the case because the local atmospheric conditions, including density and temperature, for example, and, in particular, the magnetic cutoff rigidity change with the Earth’s latitude and longitude (Smart and Shea 2005).

In-Space Observations Passing the 100 km mark, γ -ray instruments experience the space environment which mainly concerns the distributions of charged particles. In terms of onboard electronics, the instruments start to suffer more single event latch-ups and other effects. These are short circuits caused by heavy ions or protons hitting the electronics and triggering semiconductor band transitions. Apart from the latchups, the detectors themselves are also more susceptible to incoming radiation. This can be used as an advantage to measure the in-orbit particle spectrum and therefore provide a measure for the instrumental background (section “Instrumental Background”). Depending on the energy of the charged particles, they produce secondary particles when interacting with the instrument or satellite material. The secondary particles compose most of the instrumental background for γ -ray measurements in space, especially in the MeV range. The concentration of charged particles around Earth is not homogeneous. Because of the Earth’s magnetic field, charged particles are trapped around the planet in torus-like accumulations (Fig. 8). These are known as the Van Allen radiation belts (e.g., Ganushkina et al. 2011). Two tori trap electrons and protons, and to a lesser extent α particles, reaching from 0.2 out to 2 Earth radii (inner belt) and from 3 to 10 Earth radii (outer belt), respectively. While the inner belt contains sub-relativistic electrons (few hundred keV) and protons (∼100 MeV), the outer belt also holds relativistic electrons (up to 10 MeV). The outer belt is more easily influenced by the Sun and therefore more variable than the inner belt.

Fig. 8 Van Allen radiation belts around Earth (left) with inner and outer belts (to scale). Because the Earth’s magnetic field is tilted with respect to its rotational axis (dashed line), the closest part of the inner belt can reach to about 200 km above the southern Atlantic. This is called the South Atlantic Anomaly (SAA, right, adapted from Finlay et al. (2020) and reproduced with permission). Shown is the difference to the mean magnetic field intensity of 45.8 µT (red solid line) in steps of 4.1 µT until the region defining the SAA (solid purple line). Inside the purple region, the steps are 0.6 µT for a minimum around Earth longitude and latitude of 60◦ W and 28◦ S

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Because the magnetic field of the Earth is slightly tilted with respect to its rotational axis and the belts’ centers furthermore shifted from Earth’s center, the inner belt has an anomalously close approach at one specific region to the East of the South American continent. This is called the South Atlantic Anomaly (SAA, e.g., Pavón-Carrasco and De Santis 2016; Finlay et al. 2020). The anomaly represents an area in which the Earth’s magnetic field is weakest relative to its surroundings (Fig. 8, right). In this region, the inner belt approaches within 200 km of the surface which results in higher abundances of energetic particles. This leads to an enhanced instrumental background for satellite observatories (section “Instrumental Background” and ⊲ Chap. 54, “Orbits and Background of Gamma-Ray Space Instruments”).

Orbit Considerations There are options to alleviate the impact of the SAA and Van Allen radiation belts when the orbit of the satellite onboard which the instrument will be mounted is chosen. However, not all instruments suffer from the effects of the increased radiation in the same way. While MeV telescopes without major event selection capabilities (section “Tailored Data Selections”) should avoid the SAA altogether, GeV instruments are typically placed in LEO, i.e., orbits between 200 and 2000 km. Most astronomical observatories in LEO are found between 450 and 600 km. Above an orbit of 1200 km, the radiation belts would again lead to a much increased instrumental background. For MeV transient observatories in particular, for example, Fermi-GBM, the enhanced particle flux at LEO is of only mediocre concern because the background for short timescales (on the order of seconds or less) can easily be determined from adjacent times. For longer and targeted MeV observations, the radiation belts would lead to an insurmountable background rate which would heavily reduce the sensitivity of the instrument. For this reason, MeV observatories like INTEGRAL chose high eccentricity and high inclination orbits to escape the radiation belts for a significant amount of their orbits. The initial INTEGRAL orbit, for example, was a 72-hour orbit with an inclination of 52◦ and an apogee and perigee of 154,000 and 9000 km, respectively. Since the outer belt is populated with charged particles to at most 10 Earth radii (∼65,000 km), most of the time spent in this orbit (∼90%) is far away from the increased radiation. However, the instruments onboard INTEGRAL have to be switched off every time it approaches the Earth. For special tasks which cannot (or can only inaccurately) be performed by single instruments, special orbits can be considered. For example, some transient monitors have hardly any spatial resolution but can, however, be used in combination to provide highly accurate localizations (section “Interplanetary Network”). The difference in the photon arrival times of transients can be used in triangulation to map overlapping annuli onto the sphere of the sky. The larger the leverage arm, i.e., the larger the light travel distance between instruments, the better the localization accuracy. In particular, the gamma-ray spectrometer onboard Mars Odyssey in a Mars orbit provides a valuable baseline for Earth-orbiting transient detectors. This technique led to the term interplanetary network (IPN, e.g., Hurley et al. 2009;

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Fig. 9 Satellite orbits and balloon flight paths. From left to right are shown the Fermi orbit, the INTEGRAL orbit, and the COSI balloon path from a campaign during 2016. The orbits in each panel are to scale

section “Interplanetary Network”), for transient localization with triangulation. Another “orbit” of interest for γ -ray and other observatories is the Lagrange points, L2, of the Sun-Earth system (e.g., Wind, Spektr-RG), which also provide an excellent baseline for IPN measurements. While satellites follow a specified path and can, most of the time, perform maneuvers to correct their orbits (and to make sure that they re-enter the atmosphere when the mission is decommissioned), balloons have no or only little capability to adjust their flight paths. Because of security concerns, among others, balloon flights are typically launched from remote areas, such as Antarctica, or those which are only thinly populated. After the launch, the balloons experience the natural Earth environment and float freely governed by wind (lower atmosphere), temperature (day and night cycle), and torque (rotation of the Earth). Because the power generation has to be secured, which is mostly done with solar panels, the balloon gondolas are rotated toward the Sun during daylight. This also holds the aspect angle of the instruments, which simplifies the analysis. At night, the gondolas can again tumble freely, and minuscule changes in the altitude can lead to extreme variations in the flight paths. As examples, we show two satellite orbits as well as the longduration balloon flight path of the COSI prototype in Fig. 9. For more details on orbital considerations, the reader is referred to ⊲ Chap. 54, “Orbits and Background of Gamma-Ray Space Instruments”.

Instrumental Background Variations of the Background The interaction of charged particles, i.e., in general CRs, with instrument and satellite material leads to several different components that are summarized under the term instrumental background (for a more in-depth treatment of this subject,

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see ⊲ Chap. 54, “Orbits and Background of Gamma-Ray Space Instruments”). These are all unwanted primary and secondary particles and photons which lead to enhanced count rates in the instruments, diluting the celestial signals of interest. The interactions of CRs with matter lead to inverse Compton scattering, bremsstrahlung, nuclear excitation, spallation, radioactive buildup and decay, particle-antiparticle annihilation, and secondary particle production which can also undergo all of the previous interactions again. This results in a cascade of interactions that, depending on the energy range of the instruments, are measured continuously. The largest impact on the amplitudes of these processes is given by the solar activity and the terrestrial and solar magnetic field. Long-term trends in the instrumental background rate of MeV instruments are anticorrelated with the Sunspot number (e.g., Clette et al. 2014, 2016), which is a direct indicator of the solar magnetic activity cycle of 11 years (Fig. 10, top left). The solar modulation of CRs is related to the intensity of the turbulent solar wind, which increases when the Sun’s magnetic field is strong. In other words, this means that when there is a high number

Fig. 10 CR-induced background rates for different processes from different origins. Top left: Prompt MeV background is anticorrelated to the Sunspot number and thus with the solar magnetic field. Top right: Radioactive buildup can occur when the lifetime of isotopes (here 60 Co) is much longer than the activation function (cosmic-ray flux, inverse proportional to Sunspot number). Bottom left: Solar flare events provide a large single dose of mainly protons during a short amount of time. Intermediate lifetime isotopes (here 48 V) are enhanced by a factor of 10 and then decay according to their decay constants. Bottom right: Equatorial LEO satellites pass the SAA every 90 min, activating numerous short-lived isotopes which then decay during the next orbit. (Adapted and updated from Diehl et al. (2018) and Biltzinger et al. (2020) – reproduced with permission)

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of Sunspots, the instruments are better shielded from CRs. This leads to a reduction of the instrumental background rate which is why γ -ray missions are typically launched during or before the solar maximum. One famous example for this is the Solar Maximum Mission (SMM) launched in 1980. Two solar cycles later in 2002, INTEGRAL was launched – also near the solar maximum. Depending in addition on the chosen satellite orbit, the background rate can more than double between the solar maximum and minimum. This effect is visible for prompt background phenomena such as continuous processes (e.g., bremsstrahlung; Fig. 10 top left), nuclear excitation followed by fast de-excitation which typically happens on the order of nanoseconds, and particle production with fast decays from pions or βunstable elements. If the lifetime of the particles produced is (much) longer than the production timescale through CR bombardment, two other temporal evolutions of the background can be found. For example, if the radiation dose hitting the satellite is drastically increased, such as during a solar flare event with a coronal mass ejection, the background rates from γ -rays of all isotopes in the satellite can rise by several orders of magnitude. For isotopes produced during such events that are longer-lived, the background rate then stays at a high level even long after the initial dose. In Fig. 10, bottom left, the rise of the background rate from the element 48 V is shown. From a rather constant background rate of ∼6 × 10−4 cnts s−1 before the X-class solar flare on October 23, 2003 (= MJD 52935), the 48 V rate rises to more than 1 × 10−2 cnts s−1 . Because 48 V has a half-life time of 16 days, its rate decays only according to this decay time; the expected exponential decay is clearly seen. Such nuclear reactions occur continuously, either converting stable satellite materiel to radioactive isotopes, which then decay promptly or with some delay, or directly exciting the nuclei of the instrument which then de-excite by the emission of γ -ray photons. These γ -ray photons have specific energies so that individual isotopes and processes can be identified which helps in suppressing the instrumental background as a whole. In the case of a regularly enhanced dose of radiation, for example, by the passage through the SAA for LEO missions, the decays might not even go back to the base level because after about 90 min, the next passage of enhanced radiation occurs. This is shown in Fig. 10, bottom right, from a measurement of Fermi-GBM over the course of one day. Sixteen subsequent orbits and the different components making up the total measurement are shown. While, after the first three SAA passages, the corresponding levels go back to nearly zero, orbits 4–7 obtain a higher radiation dose so that until 40,000 seconds, the background rate gradually builds up. After orbit 8, only the very short-lived isotopes are seen in the data, while the buildup is still decaying on its own timescale. Other components, such as the Earth albedo, the general CR activation rate outside the SAA, the cosmic γ -ray background, as well as the Sun as a γ -ray source itself, stay constant. Only the change in orientation and aspect of the instrument with respect to the different astrophysical and background sources let the rates appear varying (Biltzinger et al. 2020). If the radioactive decay time of isotopes is much longer than the activation function from CRs, more and more radioactivity is created inside the instruments. In the case of 60 Co,

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for example, with a half-life time of 5.27 years, the decay rate is so small that over very long times, the background rate rises because there is radioactivity that built up. Figure 10, top right, shows the rate of the two γ -ray lines at 1173 and 1332 keV from the decay of 60 Co over 19 years of INTEGRAL/SPI measurements. Clearly, as the Sunspot number goes down, i.e., the activation rate goes up, the 60 Co rate also rises. Since the activation rate drops again after the solar minimum, but the material still decays, the background rate in these lines appears constant. Then after the second maximum, the rate rises again.

Background as a Function of Energy Since most γ -ray telescopes cover one or more decades of the electromagnetic spectrum, their measurements, and in particular their background, can appear quite different. Depending on the spectral resolution, which, technologically, can be much higher at MeV energies compared to GeV energies, the general appearance changes. At MeV energies, the background spectra are dominated by an electron bremsstrahlung continuum with a multitude of γ -ray lines on top (see Fig. 11 for an overview of background processes). Above ∼20 MeV, the decay and de-excitation lines from nuclei cease, and the spectrum is a pure continuum up even to very high energies (TeV). Pion production and decay (e.g., p + p → p + p + π 0 , followed by π 0 → γ γ ) describes the transition region from the MeV to the GeV background. While these interactions would produce a spectrum peaking at 67.5 MeV (half the rest mass of π 0 ) with a high-energy tail mimicking the incident proton spectrum, most of these interactions inside the instrument can be rejected due to their different signatures. The nuclear lines directly reflect the elemental composition of the satellite, the instrument, and the Earth’s atmosphere. For example, shown in Fig. 12, top, are the highly resolved NuSTAR and SPI background spectra. Most of the lines below ∼100 keV are due to X-ray fluorescence of satellite material, i.e., atoms become ionized due to impinging radiation, which leads to an electronic transition from higher to lower shells, followed by the emission of a characteristic photon. Depending on the element, these fluorescence photons can reach up to 115.6 keV (uranium K-shell), formally being an X-ray photon due to its electronic nature, however, falling into the “γ -ray” regime. The strongest instrumental lines in NuSTAR are due to K-shell fluorescences of cesium and iodine at 28 and 31 keV, respectively. Beyond the fluorescence lines, nuclear excitation lines, also appearing below 100 keV, shape the background spectra up to ∼20 MeV. Nuclear excitation is the interaction of an incoming particle with only the nucleus of an atom, therefore enhancing the energy scale of the process. In instruments, either stable nuclei are excited directly by 1–100 MeV particles or nuclear reactions, such as proton or neutron capture, lead to new nuclei which are produced in an excited state and de-excite promptly. For example, many of the strongest background lines in SPI are due to neutron captures and isomeric transitions of germanium isotopes. Isomeric transitions are the spontaneous nuclear transitions of a meta-stable nuclear configuration to a less excited state by the emission of a characteristic γ -ray

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Fig. 11 Instrumental background processes. Top: Nuclear excitation of instrument and satellite material by CR bombardment. An incident particle interacts with a nucleus from the instrument and forms a new isotope. This is formed in an excited state and de-excites by the emission of a prompt photon. The nucleus might still be left radioactive and decays (shown here as βdecay) toward a final nucleus, which may also involve the emission of a then delayed photon. Bottom left: Bremsstrahlung of a charged particle moving in the field of a nucleus. A negatively charged electron approaches the positively charged electric field of a target nucleus. By a change of direction due to electrostatic attraction (or repulsion in the case of positrons), the electron is emitting bremsstrahlung photons equivalent to the change of its kinetic energy. Bottom right: Particle production by relativistic CRs. If the incident CR is energetic enough, particle production can occur (similar to accelerator experiments). The thresholds to produce certain particles depend on the particles’ rest masses and the interacting nuclei. In the case of mesons being produced, for example, neutral pions (π 0 ), they decay on timescales of nanoseconds or less and emit γ -ray photons

photon. In SPI and other germanium detectors, multiple isotopes of germanium are naturally included in the crystals, so that multiple lines according to the different isotopes occur. The SPI lines at 23.4 and 175.0 keV are due to the second isomeric state of 71m Ge (T1/2 = 20 ms) and are coincidentally measured at 23.4 + 175.0 (T1/2 = 79 ns) = 198.4 keV to form its strongest background line (Bunting and Kraushaar 1974).

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Fig. 12 Example of measured (background) spectra. Top left: NuSTAR1 . Top right: INTEGRAL/SPI (Diehl et al. 2018). Bottom left: COMPTEL. (Reproduced with permission from Schoenfelder et al. 1993). Bottom right: Fermi-LAT. (Reproduced with permission from Ackermann et al. 2015)

Another strong line which always occurs in γ -ray measurements is the 511 keV electron-positron annihilation line. Either β + -unstable isotopes decay inside the satellite and produce a positron which quickly finds an electron to annihilate with or CR bombardment leads to secondary positrons which slow down and also annihilate inside the satellite. Compared to SPI, COMPTEL had poorer spectral resolution (Fig. 12, bottom left), so that multiple lines overlapped and merged together as distinct line complexes, or weak lines were just smeared out and drowned in the continuum background. A prominent line in the COMPTEL background was the neutron capture line on protons leading to a strong feature at 2.223 MeV. Most of these interactions occur for high accumulations of protons (hydrogen) which in COMPTEL was found either in its upper detector module filled with the liquid scintillator NE 213A (i.e., xylene, C8 H10 ) or in CGRO’s fuel tanks filled with hydrazine (N2 H4 ) (Schoenfelder et al. 1993). In the pair-production regime, a reduction in the γ -ray detection efficiency can be due to a number of effects including instrumental pile-up, the incorrect vetoing of γ rays, and particle leakage into the detector. One source of instrumental background

1 NuSTAR

observatory guide: https://heasarc.gsfc.nasa.gov/docs/nustar/NuSTAR_observatory_ guide-v1.0.pdf

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is the residual signal that remains from the shower initiated by a charged particle, which has been vetoed, but whose decay time is such that traces still remain when a γ -ray enters the detector volume and causes a trigger (Rochester et al. 2010). In this case, when the signals from the instrument are read out, there will be the signal NuSTAR observatory guide: https://heasarc.gsfc.nasa.gov/docs/nustar/ NuSTAR_observatory_guide-v1.0.pdf due to the genuine γ -ray event but also the residual signal that remains from the previously vetoed event. This can be seen schematically in Fig. 13. In Fermi-LAT, this residual signal is referred to as a “ghost” event, and it can be present in the tracker, the calorimeter, the ACD, or, indeed, in all three as is shown in Fig. 14. The effect has been modelled using simulations, so its effects are well understood and are incorporated in the analysis of LAT data (Ackermann et al. 2012).

Fig. 13 Schematic illustration of a ghost event. The remnants of electronic signals from the particles of a background event (1) that traversed the detector volume prior to the gamma ray (2) that triggered the instrument get read out along with the γ -ray signal

Fig. 14 Left: From Ackermann et al. (2012), an example of ghost activity in the LAT. On the right of the figure is a genuine γ -ray whose reconstructed track is shown by the dashed line. The ghost activity is visible in the ACD, tracker, and calorimeter. Only those ACD tiles with a signal are shown. Right: Reproduced with permission from Moiseev et al. (2007) – an illustration of the effect of backsplash in the simulation of the LAT ACD. Red lines show the charged particles and blue dashed lines show the photons. The red dots show the signals in the ACD due to backsplash

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Other sources of background that have been identified and effectively removed from the LAT data include non-interacting heavy ions and CR electrons that leak through the ribbons of the ACD (Bruel et al. 2018). Improvements to the analysis and simulations post-launch have led to better particle-tracking algorithms (Atwood et al. 2013) and γ -ray selections (Bruel et al. 2018). Thus, the effects of ghost events, leakage, and non-interacting particles result in only a minor loss of efficiency in the LAT’s γ -ray detection capabilities. Another way in which an inefficiency is introduced for the detection of γ -rays at GeV energies is when a true γ -ray gets incorrectly vetoed. In EGRET, this was referred to as “backsplash” (Thompson et al. 1993). Although most of the particles in the electromagnetic shower travel along the direction of the incident γ -ray, a small fraction of them go in the backward direction. The low-energy photons in these showers Compton scatter electrons in the ACD and these charged particles can then cause a veto. The effect became more pronounced at higher energies with EGRET’s detection efficiency degraded by a factor of 2 at 10 GeV compared to that at 1 GeV (Moiseev et al. 2004). The ACD for the Fermi-LAT was then optimized to avoid this issue (Moiseev et al. 2004). An illustration of the effect of backsplash in the LAT ACD simulation model is shown in Fig. 14, right.

Background Suppression As shown in Fig. 12, the measured detector rates from different instruments in the MeV to GeV range are on the order of 10−5 –101 cnts s−1 keV−1 . These rates are already reduced by different suppression mechanisms which decrease the rate of incoming particles and photons by several orders of magnitude. Depending on the energy range and instrument again, the methods to reduce (instrumental) background begin with the choice of the orbit (section “Orbit Considerations”). However, most of the reduction in the MeV–GeV range is achieved by active anticoincidence shields, by discrimination of signals in the readout electronics (⊲ Chap. 53, “Readout Electronics for Gamma-Ray Astronomy”), and through casespecific data selections in the multidimensional data spaces of γ -ray telescopes.

Anticoincidence Shields The general idea of an anticoincidence shield is to veto unwanted particles and/or photons that would enter the detector. This means the active detector is surrounded by another, sometimes U-shaped, active detector with a fast readout system. In the case of a U-shaped detector, the effects are twofold: first, the inner detectors are shielded physically from all directions except for close to zenith (the size of the shield defines the field of view, section “General Considerations: A Gamma-Ray Collimator”), and second, the inner detectors are shielded electronically from events that interact with the anticoincidence system. In Fig. 15, the normal, unvetoed observation case (top) and the vetoed observation case (bottom) with an anticoincidence signal triggered are shown.

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Fig. 15 Anticoincidence systems logics. Top: Two photons, (1) and (2), arrive from inside the field of view of the instrument and deposit their energies in the active detector (left). In the electronics readout (schematic, right), a pulse is registered for each event, and with its start, the detecting system is unable to record any more events during a specified time ∆T (dead time). Either the pulse height or the integral over the entire pulse over the time of measurement ∆T converts the registered event into an electronic channel number, which will be associated with a photon energy after calibration. Bottom: After photon event (1), a particle (2) hits the veto shield from the side. Shortly after, another photon (3) interacts with the detecting system. Because the veto shield triggers an anticoincidence (purple range, right), events (2) and (3) are both vetoed, and only event (1) is recorded

Most modern MeV and GeV telescopes have veto systems made of scintillator crystals with a high light yield. For example, the veto shields of the IBIS and SPI telescopes onboard INTEGRAL are made of BGO and show a typical count rate of up to 105 cnts s−1 . A considerable fraction of these counts would necessarily be measured in the main detectors and would heavily increase the average rate. However, the veto shields also have a huge disadvantage: they are heavy and come with more mass than would actually be needed for the main detectors, effectively reducing their sensitivity. More mass is equivalent to more instrumental background because CRs have more area to interact with. That means that there is a trade-off between the increased mass and the background reduction where the latter typically gets precedence. A major advantage of the massively increased photon collecting area of veto systems is their transient monitoring capabilities thanks to their quasi-all-sky fields of view. While the main detectors of many instruments only observe in the zenith

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Fig. 16 The INTEGRAL satellite as all-sky observatory. Shown are the different instruments and veto shields in the study of Savchenko et al. (2017a, left) and the efficiency of the instruments with respect to the SPI-ACS (right). For a given gamma-ray burst (GRB) spectrum and duration (here Band function (Band et al. 1993) with α = −1, Ep = 300 keV, and β = −2.5 for 8 s), the different instruments would be expected to measure certain rates relative to each other. This describes a “4π response”

direction, the veto shields see the entire sky, unless blocked by the Earth. If multiple instruments and shields onboard a satellite are combined, the sensitivity to transient events is largely enhanced, and the satellite functions as one big observatory. Savchenko et al. (2017a,b) showed and used this for the INTEGRAL observatories (Fig. 16). Because the mass required to shield MeV detectors can comprise a considerable portion of the satellite payload, the effective collecting area supersedes that of the main camera by up to two orders of magnitude. For example, the SPI veto shield ACS weighs 512 kg and reaches a maximum effective area of ∼104 cm2 (e.g., Savchenko et al. 2017a), however, without any spectral information (compared to the 10–102 cm2 of SPI). The veto system on COSI, for example, made of CsI, weighs about 100 kg (Tomsick et al. 2019). This means that whenever an active veto system is installed, careful consideration should be given to whether spectral information can be added to its detection system so that a spectral analysis of transients can also be performed. In the pair-production regime, where the background of charged CR particles outnumbers the γ -ray events by a factor of 104 –105 , plastic scintillator tiles are mostly used nowadays for the ACD; this is the case for both LAT (Moiseev et al. 2007) and AGILE (Tavani et al. 2009). These plastic tiles do not add too much weight and are a well-understood, efficient, reliable, and inexpensive technology (Atwood et al. 2009). The ACD of LAT comprises a total of 89 scintillating plastic tiles, with varying surface areas (between 561 and 2650 cm2 ) and thicknesses (between 10 and 12 mm), 16 of them on each of the 4 sides and 25 on the top of the instrument (Ackermann et al. 2012). The ACD of AGILE comprises 13 independent charged particle detectors (Perotti et al. 2006). As discussed in section “Background Suppression”, the segmentation of the ACDs of both LAT and AGILE allows for a localization of the veto signal to avoid false vetoes due to backsplash. To cover

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the gaps between ACD tiles in the X- and Y-axis, the LAT also has eight flexible scintillating ribbons. In LAT, the signal generated upon the passage of a charged particle is transmitted to the 194 PMTs (two for each ACD tile and two for each of the ribbons) via wavelength shifting fibers and clear fibers so that the veto can be registered. The signals from the AGILE plastic scintillators are read out via optical fibers connected to 16 subminiature PMTs. The total mass of the ACD on the LAT is 284 kg (the combined mass of the LAT is 2789 kg), while that of AGILE is 22.5 kg (the combined mass the AGILE scientific instruments is ∼100 kg).

Pulse Shape Discrimination Another useful technique to filter out particle events, for example, in MeV telescopes, can be achieved by measuring the shape of the incident pulse in the electronics. These pulse shape discriminators (PSD) include templates of rise times to peak and fall times to base level for different particle types so that unwanted particles can efficiently be ignored. The templates depend on the interaction locations in the detectors as well as on the charge carrier mobility as a result of the electric fields and applied voltages (Philhour et al. 1998). The general idea to distinguish, for example, β-particles from photons interacting with the detectors, is that the particles mostly interact in one particular site to deposit parts of their kinetic energy, whereas photons show deposits in multiple sites. This means that single-site events from electrons could potentially be rejected, which enhances the sensitivity of the instrument whenever the photon energies imply a high probability of scattering within the detector volume. Because photons can also be directly absorbed in only one interaction, the energy threshold for a PSD should be set around the turnover from photo-electric absorption to Compton scattering (Fig. 5), which depends on the material and geometry of the instruments. In Fig. 17, a sketch of pulse-shape-discriminated particles compared to photons is shown. PSD electronics have been employed, for example, in INTEGRAL/SPI and are also used to suppress electronic noise which arises from the saturation of its analog front-end electronics (Roques and Jourdain 2019).

Fig. 17 Working principle of a pulse shape discriminator. Events (1) (photon) and (2) (electron) are recorded by the detector. Their pulse shapes are compared to a template (dotted red). If the pulse shape is similar to a β-particle template, it is recognized and filtered out

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Tailored Data Selections The data that can be sent from the satellite to ground stations for further analysis and diagnostics is limited, and so, those that are downloaded must be considered and selected carefully. In the case of the LAT, for example, the onboard trigger is designed to pre-scale the volume of each particular event class that is downloaded so that a maximum of γ -ray candidates can be kept while also sampling a sufficient quantity of particular background and periodic trigger events to help characterize and keep track of the conditions under which the signal is detected. A more detailed discussion can be found in ⊲ Chap. 68, “The Fermi Large Area Telescope”. Once downloaded, the data can be subjected to different sets of analysis cuts, each designed with particular scientific goals in mind. The LAT, these are known as event classes, and they are optimized to address different science cases including, for example, transients, steady point sources or diffuse backgrounds. The quality and efficiency of the cuts are different for each class. Similar data selections can apply for the event selections in Compton telescopes, for example, then utilizing the Compton Data Space (Schoenfelder et al. 1993) to distinguish background and sky photons.

Astrophysical Sources of Gamma Rays: Not One Fits All Depending on the scientific goal of the observations being undertaken, the γ -ray instruments look very different because they are designed for specific tasks. Figure 18 shows a selection of images which highlight the diversity of the science that can be studied at γ -ray energies. The instrument capabilities need to be optimized according to both the energy range of the γ -rays being sought and the science case under study. An in-depth description of both Galactic and extragalactic γ -ray science can be found in Volume 3 of this handbook. Once the instrumental background has been taken into account in the data analysis, the signal that remains is that due to astrophysical γ -rays. Depending upon the energy range being investigated and on the pointing direction on the sky, this could be a superposition of a number of different components. Each of these components needs to be modelled and understood in order to study the γ -ray emission detected. Gamma-ray sources can appear point-like or extended, depending upon the combination of their intrinsic nature and on the angular resolution and exposure time of the instrument. The γ -ray emission from resolved sources will lie on top of that from the diffuse γ -ray background, itself a combination of unresolved point sources, the isotropic diffuse background and possibly containing the so-called exotic components such as contributions from dark matter annihilation and axions. Many solar system objects, for example, the Sun and the Moon, are γ -ray emitters and, in addition to being studied in their own right, constitute a foreground source that has to be accounted for when they pass between the γ -ray telescope and more distant sources for those instruments who can operate in their presence. The spatial, spectral, and temporal nature of the γ -ray sources being investigated are important considerations when designing an instrument and optimizing the observational and analysis strategy.

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Fig. 18 Top left: Gamma-ray spectroscopy using INTEGRAL/SPI. The spectral decomposition into lines is shown for near the 26 Al line (Diehl et al. 2018). Top right: A significance map showing the γ -ray sky above 15 GeV around the supernova remnant γ -Cygni (G78.2+2.1/VER J2019+407) reproduced with permission from Fraija and Araya (2016). Shown are the 1420 MHz observation from the Canadian Galactic Plane Survey at brightness temperatures from 22 to 60 K (green), the VHE source, VER J2019+407, smoothed photon excess contours (magenta), and the location of the γ -ray pulsar, PSR J2021+4026 (blue cross). The boundary of the extended LAT source 3FGL J2021.0+4031e is indicated by the white dashed circle. Bottom left: The light curve of GRB131014 in the 0.03–1 GeV energy range. The polynomial fit to the background is shown by a red line. The data are analyzed using the LAT low-energy technique, designed to optimize the study of bright transient events below ∼1 GeV (Ajello et al. 2019). Bottom right: The spectral energy distribution of the blazar 1ES 1215+304 from Valverde et al. (2020). The data and model are from the source when it was found to be in a low state. Shown are the blob synchrotron and synchrotron self-Compton (SSC) contributions (pale blue), the jet synchrotron and SSC emission (dotted– dashed pink), the intrinsic SSC emission without absorption from the extra-galactic background light (dotted blue), and the sums of all components (thick brown and thick black dotted–dashed)

Some γ -ray sources, certain supernova remnants or radio galaxies, for example, are extended and can have multiple emission components or exhibit different spectral features at different locations. The identification of a position-dependent photon index can help map out the underlying structure of the source, and thus, high angular and spectral resolution is a requirement. Sources can be steady emitters, meaning that they emit a flux that does not vary significantly with time. Often, extended sources of γ -rays have been found to belong to the class of steady emitters. The γ -ray emission from point-like sources can be

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variable over many different timescales from minutes (some AGN) to years (e.g., some binary systems), or, indeed, it can be periodic (pulsars and binaries), quasiperiodic (some AGN), or episodic (AGN, some pulsar wind systems). This variable signal may well sit on top of a more steady component. Other sources of γ -rays, such as GRBs and perhaps fast radio bursts, are one-off events meaning that their detection is dependent upon having a large enough field of view. The spectral properties of the γ -rays being studied should also be considered. Many γ -ray sources have continuous spectra that follow a power law, due to the nonthermal nature of their emission. The spectra of sources whose γ -ray emission is due to nuclear transitions will have a line nature. Many dark matter models also predict mono-energetic γ -ray signals meaning that spectral lines at an energy corresponding to the mass of the annihilating or decaying particle are sought. Similarly, the annihilation signature of neutral pions (an indicator of hadronic processes at work in the γ -ray source) will exhibit a characteristic bump. Many γ -ray sources also exhibit spectral breaks and cutoffs, so, depending upon the importance of accurately measuring these spectral features, the energy resolution of the instrument is an important consideration.

Instrument Designs Gamma-ray measurements in the MeV and GeV range classically rely on the modulation of one or more data space dimensions. Because single photons are counted in individual detector units, such a variation can appear minuscule and still lead to a significant change if treated properly by statistical means. The recognition of one or zero counts in the complex data spaces over a longer period of time leads to almost unique inferences when the full instrument response is applied. The instrument response is, in general, a kernel function that converts an (astro)physical model, such as a point-like or extended source with a certain spectral shape with physical units, into the native data space of the instrument, always counting photons per detector, time, energy (electronic readout channel), or other entities, as a function of its intrinsic coordinates given as zenith and azimuth angle. The instrument’s geometrical detecting area Ageom is therefore reduced to an effective area Aeff which depends not only on the incident photon energy Einc , time T , and zenith and azimuth angle (Z, A) of the source but also on the entire structure of the instrument, on environmental conditions (temperatures, voltages, etc.), and on the satellite mountings and orbit. Even for the simplest of all instrument designs, collimators (section “General Considerations: A Gamma-Ray Collimator”), it holds true that Aeff (Einc , Z, A, T , . . . ) ≤ Ageom .

(5)

For example, the geometrical detecting area of INTEGRAL/SPI’s 19 Ge detectors is 508 cm2 , while the maximum effective area for Z = 0◦ is 125 and 65 cm2 for 0.1 and 1.0 MeV, respectively (Vedrenne et al. 2003; Sturner et al. 2003; Attié et al. 2003).

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In what follows, different instrument designs, i.e., different aspects of modulation in various data spaces, are outlined briefly. The reader is referred to the subsequent chapters in which each of the γ -ray telescope apertures is explained in more detail.

General Considerations: A Gamma-Ray Collimator The basic modulation categories are summarized into temporal, spatial, energetic, and other apertures, as well as combinations thereof. As described earlier in this chapter, the history of low-energy γ -ray detectors started with collimators which should be considered a temporal and spatial modulator by the classification above. They are described as the basic principle from which other designs can be derived in the following. Collimator apertures are designed as large, often cylindrical, tubes with a detector unit (the camera) at the base of the tube (Fig. 19, left). The tube itself shields photons and particles from the side and the back, most of the time being itself an active γ ray detector to veto those unwanted events. In this way, the central camera only observes in the zenith direction with a field of view given by the measurements of the tube. As an example, if we take a cylindrical camera with diameter d, placed in a collimating tube with height h, the field of view, defined by the opening angle α of the aperture, would be given by α = 2 arctan(d/ h).

(6)

Fig. 19 Sketches for collimator and coded mask telescopes. Left: A collimator is built from an active detector that is surrounded by passive or active material to block photons and particles from the side. Only photons within the field of view, defined by the opening angle, α, are recorded. Right: A coded mask telescope adds opaque and transparent mask elements at the opening of the collimator tube. If the active detector is pixelated, this encodes incoming gamma-ray photons spatially, and their origin can be inferred

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If material opacities are ignored for the moment, the angular response of the collimator with one detector unit as the camera can be expressed analytically for a plane-parallel beam of light as Aeff (Z, A) = Ageom (Θ(Z + α/2) − Θ(Z − α/2)), where Θ(x) is the Heaviside step function and Z and A are the zenith and azimuth angle, respectively. This means that if the source is inside the field of view, the camera can detect all of the emitted photons, while it sees zero counts when the source’s aspect angle is greater than half the opening angle. Departing from this ideal view, for example, if the central camera consists of more than one detector and is therefore pixelated, the rise of a source with respect to the camera (decreasing zenith) now leads to a gradual increase of the effective area until the source is directly above the camera. For small fields of view, this results in an effective A area of approximately Aeff (Z, A) = geom π (arccos(τ ) − sin(2 arccos(τ ))), where τ = tan(Z)/ tan(α/2). This is strongly simplified and only serves as a means to describe the zenith dependence of a collimator-type instrument. These ideal treatments are erroneous once a real instrument is considered: The field of view is not a sharply defined region as described above but depends on energy. The higher the photon energy, the higher the probability that the photon is not absorbed by the collimating material so that it may be detected even from “outside” the field of view. If the instrument is not perfectly cylindrical, for example, if it is hexagonal or octagonal, the effective area gains an azimuth dependence. Finally, and probably most importantly for the analysis of γ -ray data, the incident photon energy Einc is not necessarily the measured photon energy Emeas : Because of Compton scattering, escape peaks, and instrumental spectral resolution, the measured photon energy is related to the incident photon energy only by a known but non-invertible redistribution matrix (section “Understanding Gamma-Ray Measurements”). This means that a measured spectrum is never representative of the source spectrum so that the latter must be inferred by forward modelling. The forward modelling then requires complete knowledge of the instrument, which is condensed in the response, often separated into an effective area contribution plus an energy redistribution, and which assumes a certain source model. The responses of γ -ray telescopes are typically determined by particle physics simulations using GEANT (section “Simulations”), which are then validated by calibration measurements on Earth using either radioactive sources or particle accelerator beams (section “Calibrations”). The source model can be versatile but requires the basic parameters of the object of interest, such as position, spatial extent, spectral shape, and temporal behavior. If the spectrum of a point source is being analyzed, the first two properties are typically fixed to known values. With more elaborate techniques, however, all unknown parameters of the observed target can be inferred in a single inference step. Different collimators have already been flown on balloon experiments between the 1960s and 1990s. The most successful collimator aperture was OSSE on CGRO (Johnson et al. 1993). It consisted of four independent, single-axis orientable, and actively shielded NaI(Tl)-CsI(Na) detectors, each surrounded by a tungsten shield. The fields of view of the detectors were 3.8◦ × 11.0◦ and sensitive in the 0.05– 10 MeV photon range. Due to its four independent units, OSSE could measure the

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instrumental background by simultaneously pointing away from and at the source of interest. This has the advantage that only the instruments themselves are moved and not the entire satellite. This technique was then further used to perform the first temporal and spatial modulated measurement which led to the first image reconstruction ever of the Galactic diffuse 511 keV emission (Purcell et al. 1993, 1997). Because the rise into and away from the fields of view of the four detectors changes uniquely with time over several years, an image could be reconstructed by singular value decomposition. It was shown for the first time that the 511 keV emission from the center of the Galaxy was not point-like and variable, but extended and constant.

Temporal and Spatial Modulation Apertures, Geometry Optics: Coded Mask Telescopes Collimators have no spatial, i.e., angular, resolution. The camera is pointed at a source to detect photons and is then moved away so that a background estimate can be provided. This is the simplest form of a temporal (or spatial) modulation: on-off observations. However, if more than one source is in the field of view, they might be difficult to analyze separately, especially if the field of view is large. The apertures are therefore changed to include more information. One way to improve the angular resolution is to place a mask on the top of the collimator’s shielding tube which encodes the incoming light beam to cast shadows onto the detecting area, the so-called shadowgrams. The first mentioning of coding γ -rays appears in Mertz and Young (1962) in the context of Fresnel transformations of images. This mask consists of opaque and transparent elements so that a fraction of the incoming light is blocked and only certain parts of the camera are illuminated. Much finer variations in the aspect angle change between source and telescope can be recorded with such a coded mask. The improvement in angular resolution then depends on the mask element size m, the size of the detector pixels d, and the separation between mask and camera l. In order to separate shadowgrams from different source positions inside the field of view, the detector plane must therefore be pixelated. For technical reasons, the detector size is adjusted to the science case and in particular the photon energy. While in the MeV range this means that one detector (one “pixel”) is several cm in size, which ultimately limits the angular resolution, the pixels can be much smaller (few mm) in the case of 100 keV detectors. This originates from the attenuation lengths required to stop a 1 MeV photon (e.g., in tungsten µ−1 ≈ 1.6 cm) compared to a 100 keV photon (µ−1 ≈ 250 µm). The mask elements should be as small as possible for the angular resolution to be maximized. However, the sensitivity of the instrument suffers when the mask element size is smaller than the detector size. The angular resolution of a coded mask telescope is approximately given by

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δΘ =



(m/ l)2 + (d/ l)2 ,

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(7)

and the positioning accuracy by δα ≈ (S/N )−1 δΘ with S/N being the signal-tonoise ratio of the source given a suitable background estimate. This means that the localization of a coded mask telescope naturally supersedes its angular resolution when the source is strong. The optimal trade-off between angular resolution, localization accuracy, and sensitivity is provided when m ≈ d (Skinner 2008). In order to remove ambiguities in the mask patterns that can emerge if a certain degree of symmetry is involved in the instrument design, targeting coded mask telescopes follow a particular observing strategy. Given the angular resolution and specific geometry of the instrument (symmetries, field of view), an observation pattern can be performed instead of staring at the source of interest for a long time. For example, INTEGRAL performs a rectangular 5 × 5 pattern around the source of interest, called dithering, to optimally sample the different shadowgrams of the mask onto the camera. This can also provide a measure of the unknown instrumental background during this observation because the shadowgrams of the sources inside the field of view smear out over longer periods of time (Siegert et al. 2019). Present and past coded mask telescopes are ISGRI (0.03–0.4 MeV, Ubertini et al. 2003) and SPI (0.02–8 MeV, Vedrenne et al. 2003) onboard INTEGRAL (⊲ Chap. 65, “The INTEGRAL Mission”), Swift-BAT (0.015–0.15 MeV, Krimm et al. 2013; ⊲ Chap. 44, “The Neil Gehrels Swift Observatory”), the CZT Imager onboard AstroSat (0.01–0.15 MeV; ⊲ Chap. 29, “The AstroSat Observatory”), the All-Sky Monitor (ASM) onboard RXTE (0.002–0.012 MeV), and the Wide Field Camera (WFC) onboard BeppoSAX (0.002–0.030 MeV). Details about coded mask telescopes are provided in ⊲ Chap. 48, “Coded Mask Instruments for Gamma-Ray Astronomy”. Another possibility to remedy the need for spatial variation can be achieved if parts of the instrument itself are movable. With several sub-collimators, which had been realized in the RHESSI imaging system (Hurford et al. 2002; Smith 2004), for example, an arcsec angular resolution had been achieved in γ -ray observations of the Sun. In the case of RHESSI, a pair of separated but parallel grids (opaque slats and transparent slit-like elements) inside each of its nine collimator tubes is rotated with respect to the detector plane at 15 revolutions per minute. This leads to the effect that a change in aspect angle produces a modulation of the transmission of the grid pair in time. The rotating shadow of the slats in the top grid then falls on the slits or slats of the read grid which results in a time-modulated transmission from 0 to 50% and back. Similar techniques have been applied for solar flare observations onboard the Hinotori mission with its rotating modulation collimator (RMC, 0.02–0.04 MeV; Sakurai 1991), HXT onboard Yohkoh (0.02–0.1 MeV; Acton et al. 1992), and the balloon-borne HEIDI (High Energy Imaging Device; Crannell et al. 1992) solar telescope with two RMCs. A currently active temporal modulation telescope is Insight-HXMT (0.02–0.25 MeV; Zhang et al. 2018).

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Quantum Optics in the MeV: Compton Telescopes In the 1920s, A. H. Compton introduced the classical concept of elastic scattering for the interaction of photons with matter. He showed that, in the energy range from ∼100 keV to ∼10 MeV, this scattering takes place between the incoming photon and an atomic electron. This results in an energized recoil electron and a deflected photon of reduced energy: in order to characterize the interaction, both secondary components must be measured. Elastic scattering conserves energy and momentum E0 = Escat + Ee , p0 = pscat + pe , where |p0 | = hν0 /c |pscat | = hνscat /c, and |pe | = me vγ with γ = 1/ 1 − β 2 with β = v/c, which leads to the so-called Compton equation: λscat − λ0 =

h (1 − cos ϕ) me c

(8)

where h, me , and c are Planck’s constant, the electron rest mass, and the speed of light, respectively. The fraction h/me c = 2.426 × 10−12 m is often called the Compton wavelength, which is the wavelength shift for a 90◦ scattering. It is important to note that, in a Compton scattering interaction, the incident photon can never lose all of its energy even if it is completely backscattered. Since, in this energy range, the photon energy is much higher than the binding energy of atomic electrons, the target electrons are taken to be free and non-interacting. This is a good approximation at these energies. For low-energy photons interacting with inner-shell atomic electrons, however, “Doppler broadening” of the angular response occurs (Zoglauer and Kanbach 2003; see also ⊲ Chap. 50, “Compton Telescopes for Gamma-Ray Astrophysics”). The total cross section (or absorption coefficient) of Compton scattering in any target material depends directly on the electron density and therefore on the nuclear charge, Z, of the detector material (section “Interactions of Light with Matter”). Equation (8) can be solved for ϕ and the wavelengths converted to energy,    1 1 , − ϕ = arccos 1 − me c2 Escat E0

(9)

where the energy of the scattered photon is Escat = hνscat =

1+

E0 , E0 (1 − cos ϕ) me c 2

(10)

and the kinetic energy of the recoil electron is Ke = E0 − Escat =

E0 (1 − cos ϕ) . me + E0 (1 − cos ϕ) c2

(11)

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Ke can also be expressed in terms of the angle Θ between the incident photon and the direction of the recoil electron, making use of the relation cot(Θ) = (1 + α) tan(ϕ/2) where α = E0 /me c2 , such that Ke =

2E0 α cos2 Θ . (1 + α)2 − α 2 cos2 Θ

(12)

Equations (8), (9), (10), (11), and (12) are directly based on the kinematics of the elastic Compton scattering process and are the basis for various realizations of Compton telescopes. In the “classical” two separated detector designs (e.g., COMPTEL; Fig. 20, left), a scattering detector D1 and an absorbing detector D2 trigger on a time-of-flight delayed coincidence signal and measure the positions and energy deposits of the two interactions. The positions indicate the path of the scattered photon between D1 and D2. Assuming the primary photon’s energy is the sum of both energy deposits (i.e., no undetected energy leakage occurred), the scattering angle is given by Eq. (9). The direction of the incident photon will then be somewhere on a cone around the scattered photon trajectory. If many photons from a distant point source are registered, their individual “event cones” all intersect at the direction to this source. For compact Compton telescopes (Fig. 20, right), the basic principle is the same; however, instead of two interaction layers, a position-sensitive detector volume is

Fig. 20 Compton telescope designs. Left: Classic two-layer Compton telescope. Photons scatter in the upper detector layer 1 via Compton scattering and are absorbed in the lower detector layer 2. Given the Compton scattering Eq. (8), each photon can be associated with a circle in the sky that forms a cone with the interaction point in the upper layer. The opening angle of this cone is given by the Compton scattering angle ϕ. Individual astrophysical sources can be identified by intersections of rings (orange photons). The time of flight (T OF ) between the two layers is indicated with its minimal value (perpendicular path between layers) and maximal value (defined by the opposite edges of the layers). Right: Instead of two layers, a position-sensitive detector, for example, made of several detector strips or with gas, allows the photons potentially to scatter more often (zigzag paths), always according to Compton scattering. The first interaction inside the detector volume again defines the Compton scattering angle. Three or more scatters help to identify the photon origins more clearly. In the case of the yellow photon on the right, only photo-absorption occurs, so that no Compton event reconstruction is possible

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used. This decreases the size of the telescope because no time-of-flight information is used and instead event reconstruction techniques are applied to identify the possible paths of scattering γ -rays inside the instrument. If the pixelation and threshold sensitivity allows recording the track of a Compton recoil electron, its initial direction (before Molière scattering disturbs it) can be used to reduce the event circle to an arc length. This can improve the overall sensitivity considerably. The distribution of closest offsets between the event cones and the true source direction is called the angular resolution measure (ARM). The width and “lopsidedness” of the ARM distribution is caused by uncertainties in the position and energy measurements and by possible energy leakage from the system.

Quantum Optics for Higher Energies: Pair Tracking Telescopes The measurement of the energy of a γ -ray in the pair-production regime is done by measuring the secondary products: electrons, positrons, and recoils on the target nucleus or electron. The latter recoils are not easily measurable, but they are of minor importance for higher γ -ray energies. The energies of the pair particles can be characterized by their scattering behavior (Molière scattering for low-energy electrons), or they can be totally absorbed in a deep calorimeter, where the initiated shower at high energies gives additional information for the total energy. Thus, to first order in most cases, the energy of the γ -ray is calculated by summing the energy deposited in each of the crystals of the calorimeter in the case of the calorimeter on LAT or AGILE or by means of the pulse height analyzers (PHAs) for the Total Absorption Shower Counter (TASC) NaI(T1) calorimeter on EGRET. Of course, some fraction of the energy of the incident γ -ray will have been deposited elsewhere in the detector prior to the shower’s arrival in the calorimeter. So, this energy must be estimated and added on to that deposited in the calorimeter. The tracking information deduced from the tracker and the shower’s position or trajectory into the calorimeter can be used to estimate its path through the detector and, combined with the energy measured in the calorimeter, can be used to estimate the energy deposited elsewhere in the detector (Fig. 21). The 3D passage of the electrons and positrons until they reach the calorimeter is reconstructed using a track finding algorithm. For Fermi-LAT, for example, the algorithm starts by generating a track hypothesis, i.e., a proposed trajectory made of locations and directions, that is accepted or rejected given the detector signals (Atwood et al. 2009). One possibility to fit these tracks and therefore to identify origin of the initial photon on the celestial sphere is by pattern recognition: The algorithm starts by assuming an (x, y) position in the top layer, which is compared to a subsequent hit as well as the energy deposited in the calorimeter. If these positions are close in the multidimensional data space, a candidate track is created by Kalman fitting. This process is repeated into the next layers, always taking into account the covariance matrices of the previous steps, until an adequate figure-of-merit is found. This ensures the correct propagation of uncertainties when scattering in different materials. In the calorimeter-seeded pattern recognition for Fermi-LAT, this process

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Fig. 21 Pair tracking telescope design. Incoming high-energy photons are converted into electronpositron pairs in passive material. With position-sensitive detectors, the electrons and positrons are tracked until they deposit all their energy in a calorimeter. The tracks and final energy deposit are used to determine the total energy and direction of the incoming photons. In contrast to MeV telescopes, the background is dominantly from CRs, so that the anticoincidence system is building a shield above the tracker and calorimeter

provides a χ 2 goodness-of-fit criterion for the Kalman fit, the number of hits in the tracker, and the number of gaps (layers not hit or unrecognized). A quality parameter is derived from a combination of these values, sequencing the possible candidate tracks from “best” to “worst.” In addition, the fitted values also return an error ellipse to each photon’s position in the sky. For the higher-energy γ -rays, the shower will not be completely absorbed by the calorimeter, so this missing energy must also be estimated. For low-energy γ -rays, a significant fraction of their energy can be deposited in the tracker. In these cases, the tracker is considered to be a sampling calorimeter (Atwood et al. 2009), and, in the case of the LAT, the number of silicon strips that had hits in them is used to estimate the energy deposited therein. In the case of EGRET, by the time the shower induced by a low-energy γ -ray reached the TASC, there may not have been sufficient energy deposit to trigger one or both of the PHAs (Thompson et al. 1993). These events were assigned a different class, and the energy was estimated by an alternative means. Another case in which the calorimeter cannot be used to estimate the energy of the incident γ -ray is when the direction is such that the shower misses the calorimeter. In these cases, again, the energy deposited in the tracker can be used to provide an estimate of the energy albeit one with a larger uncertainty. In all cases, energy loss due to leakage must be taken into account. This leakage can occur out the sides and back of the calorimeter, in the various materials that comprise the detector volume and, in the case of the LAT and AGILE, between the internal gaps in the calorimeter modules.

Scattering Information: Gamma-Ray Polarimeters All basic interactions of light with matter from section “Interactions of Light with Matter” are intrinsically sensitive to the polarization properties of the photons.

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In the case of longer wavelengths, filters can be used to distinguish between different polarization angles η and the polarization degree Π . In the case of hard X-rays to high-energy, GeV photons, such filters are impossible to construct so that the polarization parameters of astrophysical sources are inferred from the distribution of secondary particles in the instruments. The differential cross sections for photoelectric effect, Compton scattering, and pair production show an asymmetry with respect to the incoming photon’s polarization angle, whose amplitude is proportional to the polarization degree (also called polarization amplitude). This asymmetry can be measured if position-sensitive detectors for photons and resulting particles are employed. It is important to note that the total cross sections for the three main interactions are unchanged by photon polarization and that, with these techniques, only linear polarization can be measured. Conceptually, the polarization degree can be defined as the maximum variation in the azimuthal scattering probability (Novick 1975; Lei et al. 1997) as Π=

dσ⊥ − dσ , dσ⊥ + dσ

(13)

which is to be compared to the actually possible modulation capabilities of the instruments. In Eq. (13), dσ⊥ and dσ are the scattering cross sections for photons perpendicular and parallel to the emission plane. Photoelectric absorption produces an electron whose angular distribution depends on the polarization of the incident photon. In the classical sense, the electrons accelerate in the direction of the electric field of the incident photon. However, the exact distribution of photoelectrons also depends on the microscopic properties of the absorbing material, for example, the electronic band structure in solids, which makes an exact derivation of the differential cross section as a function of polarization angle cumbersome. In the Born approximation (Sauter 1931; Scofield 1989; Costa et al. 2001; Sabbatucci and Salvat 2016), the differential cross section can be expressed as dσPE (Eγ , η) = re2 Z 5 α 4 dΩ



me c 2 Eγ

7/2 √ 4 2 sin2 θ cos2 η (1 − β cos θ )4

(14)

where Eγ is the total energy of incoming photon, re the classical electron radius, Z the material’s charge number, and α the fine-structure constant. The initial derivation of the Compton scattering cross section already included the polarization angle of incident photons (Klein and Nishina 1929), dσCE (Eγ , η) 1 = re2 dΩ 2



λ λ′

2 

 λ λ′ 2 2 + − 2 sin θ cos η , λ′ λ

(15)

with λ/λ′ = (1 + (Eγ /(me c2 ))(1 − cos θ ))−1 . In this case, the scattered photon obtains a preferred direction with respect to the incident polarization angle.

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The differential cross sections for pair production with polarized photons have been calculated and studied in e.g., Maximon and Olsen (1962); Motz et al. (1969); Depaola and Kozameh (1998); Bakmaev et al. (2008), among others, for numerous cases including form factors, partial screening of the nucleus charge, and pair creation in the electron field, etc. The equations resulting from these calculations are too long to be useful in this summary; however, they all have one factor in common: they depend on the polarization angle η as dσPP (Eγ , η)/dΩ ∝ A(1+B cos2 η). The factor cos2 η appears in all the differential cross sections for the basic interactions of polarized light with matter. Making use of the resulting azimuthal distributions of either scatter photons (Compton scattering) or produced particles (photoelectrons, pairs) will infer the polarization of the incoming photons. Dedicated instruments that use these techniques are, for example, IXPE (Weisskopf et al. 2016) in the photon range 2–8 keV (photoelectric effect) and POLAR in the energy range 50–500 keV (Compton scattering; Produit et al. 2005). Other instruments can measure polarization of low- and high-energy γ -rays; however, they have not been initially designed for this task. These include INTEGRAL/SPI (e.g., Kalemci et al. 2004; Chauvin et al. 2013) by scatterings between its detectors, CGRO-COMPTEL (e.g., McConnell and Collmar 2016), and the COSI balloon (Lowell et al. 2017; see also chapter “COSI Polarisation”), all in the photon range 0.1–10 MeV, and Fermi-LAT (e.g., Giomi et al. 2017).

Other Apertures: Combinations and Wave Optics There are more γ -ray telescope concepts, some of which never flew until today and some of which are not feasible technically without major advances in space flight, for example. In the following, an overview of other such apertures is given.

Coded Mask Compton Telescopes Using the angular resolution from coded mask telescopes, Eq. (7), it is clear that the separation between the detector and the mask impacts the resolution as δΘ ∝ l −1 . Therefore, increasing the collimator tube (anticoincidence shield) length will result in better angular resolution; however, this comes with the problem of enhanced mass and consequently higher background and narrower field of view. One possibility to alleviate this problem is to use a combination of a coded aperture mask with a Compton telescope: in this way, the anticoincidence shield does not necessarily need to fill the gap between the detectors and the mask but only need to cover the position-sensitive detectors. Thus, there are two fields of views, one covering a small region from the mask to the detector and one defined by the veto shield that surrounds the detectors. A deployable mast (see also section “Reflective Optics for Gamma-Rays”) could place the mask several tens of meters above the camera, which narrows the field of view to α ∝ 2l −1 while at the same time improving the angular resolution by a similar factor δΘ ∝ l −1 . The Compton telescope part can then be used to only select photons that passed through the mask which results in considerable background rejection in addition to the veto shield.

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The imager IBIS aboard INTEGRAL is composed of two layers below a coding aperture, ISGRI and PICsiT (Lubi´nski 2009). This may be considered a coded mask Compton telescope; however, it only works up to ≈3 MeV because the mask becomes too transparent at higher energies. The separation between mask and camera is 3.2 m, and the Compton telescope layers are 9 cm apart; however, everything is still shielded by the IBIS veto system. This results in an angular resolution of 12 arcmin within a field of view of 9◦ . A proposed instrument that would extend these capabilities is GECCO, the Galactic Explorer with a Coded Aperture Mask Compton Telescope (Orlando et al. 2021). GECCO’s mask-detector separation would be about 20 m, resulting in a 4◦ field of view with an angular resolution of 1 arcmin. The pixelized camera would be made of CZT, resulting in a spectral resolution of ≈1%.

Reflective Optics for Gamma-Rays X- and γ -rays that approach any material perpendicular to its surface will either be absorbed, undergo Compton scattering, or produce pairs, so that refraction of high-energy photons onto a focal plane – the typical case for optical photons – is difficult. The refractive index for most materials in X- and γ -ray are close to 1.0 (or smaller) so that refractive optics (classical lenses) cannot be used for highenergy photons (see, however, section “Diffractive Optics”). Therefore, the only way to “focus” high-energy photons is to use grazing incident optics that rely on reflection off mirrors in an X-ray Wolter-type telescope (Wolter 1952a,b), for example. For incident angles smaller than some critical value that depends on the photon energy and refraction index of the material, the photons undergo total reflection and thereby avoid photoelectric absorption. In general, the critical angle √ is proportional to ρ/Eγ , where ρ is the density of the material. Thus, for a fixed incidence angle, photons can only be totally reflected up to a cutoff energy that is related to the K-edge of the reflecting material. For photons above 10 keV, the critical angles approach too small values to be used in Wolter telescopes unless the reflective coatings are very thin or the focal length very high: For example, platinum at an incidence angle of 0.07◦ shows a reflectivity of more than 90% up to 68 keV and sharply drops below 20% at higher energies. Wolter telescopes have an effective area that is approximately Aeff (Eγ ) ≈ 8πf Lθ 2 R 2 (Eγ ),

(16)

where f is the instrument’s focal length, L is the mirror length, θ is the incidence angle, and R(Eγ ) is the reflectivity as a function of photon energy Eγ (X-ray Telescopes Based on Wolter-I Optics|The WSPC Handbook of Astronomical Instrumentation). Clearly, for the highest possible effective area, the focal length should be maximized as the material parameters R(E) and L are naturally limited. One instrument in which this focal length maximization, together with Pt/C multilayer coatings to effectively reflect photons below the Pt K-absorption edge at 78.4 keV, is NuSTAR (Harrison et al. 2013). NuSTAR is the first focusing hard

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X-ray telescope ever launched into orbit. It employs 133 nested grazing-incidence shells in a conical approximation to a Wolter telescope to focus photons onto a focal plane made of a pixelated CZT detector. NuSTAR’s focal length of 10 m is achieved by a deployable mast that was extended after the satellite was launched into its orbit. Because reflective optics are ultimately limited by Eq. (16), i.e., focusing higher photon energies would require smaller incidence angles (∝ θ 2 ) and a much larger focal lengths (∝ f ) to accommodate a high level of effective area, these types of apertures are probably not suited beyond photon energies of ∼200 keV. A proposed instrument that is based on reflective optics is PheniX (Roques et al. 2012), which would have a focal length of 40 m, also obtained by an extensible mast.

Diffractive Optics Beyond total reflection, there are the possibilities for refraction and diffraction of γ -ray photons. Yang (1993) who discussed refractive optics for photon energies up to 1 MeV, however, found that absorption and scattering severely limits the ability to form an efficient telescope with large effective area. Therefore, only diffraction permits improvement upon the classic non-focusing γ -ray instruments. In general, the diffraction limit defines the spatial resolution sd = 1.22λf/d, with f being the focal length, λ the photon wavelength, and d lens diameter, and provides the fundamental limit to the achievable angular resolution, θd = sd /f . Thus, for photon energies around 1 MeV (λ ≈ 1.24 pm), the angular resolution approaches microarcseconds (m′′ ). This is possible by the use of phase Fresnel lenses (Miyamoto 1961) in which concentric rings of precisely placed crystals diffract the high-energy photons onto a detector at the focal point. The distance of the focal point where the γ -ray detector is placed, however, is related to the lens diameter d, the photon energy E, and the pitch size of the Fresnel lens p by

p  d  E  f = 0.4 × 10 km, 1 mm 1m 1 MeV 6

(17)

which makes the realization of a telescope on a single spacecraft almost impossible (Skinner 2001). It should be noted that Fresnel lenses suffer severely from chromatic aberration, effectively worsening the achievable angular resolution by factors of a few, and distorting the received spectrum. Nevertheless, concepts to build γ -ray-focusing (concentrating) telescopes exist and are discussed in this book (chapter “Gamma-Ray Lens”). An important part of these concepts is the formation flight of two or more spacecrafts in sync. Another possibility to achieve a much enhanced sensitivity would also be to use a deployable boom, such as used in the ASTENA proposal (Frontera et al. 2019, 2021). Here, the goal is not to approach the diffraction limit, but to construct a design feasible with current technologies. With a 20 m focal length, an angular resolution of 30 arcmin could be achieved in the bandpass between 50 and 600 keV, reaching a continuum sensitivity of more than two orders of magnitude better than INTEGRAL/SPI thanks to ASTENA’s effective area of more than 7 m2 (Frontera et al. 2019).

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Interplanetary Network In fact, several spacecrafts are already used in combination in the so-called Interplanetary Network (IPN; e.g. Hurley et al. 2009). While the spacecrafts are not flying in formation, their absolute distances to each other can be used for triangulation of celestial burst-like signals, such as GRBs or soft gamma repeaters. In particular, the localization is performed by a comparison of the arrival times from the different γ -ray instruments wherein the precision is given by the distances of the spacecrafts and the absolute number of detected photons. The further the instruments are separated, i.e., the larger the baseline of potentially several hundred millions of kilometers, the more accurate the localization will be. The triangulation technique is explained in Hurley et al. (2013), for example, and depicted here briefly: A transient event is measured with a delay time δT at two different spacecrafts. Given the separation D of the spacecrafts, the transient is localized onto an annulus on the celestial sphere with half-angle Θ as cos(Θ) =

cδT , D

(18)

with c being the speed of light. The “error box” or width of the annulus is provided by the uncertainty of the time delay as σΘ = cσδT /(D sin(Θ)). Burgess et al. (2021) showed that this classical triangulation method has weaknesses because the choice of uncertainties may be ill-defined. The authors developed a novel method that can robustly estimate the position of a transient via a hierarchical Bayesian model. In particular, they forward-fold the unknown temporal signal evolution, described by random Fourier features, and fit this model to the time series data of each instrument. This takes into account the appropriate Poisson likelihood, and consequently the uncertainties generated by the method are more robust and in many cases more precise compared to the classical method. The IPN started in 1977; its third version, IPN3, was operating with Ulysses, CGRO, Pioneer Venus Orbiter, Mars Observer, and BeppoSAX. Currently, the IPN localizations come from Konus-Wind, Mars Odyssey, INTEGRAL, Swift, AGILE, BepiColombo, and Fermi. In total, more than 32 spacecrafts have been involved in the IPN so far.

Gamma-Ray Detectors Most γ -ray emission processes are continuum-like. Instrumental resolution is, therefore, not too important except for when one wants to do line spectroscopy. Since lines only appear up to the MeV range (20 MeV), spectral resolution is less of an instrument design driving factor above ∼20 MeV. When choosing the materials that compose the target for the incident γ -ray signal, a trade-off between instrumental resolution, weight, sensitivity, and power is always at play. The materials that are used to detect the by-products (charged particles) of the incident γ -ray at these energies broadly comprise two main categories, solid-

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state detectors and scintillators. Solid-state detectors are discussed in detail in chapters (chapters “Germanium Detectors for Gamma-Ray Astronomy” – Roques; and “Silicon Detectors for Gamma-Ray Astronomy” – Caputo; and ⊲ Chap. 57, “Cd(Zn)Te Detectors for Hard X-ray and Gamma-ray Astronomy” – Meuris). They are lightweight, compact, and more tolerant to a space environment than vacuum or gas-based detectors. In general, they comprise a semiconductor material (such as silicon, germanium, or CZT) which is reverse-biased so that the electrons and holes can move freely in the so-called depletion region. When a charged particle (electron or positron) enters this sensitive area of the crystal, ionization is produced. This signal is then transferred via a charge-sensitive preamplifier where it is converted to a voltage pulse proportional to the strength of the ionization signal. For example, the spectrometer SPI uses an array of 19 high-purity cooled germanium detectors to perform high-resolution spectral measurements between 18 keV and 8 MeV (Fig. 22). Silicon strip detectors are used to detect the passage of the electron-positron pairs for both the LAT on Fermi (Atwood et al. 2009) and for the GRID on AGILE (Perotti et al. 2006) Scintillation detectors comprise a material that produces light when it is traversed by a charged particle. They are described in detail in chapter “Scintillators for Gamma-Ray Astronomy” – Iyudin. The scintillation light is recorded by a photodetector (often a photomultiplier tube or photodiode) so that the passage of the charged particle and, in certain cases, its energy can be measured. Scintillator materials can be organic or inorganic in nature. Inorganic scintillators, including NaI and BGO, are usually chosen for calorimeter systems due to their high density and effective atomic number which means that they have a high stopping power. Inorganic scintillators comprise four main categories: plastic, glass, single crystal, and liquid. Plastic scintillators are those most commonly used in γ -ray applications due to their lightweight, low cost, and robustness. The light yield from inorganic scintillators is typically higher than those from organic scintillators so that it is typically used as a material for veto shields.

Fig. 22 General MeV γ -ray measurement features as observed in detectors. A beam of photons with energies Eγ creates a photopeak at this energy. Compton scattering inside the detector leads to a characteristic continuum below the photopeak. If the incoming photon energy is greater than 2me c2 = 1.022 MeV, single and double escape peaks can emerge

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Understanding Gamma-Ray Measurements The nature of γ -ray measurements can be understood as the recording of photons into complex data spaces due to the vastly different apertures. These data spaces are typically shown in the form of back projections, such as the shadow pattern of coded mask instruments or the rings from Compton telescopes. In the case of GeV instruments, this “imaging” is only weakly influenced by dispersion which is why we focus more on the MeV instruments here. Nevertheless, the concepts here apply to all dispersed measurements. The abstract data spaces of γ -ray instruments are spanned by reconstructed or inferred variables, such as the three scattering angles in Compton telescopes or the number of pixels (detectors) in coded mask telescopes. Typically, these data spaces are not necessarily the real instrument spaces because they can have considerable uncertainties which are often omitted in the subsequent data analysis steps or because data filtering due to quality criteria after reconstruction skewed the true generating process: counting photons. The real data space of each instrument goes down to the level of its electronics and the specific geometry – a coding mask, shadow patterns, Compton cones, iterative deconvolutions, polarigrams, scattering angle distributions, a coding mask etc., – are always abstractions of how to possibly visualize raw data. In the reconstructed variables or data spaces, data analysis should be treated with care because there are often (hidden) assumptions which destroy the character of the measurement, change its likelihood, or are ill-defined because the instruments suffer from dispersion. Instead, the method of forward-folding should be used to convolve models with physical units into the raw data space of channel number per detector unit. Forward modelling is the only statistically proper way to analyze γ -ray data d, which, without loss of generality, can be described as matrix equation d = R · m,

(19)

with R being the response matrix and m an (unknown) model that is to be inferred. Except for approximate cases (e.g., mask coding with fully transparent and opaque elements, ⊲ Chap. 48, “Coded Mask Instruments for Gamma-Ray Astronomy”), R is not invertible which means that a solution shaped like m = R−1 d does not exist. The model m is not measured; only the data d are, which means in turn that m must be assumed, i.e., modelled to explain the data. This is done by parameterizing the model with a set of variables, the so-called fit parameters ϕ, so that the model becomes a function of unknown parameters: m(ϕ). The model includes everything that is required to describe the astrophysical source of interest. This means it includes a spectral shape, temporal variability, spatial extent, and polarization parameters, among others. These properties can be interdependent, which can be incorporated in the response function R (Fig. 23). The response is described in units of cm2 and is equivalent to the effective area, i.e.,

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it changes as a function of zenith, azimuth, initial energy, polarization angle, and instrumental environment parameters (temperature, voltage, etc.). Typical features visible in spectral dispersion matrices are the Compton edges (at measured energies Ef = Ei (1 − (1 + 2Ei /(me c2 ))−1 ), approaching Ei − 0.25 MeV for large Ei , Compton continuum (single and multiple scatters), first and second escape peaks (Fig. 22), and emergence of a 511 keV line for initial energies above 1.022 MeV. Conceptually, the data are generated by assuming a source’s position (in astronomical coordinates) which converts to instrument coordinates (zenith/azimuth) for which an instrumental response is created. A differential spectrum (in physical units, e.g., ph cm−2 s−1 keV−1 ) is integrated over the energy to obtain the expected flux per response element (→ ph cm−2 s−1 ), to which the response function is applied, resulting in an expected rate per data space bin (→ cnts s−1 ). Note the change of notation here from physical photons to received number of counts after the application of the response. Given the exposure time, the model counts per data space bin i (→ cnts) can be compared to the data via the Poisson likelihood

Fig. 23 Visualization of MeV telescope responses. Left: Back projection of the SPI coded mask response seen from its central detector (unit 00) at an energy of 66 keV. The same mask pattern is visible for an outer detector (second image, unit 12, which is equivalent to shifting the source position) at an energy of 5 MeV; however, the edges are not as sharp because the transparency of the material increases with photon energy. The inner edge of SPI’s anticoincidence shield is visible (hexagonal shape outside the central ring). Right: Back projection of Compton circles from the COSI balloon response. Shown are 20 Compton circles at an energy of 511 keV, overlapping in the source position. An iterative deconvolution algorithm (fourth image) is applied to reduce improbable regions so that a point source emerges

Fig. 24 Energy dispersion of different γ -ray detectors in units of cm2 . Given a photon with true (initial) energy Ei , there is a probability that the photon is measured at a lower (final) energy Ef . The diagonal represents the photopeak efficiency. Left: NaI detector onboard GBM. Middle: BGO detector from GBM. Right: SPI germanium detector. The scale of the color bar is enhanced by two orders of magnitude for SPI to indicate the features away from the diagonal

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Fig. 25 Forward folding of spectral models into the count data space of different detectors. Top: Selection of five spectral models. A broken power law representing the Crab spectrum (Jourdain and Roques 2009); a Band function (Band et al. 1993) with 10% of the Crab flux, α = −1.5, β = −3.0, and Epeak = 1.5 MeV; a cutoff power law with 10 times the Crab flux, α = −3.0, EC = 100 keV; a positronium (ortho+para, Ore and Powell 1949) spectrum with a line flux of 6 × 10−3 ph cm−2 s−1 ; and a 100 keV broadened 12 C line with the same line flux. Bottom: The models convolved with the energy responses from Fig. 24 for BGO (left), NaI (middle), and Ge (right). The resolution of the detectors is increasing from left to right. It is seen that different spectral models (e.g., the broken power law and the Band function) can appear very similar in the data space. Likewise, components above the maximum considered energy of the instrument contribute to the counts at lower energies because of dispersion

L(d|m(ϕ)) =

mi (ϕ)di exp(−mi (ϕ)) . di !

(20)

i

Finally, the once smooth (infinitesimal) model is transferred into the (possibly) binned data space. Examples of how such a convolution appears are shown in Fig. 25. Here, the same five models are folded through the responses of one of GBM’s NaI and BGO detectors and through the response of SPI’s central detector. Depending on the orientation of the detector with respect to the source in the sky (assumed to be identical here), the response changes (Fig. 24) as the incoming photons are dispersed in different ways in the same detector. It is also seen that different spectral resolutions impact the identification capabilities of different features – for example, lines can be seen more clearly with higher resolution. However, also highresolution germanium detectors suffer from dispersion, distributing more than 50% of photons with an initial energy of 4.4 MeV to lower energies.

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Simulations The above-described response functions, and therefore the entire data analysis and scientific output, rely heavily on simulations. In this handbook, an entire chapter is dedicated to the procedures, requirements, and details of particle and photon simulations (chapter “Simulation”). This also includes details about electronics simulations, detector effects, and methods to handle these in real measurements. Here, a short overview of the basic features and general idea is given to understand the need for simulations as well as a few examples and caveats. Before instrument prototypes are built, they are often simulated in the Geometry and Tracking (GEANT, e.g., Agostinelli et al. 2003) environment. In GEANT, active and passive volume elements are arranged as close as possible to the real geometry of the instrument and irradiated with particles and photons through a Monte Carlo technique. This allows the instrument designer to (1) estimate the performance of the instrument, (2) adjust the geometry and mountings before building the prototype, (3) choose appropriate materials, and (4) determine the response functions of the instrument. Because GEANT includes the most-complete database of cross sections and interactions of many particles, both the instrumental background and the sources of interest can be simulated. Using appropriate statistics, the sensitivity of the instrument can be estimated for different cases, for example, as a function of time, energy, spectral shape, and aspect angle. Including the anticoincidence shield in addition to the active detector(s) in the simulation will provide an estimate of the background reduction. Finally, for the full response as a function of initial energy, zenith, azimuth, and other environmental parameters, also the satellite (or balloon) structure must be included. The more detailed the geometrical mass model of the instrument, the better the scientific output in the end. However, the more sophisticated the mass model is, the longer the simulations will run. In addition, also the computational resources to perform the simulations might be limited. For example, the SPI response simulations (Sturner et al. 2003) have been performed for only 51 individual energies for the more than two decade spanning energy range. This was required because a full, highly resolved energy response would have taken years to simulate. With the ground calibration (Attié et al. 2003) (section “Calibrations”), the simulations have been validated so that a full response can be constructed by interpolation. Although SPI has an energy resolution of 2.7 MeV (Mandrou et al. 1997; Schanne 2002). SPI imaging was calibrated with high-flux sources of 241 Am, 137 Cs, 60 Co, and 24 Na, located outside the laboratory through a transparent window. The beams were strongly collimated to avoid radiation in other directions and scatters inside the experimenting hall. For energy calibration of SPI, the mask was removed so that all detectors could be illuminated simultaneously. Although the field of view of SPI is about 16◦ × 16◦ , the calibration took place only on axis, and no other zenith and azimuth angles have been tested. Instead, the telescope efficiency is derived from the absorption properties of the individually measured transmissivities of opaque and transparent mask elements (Sanchez et al. 2003). A mathematical model was then fit to obtain the correct mask properties given the full set of calibration measurements. For future MeV instruments, such as for COSI, a full field of view calibration is anticipated which will reduce the systematic uncertainties from calibrations with a single beam line plus simulations to obtain the instrument response functions.

Table 1 Radioactive isotopes and resonance photons used for the calibration of MeV instruments between 10 keV and 10 MeV (including K- and L-shell X-rays) with at least a branching ratio of 0.01 (in parentheses) (NUDAT; Kiener et al. 2004; Antilla et al. 1977) Isotope/reaction 241 Am

Half-life time 432.6 years

133 Ba

10.55 years

57 Co

271.74 days

139 Ce

137.64 days

137 Cs 54 Mn

30.08 years 312.20 days

152 Eu

13.517 years

65 Zn

13 C(p,γ )14 N

243.93 days 5.2714 years 2.6018 years –

27 Al(p,γ )28 N

–

60 Co 22 Na

Line energy [keV] 13.9 (0.37), 26.34 (0.02), 59.54 (0.36) 30.63 (0.34), 30.97 (0.62), 34.92 (0.06), 34.99 (0.11), 35.82 (0.04), 53.16 (0.02), 79.61 (0.03), 81.00 (0.33), 276.40 (0.07), 302.85 (0.18), 356.01 (0.62), 383.85 (0.09) 14.41 (0.09), 122.06 (0.86), 136.47 (0.11) 33.03 (0.23), 33.44 (0.41), 37.72 (0.04), 37.80 (0.08), 38.73 (0.02), 165.86 (0.80) 31.82 (0.02), 32.19 (0.04), 661.66 (0.85) 834.85 (1.00) 344.28 (0.27), 411.12 (0.02), 778.90 (0.13), 1089.74 (0.02), 1299.14 (0.02) 1115.54 (0.50), [511.0 (0.03)] 1173.23 (1.00), 1332.49 (1.00) 1274.54 (1.00), [511.0 (1.80)] 1635, 2313, 3948, 5105, 5690, 6445, 6858, 7027, 8062, 9169 1522, 1779, 2839, 3063, 4498, 4608, 4743, 6020, 6265, 7924, 7933, 10763

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GeV: Particle Accelerators There have been different ways to derive the instrument functions for past and present GeV telescopes: in pioneering counter-type instruments (e.g., OSO-3, Explorer XI), design and calibrations were based on analytical estimates (geometry, cross sections, and individual detector responses) which were verified on beam tests using π 0 decay photons or a synchrotron beam and the response to CR muons at ground level. The first imaging telescopes (e.g., SAS-2, COS-B) were calibrated with γ -ray synchrotron beams (up to a few 100 MeV), electron beams (to characterize the tracking), and CR muons (to test the anticoincidence counters). A full-scale beam calibration was performed on the next-generation EGRET instrument (Thompson et al. 1987; Kanbach et al. 1989). The γ -ray beam at the Stanford Linear Accelerator (SLAC) was generated by inverse Compton scattering of laser photons (2.34 eV) on the high-energy electron pulses from the accelerator. Tuning the linac electron energy from about 0.65 to 20 GeV resulted in backscattered photons at ten energies between 15 MeV and 10 GeV, with an energy dispersion of ∼11% FWHM. The beam was constrained to a collimated pencil beam, with an intensity of ∼0.4 photons per 40 ns pulse width and about 15 pulses/s. EGRET, with a total weight of about 1.8 tons, was mounted to an electrohydraulic computer-controlled fixture which could position the telescope with 0.2 mm accuracy laterally and 0.1◦ in attitude angles. A raster scan over and beyond the sensitive volume of the telescope with scan points spaced by 5 cm was performed for attitudes out to 40◦ off-axis. These calibration measurements during 3 months in 1986 provided not only the data for a model of the efficiency of detection but also the efficiency of “recognition” of good γ -ray events in data analysis of real events. This latter point is often difficult to quantify with simulated data (section “Simulations”). Since the space shuttle accident in 1986 delayed the launch of CGRO until April 5, 1991, further calibration measurements could be performed with EGRET. At Brookhaven National Laboratory, a proton beam up to 10 GeV was used to generate background γ -rays in the material outside the anticoincidence system as a test to see the effect of CR particles on the instrumental background. This was found to be significantly below the expected cosmic γ -ray background. Final γ -ray measurements at MIT-Bates accelerator up to 830 MeV were used to verify some technical developments on the instrument after the main calibrations. With the experience from ground-level calibrations and results from EGRET on CGRO using celestial sources, e.g., pulsed photons from strong pulsars for angular resolution, the design, simulation, and calibration of the currently active GeV telescope Fermi-LAT could be undertaken without a full-instrument beam test. Subsystems, called the LAT Calibration Unit, were exposed to a large variety of beams at CERN and the GSI accelerator facilities to probe γ -ray detection and background sensitivity. Beams of photons (10 MeV thanks to the pair-production effect, but there it is more efficient to use the intrinsic directional properties of this interaction on the few detected photons rather than the collective effect of shadow projection by many rays in order to measure the source direction. X/gamma-ray astronomy is also the domain where the high and variable background becomes dominant over the source contributions, which drastically limits the performance of standard on/off monitoring techniques and where the simultaneous measurement of source and background is crucial even for the simple source detection. Coded masks were conceived in the 1970s–1980s and employed successfully in the past 40–30 years in high-energy astronomy, on balloon-borne instruments first and then onboard space missions like Spacelab 2, GRANAT, and BeppoSAX. They have been chosen as imaging systems for experiments on a number of major missions presently in operation, the European INTEGRAL, the American Swift, and the Indian ASTROSAT, and for some future projects like the Chinese-French SVOM mission. Today the NuSTAR and the Hitomi missions have successfully pushed up to 80 keV the technique of grazing incidence X-ray mirrors (Harrison et al. 2013; Takahashi et al. 2014). However the limited field of view (few arcmin) achieved by these telescopes and the variability of the sky at these energies make the coded mask systems still the best options to search for bright transient or variable events in wide field of views. Coded aperture systems have been employed also in medicine and in monitoring nuclear plants, and implementations in nuclear security programs are also envisaged (Cie´slak et al. 2016; Accorsi et al. 2001). Even if basic concepts are still valid for these systems, certain conditions, specific to gamma-ray astronomy, can be relaxed (e.g., source at infinity, high level and variable background, etc.), and therefore designs and data analysis for CMI for terrestrial studies can take a very different form. In particular for close sources (the so-called near-field condition), the system can actually provide three-dimensional imaging because of the intrinsic enlarging effect of shadow projection as the source distance decreases. This interesting property is not applicable in astronomy and we will not discuss it here. In spite of the large literature on the topic, few comprehensive reviews were dedicated to these systems; the most complete is certainly the one by Caroli et al. (1987), which however was compiled before the extensive use of CMI in actual missions. In this paper we review the basic concepts, the general characteristics, and specific terminology (throughout the paper key terms are written in bold when first defined) of coded mask imaging for gamma-ray astronomy (section “Basics Principles of Coded Mask Imaging”), with a historical presentation of the studies dedicated to the search of the optimum mask patterns and best system designs. We present (section “Image Reconstruction and Analysis”) in a simple way the standard techniques of the image reconstruction based on cross-correlation of the detector image with a function derived from the mask pattern, providing the explicit formulae for this analysis and for the associated statistical errors, and the further processing of the images which usually involves iterative noise cleaning.

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We will discuss the performance of the systems (section “Coded Mask System Performances”), in particular the sensitivity and localization accuracy, under some reasonable assumptions on the background and their relation with the instrument design. We cannot be exhaustive in all topics and references of this vast subject. Clearly the analysis of coded mask system data relies, as for any other telescope, on a careful calibration of the instrument, the understanding of systematic effects of the detector, and the measurement and proper modeling of the background. For these aspects these telescopes are not different from any other one, and we will not treat these topics, apart from the specific question of non-uniform background shape over the PSD, because they are specific to detectors, satellites, space operations, and environment of the individual missions. Also we will not discuss detailed characteristics of the PSDs, and we will neglect description of one-dimensional (1-d) aperture designs and systems that couple spatial and time modulation (like rotational collimators), as we are mainly interested in the overall 2-d coded aperture imaging system. We include a section (section “Coded Mask Instruments for High-Energy Astronomy”) on the application of CMI in high-energy astronomy with a presentation of the historical developments from rocket-borne to space-borne projects and mentioning all the experiments that were successfully flown up to today on space missions. Finally we dedicate specific sub-sections to three gamma-ray CMI telescopes: SIGMA that flew on the GRANAT space mission in the 1990s, IBIS currently operating on the INTEGRAL gamma-ray observatory, and ECLAIRs, planned for launch in the next years on board the SVOM mission. These experiments are used to illustrate the different concepts and issues presented and to show some of the most remarkable “imaging” results obtained with CMI, in high-energy astronomy in the past 30 years.

Basics Principles of Coded Mask Imaging Definitions and Main Properties In coded aperture telescopes, the source radiation is spatially modulated by a mask, a screen of opaque and transparent elements, usually of the same shape and size, ordered in some specific way (mask pattern), before being recorded by a position sensitive detector. For each source, the detector will simultaneously measure its flux together with background flux in the detector area corresponding to the projected transparent mask elements and background flux alone in detector area corresponding to the projected opaque elements (Fig. 1). From the recorded detector image (Fig. 2), which includes the shadows of parts of the mask (shadowgrams) projected by the sources in the field of view onto the detector plane and using the mask pattern itself, an image of the sky can, under certain conditions, be reconstructed.

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Fig. 1 Coded aperture principle. Two sources at infinity project a different pattern of the mask on the detector plane (shadow-gram). For a cyclic system, here a mask with a URA basic pattern of 5×3 replicated to 9×5, it is the same pattern but shifted according to the source position

Fig. 2 Coded aperture principle. The resulting images recorded by the position sensitive detector for the configuration of Fig. 1 for the two sources separately (left and right) and combined (center)

Mask patterns must be designed to allow each source in the field of view to cast a unique shadow-gram on the detector, in order to avoid ambiguities in the reconstruction of the sky image. In fact each source shadow-gram shall be as different as possible from those of the other sources. The simplest aperture that fulfills this condition is of course the one that has only one hole, the well-known pinhole camera. The response to a point source of this system is a peak of the projected size of the hole and null values elsewhere. The overall resulting image on the detector is a blurred and inverted image of the object. However the sensitive area and angular resolution, for given mask-detector distance, are inversely proportional to each other: effective area can only be increased by increasing the hole size, which worsens the angular resolution (increases the blurring). A practical alternative is to design a mask with several small transparent elements of the same size (Fig. 1), a multi-hole camera. The resolution still depends on the dimension of one individual hole, but the sensitive area can be increased by increasing the number of transparent elements. In this case however the disposition

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of the holes is important since when more than one hole is used, ambiguity can rise regarding which part of the sky is contributing to the recorded image. For example with a regular chess board pattern mask, different sources would project identical shadows, and disentangling their contributions would be impossible. Mask patterns that have good imaging properties exist, as described below. With the use of a properly designed multiple-hole mask system, an image of the sky can be recovered from the recorded shadow-gram through a convenient computation. In general the sky image reconstruction, or image deconvolution as it is often called, is based on a correlation procedure between the recorded detector image and a decoding array derived from the mask pattern. Such correlation will provide a maximum value for the decoding array “position” corresponding to the source position, where the match between the source shadow-gram and the mask pattern is optimum and generally lower values elsewhere. Note that, unlike focusing telescopes, individual recorded events are not uniquely positioned in the sky: each event is either background or coming from any of the sky areas which project an open mask element at the event detector position. The sky areas compatible with a single recorded event will draw a mask pattern in the sky. It is rather the mask shadow, collectively projected by many source rays, that can be “positioned” in the sky. Assuming a perfect detector (infinite spatial resolution) and a perfect mask (infinitely thin, totally opaque closed elements, totally transparent open elements), the angular resolution of such a system is then defined by the angle subtended by one hole at the detector. The sensitive area depends instead on the total surface of transparent mask elements viewed by the detector. So, reducing hole size or increasing mask to detector distance while increasing accordingly the number of holes improves the angular resolution without loss of sensitivity. Increasing the aperture area will increase the effective surface, but, since the estimation of the background is also a crucial element, this does not mean that the best sensitivity would increase monotonically with the increase of the mask open fraction (the ratio between transparent mask area and total mask area, also sometimes designed as aperture or transparent fraction). In the gamma-ray domain where the count rate is dominated by the background, the optimum aperture is actually one-half. In the X-ray domain, instead the optimum value rather depends on the expected sky to be imaged even if in general, because of the Cosmic X-ray Background (CXB) which dominates at low energies, the optimal aperture is somewhat less than 0.5. The field of view (FOV) of the instrument is defined as the set of sky directions from which the source radiation is modulated by the mask, and its angular dimension is determined by the mask and the detector sizes and by their respective distance, in the absence of collimators. Since only the modulated radiation can be reconstructed, in order to optimize the sensitive area of the detector and have a large FOV, masks larger than the detector plane are usually employed, even if equal dimensions (for the so-called simple or box type CMI systems) have also been used. The FOV is thus divided in two parts: the fully coded (FC) FOV for which all source radiation directed toward the detector plane is modulated by the mask and the partially coded (PC) FOV for which only a fraction of it is modulated by the mask (Fig. 3).

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Fig. 3 Left: A coded aperture telescope geometry with a mask larger than the detector and a shield connecting them. The field of views around the telescope axis are shown: the FCFOV (red), the Half Modulation EXFOV (green), and the Zero Response EXFOV (black). Right: Relation, for a square CMI, between the array sizes of mask (M), detector (D), and sky (S), with indication, in the sky, of the FOVs (same color code than left panel)

The non-modulated source radiation, even if detected, cannot be distinguished from the (non-modulated) background. In order to reduce its statistical noise and background radiation, collimators on the PSD or an absorbing tube connecting the mask and detector are used. The typical CMI geometry and its FOVs are shown in Fig. 3. If holes are uniformly distributed over the mask, the sensitivity is approximately constant in the FCFOV and decreases in the PCFOV linearly because the mask modulation decreases to zero. The total FOV (FC+PC) is often called extended (EX) FOV and can be characterized by the level of modulation of the PC. Figure 3-right shows the relative sizes of the (ZR)EXFOV, detector, and mask. For simple systems the FCFOV is limited to the on-axis direction, and all the EXFOV is PCFOV. Table 1 reports the approximate imaging characteristics provided by a coded aperture system (as illustrated in Fig. 3) as functions of its geometrical parameters along one direction. Values of the IBIS/ISGRI system (section “IBIS on INTEGRAL: The Most Performant Gamma-Ray Coded Mask Instrument”) for which the design parameters are given in the notes are reported as example. The EXFOV dimensions are given for half modulation level and for zero response. Both angular resolution and localization power, which are at the first order linked to the angle subtended by the mask element size to the detector and the detector pixel (or spatial resolution) to the mask, depend actually also on the reconstruction method and even on the distribution of holes in the mask pattern as described below.

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Table 1 Expected imaging properties of a coded aperture system Quantity FCFOV (100% sensitivity) EXFOV (50% sensitivity) EXFOV (0% sensitivity)

Angular value −LD ) 2 · arctan (LM2·H LM 2 · arctan 2·H (LM +LD ) 2 · arctan √ 2·H

Angular resolution on-axis (FWHM) Localization error radius on-axis (90% c.l.)

≈ arctan  ≈ arctan

m2 +d 2 H 1.52 d SN R H



IBIS/ISGRI 8.2◦ 18.9◦ 29.2◦ 13′ m d

−

1 3



22′′ at SNR=30

Notes: LM masklinear size, LD detector linear size, H detector-mask distance, m mask √ element linear size (m > d), d detector pixel linear size for pixelated detector, d = 2 3σD where σD = linear detector resolution (in σ ) for continuous detector. SNR here is the “imaging signal to noise ratio” SN RI for known source position (see below for definitions). IBIS/ISGRI approximate parameters: LM = 1064 mm, LD = 600 mm, H = 3200 mm, m = 11.2 mm, d = 4.6 mm

Coding and Decoding: The Case of Optimum Systems To analyze the properties of coded mask systems, we first simplify the treatment by considering an optimum coded mask system which provides after the image reconstruction a shift invariant and side-lobe-free spatial response to a point source, the so called System Point Spread Function (SPSF), in the FCFOV (see, e.g., Fenimore and Cannon 1978). We assume a fully absorbing infinitely thin mask, a perfectly defined infinitely thin PSD with infinite spatial resolution and perfect detection efficiency. The object, the sky image, described by the term S is viewed by the imaging system composed by a mask described by the function M and a detector that provides an image D. S, M, and D are then continuous real functions of two real variables. M assumes values of 1 in correspondence to transparent elements and 0 for opaque elements, and the detector array D is given by the correlation [The two-dimension integral correlation between two functions, say A and B, is indicated by the symbol ⋆ and is given ¯ by A ⋆ B = C(s, t) = A(x, y) · B(x + s, y + t)dxdy where A¯ is the complex conjugate of the function A.] of the sky image S with M plus an un-modulated background array term B D =S⋆M +B If M admits a so-called correlation inverse function, say G, such that M⋆G = δfunction, then we can reconstruct the sky by performing S′ = D ⋆ G = S ⋆ M ⋆ G + B ⋆ G = S ⋆ δ + B ⋆ G = S + B ⋆ G and S ′ differs from S only by the B ⋆ G term. In certain cases, when, for example, the mask M is derived from a cyclic replication of an optimum basic pattern, if the background is flat, then the term B ⋆G is also constant and can be removed. Since even for very high detector resolution the

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information must be digitally treated in the form of images with a finite number of image pixels, the problem must be generally considered in its discrete form. We can formulate the same process in digital form by substituting the continuous functions with discrete arrays and considering discrete operators instead of integral operators. S, M, G, D, and B terms will therefore be finite real 2-d arrays, and the delta function the delta symbol of Kronecker. The discrete correlation is obtained by finite summations and the reconstructed sky S ′ by ′ Si,j =

 kl

Dk,l Gi+k,j +l

with i, j indices that run over the sky image pixels and k, l over the detector pixels. Mask patterns that admit a correlation inverse array exist (section “Historical Developments and Mask Patterns”) and can be used to design the so-called optimum systems. For instance, for masks M that have an auto-correlation given by a delta function, the decoding array constructed posing G = 2 · M − 1 (i.e., G = +1 for M = 1 and G = −1 for M = 0) is then a correlation inverse. To have such a sidelobe-free response in an optimum system, a source must however be able to cast on the detector a whole basic pattern. To make use of all the detector area and to allow more than one source to be fully coded, the mask basic pattern is normally taken to be the same size and shape as the detector and the total mask made by a cyclic repetition of the basic pattern (in general up to a maximum of 2 times minus 1 in each dimension to avoid ambiguities) (Fig. 4). For such optimum systems, a FCFOV source will always project a cyclically shifted version of the basic pattern, and correlating the detector image with the G decoding array within the limits of the FCFOV will provide a flat side-lobe peak with position-invariant shape at the source position (Fig. 4 right). A source outside the FCFOV but within the PCFOV will instead cast an incomplete pattern, and its contribution cannot be a priori automatically subtracted by the correlation with the decoding array at other positions than its own, and it will produce secondary lobes over all the reconstructed EXFOV including the FCFOV.

Fig. 4 Mask, detector, FC sky of an optimum CMI. Left: A 33×29 replicated mask of basic pattern 17×15 (Hadamard from an m-sequence CDS with N = 255 and m = 8 disposed along the diagonal). Center: Simulated detector image of two sources in the FCFOV and low background for a CMI with the mask on the left and a detector of same size of its basic pattern, with 3×3 pixels per mask element. Right: The relative decoded SNR sky image in the FCFOV

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Following a standard nomenclature of CMI, we refer to these secondary lobes as coding noise. On the other hand, the modulated radiation from PC sources can be reconstructed by extending with a proper normalization the correlation procedure to the PCFOV. The reconstructed sky in the total field (EXFOV) is therefore composed by the central region (FCFOV) of constant sensitivity and optimum image properties, i.e., a position-invariant and flat side-lobes SPSF, surrounded by the PCFOV of decreasing sensitivity and non-perfect SPSF (Fig. 5). In the PCFOV, the SPSF includes coding noise, the sensitivity decreases, and the relative variance increases toward the edge of the field. Also, even FCFOV sources will produce coding noise in the PCFOV, while sources outside the EXFOV are not modulated by the mask and simply contribute to the background level on the detector. When a complete mask is made of a cyclic repetition of a basic pattern, then each source in the FOV will produce eight large secondary lobes (in rectangular geometry) at the positions which are symmetrical with respect to the real source position at distances given by the basic pattern: these spurious peaks of large coding noise are usually called ghosts or artifacts (Fig. 5). These optimum masks also minimize the statistical errors associated to the reconstructed peaks and make it uniform along the FCFOV. Since G is two-valued and made of +1s or −1s, the variance associated to the reconstructed image in the FCFOV is given by V = G2 ⋆ D = ΣD, the variance associated to each reconstructed sky image pixel is constant in the FCFOV and equal to the total counts

Fig. 5 Reconstructed SNR sky image in the full EXFOV for the CMI and simulation of Fig. 4 left/center. The central part corresponds to the FCFOV (same as Fig. 4 right) and shows optimal properties: the shift invariant peaks and flat side-lobes of the two simulated FC sources. In the PCFOV coding noise and the strong eight ghosts of the main source are clearly visible

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recorded by the detector. This implies that the source signal to noise ratio (SNR) is simply Reconstructed Source Counts CS = √ SNR = √ CS + CB T otal Detected Counts where CS and CB are source and background recorded counts. The deconvolution is then equivalent to summing up counts from all the detector open elements (source and background counts) and subtracting counts from the closed ones for that source (background counts only).

Historical Developments and Mask Patterns Following the first idea to modulate incident radiation using Fresnel plates, formulated by Mertz and Young (1961), the concept of a pinhole camera with multiple holes for high energy astronomy (the multiple-pinhole camera) was proposed by Ables (1968) and Dicke (1968) at the end of the 1960s. In these designs multiple holes of the same dimensions are distributed randomly on the absorbing plate and in spite of the inherent production of side-lobes in the SPSF, the increase in the aperture fraction compared to the single pinhole design highly improves the sensitivity of the system, at the same time maintaining the angular resolution. Toward the end of the 1970s, it was realized that special mask patterns could provide optimum imaging properties for coded aperture systems, and then a large number of the early works focused on the search for these optimal or nearly optimal aperture patterns. Most of these are built using binary sets called cyclic different sets (CDS) (Baumert 1971) which have the remarkable property that their cyclic auto-correlation function (ACF) is two-valued and approximates a delta function modulo a constant term. Certain of these sets can be disposed (following certain prescriptions) to form 2-d arrays, the so-called basic patterns, which also have the property of having 2-d cyclic auto-correlations which are bi-dimensional delta functions, thus allowing design of coded aperture systems where a correlation inverse is directly derived from the mask pattern. Thus by disposing, in a rectangular geometry, 2×2 such 2-d basic pattern side by side (actually less than 2 times in each direction in order to avoid full repetition of the pattern and then ambiguity in reconstruction) at a certain distance from a detector plane of the same dimension as the basic pattern, one obtains an optimum system with maximum FCFOV, free of peak repetitions and coding noise. Care must be taken on how the mosaic of the basic pattern is done in order for a source to project on the detector a shifted, but complete, version of the basic pattern.

Patterns Based on Cyclic Different Sets A cyclic different set D(N, k, λ) is a collection of k distinct integer residues d 1 , . . . d k modulo N , for which the congruence d i − d j = q mod(N ) has exactly λ distinct solution pairs (d i ,d j ) in D for every residue q = 0 mod(N ). If such a

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different set D exists, then λ = k(k − 1)/(N − 1). This mathematical definition simply means that for these sets, a cyclic (over the dimension N of the larger set to which they belong) displacement vector between any two elements of the set occurs exactly a constant number of times, given by the parameter λ, which is called the “redundancy” of the set. For this reason binary arrays based on CDS are also called uniformly redundant arrays (URA). From this property immediately follows that a 1-d binary sequence M of dimension N built from a CDS D(N, k, λ) by the following prescription

mi =



1 if i ∈ D

0 if i ∈ /D

has an ACF ai =

 j

mj mj+i =



k

for i = 0 mod N

λ for i = 0 mod N

that is a δ function. The parameter k − λ is also an important characteristic of the set since it determines the difference between the peak and the plateau of the ACF. The higher this value, the better is the signal to noise response to a point source of the derived imaging system. Several types of CDS exist, and early studies on the subject were focused to find as many such sequences as possible and establish the way to build them. A class that was already well known from the coding theory was the Non Redundant Arrays (NRA), which are in fact CDS with redundancy = 1. These have however densities of elements very small (1 are particularly interesting because they have nearly 50% open fraction and when m is even they can be factorized in p × q arrays with p = 2m/2 + 1 and q = 2m/2 − 1 in order to form rectangular (quasi-square) arrays. The first to propose to use different sets for building 2-d imaging optimum systems for X-ray astronomy were independently Gunson and Polychronopulos (1976) and Miyamoto (1977) in 1976. They both identified the m-sequences as the original set to use for the design, but with different mapping in 2-d arrays to obtain the basic pattern. The second author actually started from the Hadamard arrays that were studied in particular for spectroscopy by Harwit, Sloane, and collaborators (1979). The proposed pattern is equivalent to the one obtained by filling up the array with the PN sequence row by row. The first authors instead proposed to build basic patterns from m-sequences filling the array along extended diagonals (this further requires that p and q are mutually primes). In the two cases, the mosaic of cyclic repetition of the basic pattern must be performed in a different way in order to preserve the δ-function ACF property. For the diagonal prescription, the basic patterns can just set adjacent to each other; for the row by row construction, those

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on the side must be shifted vertically by one row (see Caroli et al. 1987 for the details). We call these masks Hadamard masks to distinguish them from the URA described below, even if both can be considered URA. A more complete discussion of the way PN-sequences are used for an imaging coded mask instrument of the type proposed by Gunson and Polychronopulos (1976), including the way of filling the 2-d array by extended diagonal, was provided soon after by Proctor et al. (1979) who also discussed the implementation in the SL1501 experiment (Proctor et al. 1978). Examples of Hadamard masks are shown in Figs. 4 left, 6 left. A particular subset of Hadamard CDS, the twin prime CDS, are those for which p and q are primes and differ by 2 (q = p − 2). These sets can be directly mapped in p × q arrays using the prescription proposed by Fenimore and Cannon (1978) in 1977. In a series of other seminal papers, these authors and collaborators improved the description of coded aperture imaging using these URA arrays and discussed their performances and a number of other associated topics (Fenimore 1978, 1980; Fenimore and Cannon 1981; Fenimore and Weston 1981). These URA masks, as we will call them following Fenimore and Cannon (1978), are generated from quadratic residue sequences of order p and q (p = q + 2) according to the following prescription:

Mij =

⎧ ⎪ 0 if i = 0 ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨1 if j = 0, i = 0 p Ci

q · Cj

⎪ 1 if = 1 where ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩0 otherwise

p Ci

=



+1 if ∃ k ∈ Z, 1 ≤ k < p, i = k2 mod p

−1 otherwise

Other 2-d rectangular arrays presenting delta function ACF were identified as Perfect Binary Arrays (PBA). Again they are a generalization in 2-d of CDS, include the URAs, and are based on different set group theory (Kopilovich and Sodin 1994). Early designs of CMI assumed rectangular geometry, but in 1985 mask patterns for hexagonal geometry were proposed by Finger and Prince (1985). These are based on Skew-Hadamard sequences (Hadamard sequences with order N prime and constructed from quadratic residues) that, for dimensions N = 12t + 7 where t is an integer, can be mapped onto hexagonal lattices, with axes at 60◦ from each other, to form hexagonal URA, the HURA. In addition to be optimum arrays (they have a δ-function ACF), they are also anti-symmetric with respect to their central element (complete inversion of the pattern) under 60◦ rotation. This property allows one to use them to subtract a non-uniform background, if a rotation of the mask of 60◦ can be implemented, and even to smear out the ghosts created by a replicated pattern if a continuous rotation can be performed. The hexagonal geometry is also particularly adapted to circular detectors. The complications induced by moving elements in satellites have limited the use of such mask/anti-mask concept based on mask rotation with respect to the detector plane. A rotating HURA mask (Fig. 6 center) was successfully implemented in the GRIP balloon-borne experiment (Althouse

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Fig. 6 Optimum coded aperture patterns; note the symmetry of URAs with respect to the “more random” Hadamard ones (also Fig. 4 left). Left: The non-replicated 255×257 Hadamard pattern of the COMIS/TTM mask (from in’t Zand 1992), from an m-sequence CDS ordered along the extended diagonal. Center: Replicated HURA mask of 127 basic pattern used in the GRIP experiment (from Althouse et al. 1985, © NASA). Right: The IBIS 95×95 mask, replication of the MURA 53×53 basic pattern (central red square)

et al. 1985) and operated during a few flights allowing for an efficient removal of the background non-uniformity. A fixed non-replicated HURA of 127 elements has been implemented for the SPI/INTEGRAL instrument.

Other Optimum Patterns The limited number of dimensions for which CDS exist coupled to the additional limitation that N must be factorized in two integers for a rectangular geometry or comply with more stringent criteria for the hexagonal one implies that a small number of sequences can actually be used for optimum masks. This led several authors to look for other optimum patterns, and several new designs were proposed in the 1980s and 1990s, even if somehow related to PN sequences. Even though for these patterns the ACF is not exactly a delta function, it is close enough that a simple modification of the decoding arrays from the simple mask pattern allows recovery of a shift invariant and side-lobe-free SPSF. For these masks therefore an inverse correlation array exists, and an optimum imaging system can be designed. The most used of them was certainly the Modified URA or MURA (Fig. 6 right) of Gottesman and Fenimore (1989). Square MURAs exist for all prime number linear dimensions, and this increases by about a factor 3 the number of rectangular optimal arrays with respect to the URA and Hadamard sets. They are basically built like URA on quadratic residues but for the first element (or central element for a 2-d pattern) which is defined as not part of the set. The MURAs also have symmetric properties with respect to the central element which permits a MURA using the complement of the pattern (but keeping the central element to 0 value). The correlation inverse is built like in URAs (+1 for mask open elements and −1 for opaque ones) apart from the central element, and its replications, if any, which are set to +1 even if the element is opaque. With this simple change from the mask

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pattern, the derived decoding array G is a correlation inverse, and the system is optimum. Other optimum rectangular designs for which a correlation inverse can be defined were obtained from the product of 1-d PN sequences, the Pseudo Noise Product (PNP), or 1-d MURAs (MP and MM products patterns).

Real Systems and Random Patterns More recent studies of mask patterns have focused on more practical issues such as how to have opaque elements all connected between them by at least one side in order to build robust self-supporting masks able to resist, without (absorbing) support structures, to the vibration levels of rocket launches. As explained above, even for an optimum mask pattern, any source in the PCFOV will produce coding noise and spurious peaks also in the FCFOV. In order to obtain a pure optimum system, one has then to implement a collimator which reduces the response to 0 at the edge of the FCFOV. This solution was proposed by Gunson and Polychronopulos (1976) who also suggested to include the collimator directly into the mask rather than in the detector plane. However the total loss of the PCFOV (even if affected by noise) and the loss of efficiency also for FC sources not perfectly on-axis are too big a price to pay to obtain a clean system and led to the abandonment of the collimator solution in favor of a shield between the mask edges and detector borders in order to reduce background and out of FOV source contributions. In addition the geometry of optimum systems cannot be, in practice, perfectly realized. Effects like dead area or noisy pixels of the detector plane, missing data from telemetry errors, not perfect alignment, tilt or rotation of the mask with respect to the detector, absorption and scattering effects of supporting structures of the mask or of the detector plane, and several other systematic effects directly increase the coding noise and ghosts and degrade the imaging quality of the system. Since the imperfect design of real instrument generally breaks down the optimum imaging properties of the cyclic optimum mask patterns, today these patterns are not anymore considered essential for a performing coded mask system, and there is a clear revival of random patterns. Indeed for the typical scientific requirements of CMI (detection/localization of sources in large FOV), one prefers to have some low level of coding noise spread over a large FOV rather than few large ghosts produced by the needed cyclic repetition of the optimum patterns giving strong ambiguities in source location. This is why the most recent instruments were designed using random or quasi-random patterns. The drawback is that, for practical reasons, like the need to have solid self-supporting masks, pure random distributions are also difficult to implement and then for these “quasi-random masks” the inherent coding noise becomes less diffuse and more structured. The issue then becomes how to optimize the choice of these quasi-random patterns in order to get best performance in terms of coding noise, SPSF, sensitivity, and localization.

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Image Reconstruction and Analysis Reconstruction Methods A coded mask telescope is a two-step imaging system where a specific processing of the recorded data is needed in order to reconstruct the sky image over the field of view of the instrument. The reconstruction is usually based on a correlation procedure; however, in principle, other methods can be envisaged. Indeed from the simple formulae that describe the image formation in a CMI (section “Coding and Decoding: The Case of Optimum Systems”) and which give the relations between the input sky S, the mask M, and the detector D, it follows that S can be derived by the simple inversion technique, by means of the Fourier transform (FT) of M and D, with S ′ = I F T (F T (D)/F T (M)) = S + I F T (F T (B)/F T (M)), where IFT stands for the inverse FT. However this direct inverse method usually produces a large amplification of the noise in the reconstructed image, since the FT of M always contains very small or even null terms, and the operation on the background component, which is always present, diverges and leads to very large terms. A way to overcome this problem is to apply a Wiener filter as a reconstruction method (Sims et al. 1980; Willingale et al. 1984) in order to reduce the frequencies where the noise is dominant over the signal when performing the inverse deconvolution. It consists in convolving the recorded image D with a filter WF whose FT is F T (W F ) = F T (M)/[(F T (M))2 + (F T (SN R))−1 ] The filter showed to be efficient to recover the input sky image especially when a non-optimal system is employed, but it requires an estimate of the spectral density of the signal to noise ratio (SNR) which is not in principle known a priori. A simple application using a constant SNR value with spatial frequency was used and compared well to correlation and also to Bayesian methods. Indeed Bayesian methods have also been specifically applied to CMI in particular in the form of an iterative Maximum Entropy Method (MEM) algorithm (Sims et al. 1980; Willingale et al. 1984). The results with MEM are not very different from those obtained by the correlation techniques. The heavy implementation of MEM compared to the latter ones and the problems linked to how to establish the criteria for stopping the iterative procedure to avoid over-fitting the data have made these techniques less popular than correlation coupled to iterative cleaning. Most of these data processes are heavy and time-consuming, especially when images are large, and the issue of computation time is relevant in CMI analysis, in particular when iterative algorithms need to compute several times the sky image or a model, like in MEM. Some studies in the past have concentrated on fast algorithms for the deconvolution. Systems based on pseudo-noise mask patterns and Hadamard arrays could exploit the Fast Hadamard Transform (FHT) which reduces

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the convolution processing from an order of N 2 to one proportional to N log N (Fenimore and Weston 1981). Another method exploits the URA/MURA symmetry (large part of these arrays are given by the multiplication of the first line with the first column) in order to reduce significantly the number of operations (Roques 1987; Goldwurm 1995). However today, at least for astronomical applications, the use of the highly optimized routines of 2-d discrete fast Fourier transform (FFT) available in most software packages for any kind of array order, is usually sufficient for the required implementations based on correlation. The search for fast algorithms or for specific patterns that allow fast decoding is therefore, these days, somehow less crucial. Recently deep learning methods mainly based on convolutional neural networks were proposed to improve the performance of image reconstruction from data of CMI in condition of near-field observations. The tests performed for these specific conditions of terrestrial applications, with their additional complexity of the source distance-dependent image magnification, show that these novel techniques provide enhanced results compared to the simple correlation analysis (Zhang et al. 2019b). Further developments in this direction can be expected in the near future.

Deconvolution by Correlation in the Extended FOV The cross-correlation deconvolution described above for the FCFOV can be applied to the PCFOV, by extending the correlation of the decoding array G with the detector array D in a non-cyclic form to the whole field (EXFOV) (Goldwurm 1995; Goldwurm et al. 2003). To perform this a FOV-size G array is derived from the mask array M following a prescription that we describe below and by padding the array with 0 elements outside M in order to complete the matrix for the correlation. Since only the detector section modulated by the PC source is used to reconstruct the signal, the statistical error at the source position and also the significance of the ghost peaks, if any, are minimized. To ensure a flat image in the absence of sources, detector pixels which for a given sky position correspond to mask opaque elements must be balanced, before subtraction, with a proper ratio of the number of transparent to opaque elements for that reconstructed sky pixel. This normalization factor is stored in a FOV-size array, called here Bal, and its use in decoding is equivalent to the so-called balance deconvolution for the FCFOV (Fenimore and Cannon 1978). In order to correctly account for detector pixel contributions or even attitude drifts or other effects, a weighting array W of the size of the detector array and with values comprised between 0 and 1 is defined and multiplied with the array D before correlation (Goldwurm 1995). It is used to neglect the detector areas which are not relevant (e.g., for bad, noisy, or dead area pixels) by setting the corresponding entries to 0. If one is interested in studying weak sources when a bright one is also present in FOV, W may be used to suppress the bright source contamination by setting to 0 the W entries corresponding to detector pixels illuminated by the

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bright source above some given fraction. The array W is also used to give different weights to parts of the detector, for example, when pixels have different efficiencies, e.g., due to different dead times or energy thresholds. The balance array Bal is built using W to properly normalize the balance considering the weights given to the detector pixels. Obviously when W contains some zero values, it means that there is not complete uniform coding of the basic pattern, and this will break the perfect character of an optimum system, introducing coding noise. In case a small fraction of pixels is concerned, the effect will be however small. In order to insure the best imaging sensitivity, G is built from the mask M by G=

1 ·M −1 a

where the factor a gives the aperture of the mask. For a = 0.5 (like in URAs) G = 2 · M − 1 and assumes values +1 or −1 as in the standard prescriptions (Fenimore 1978). Defining the two arrays G+ and G− such that +

G =



G for G ≥ 0 0 elsewhere

−

G =



G for G ≤ 0 0 elsewhere

where of course G = G+ + G− , we obtain the reconstructed sky count image from S=

G+ ⋆ (D · W ) − Bal · (G− ⋆ (D · W )) A

(1)

where dot operator or division applied to matrices indicates here element-byelement matrix multiplication or division. The balance array used to account for the different open to closed mask element ratios is given by Bal =

G+ ⋆ W G− ⋆ W

and ensures a flat image with 0 mean in absence of sources. The normalization array A = (G+ · M) ⋆ W − Bal · ((G− · M) ⋆ W ) allows a correct source flux reconstruction which takes into account the partial modulation. With this normalization the sky reconstruction gives at the source peak the mean recorded source counts within one totally illuminated detector pixel. Note that source flux shall not be computed by integrating the signal around the peak, as this is a correlation image. An additional correction for off-axis effects (including, e.g., variations of material transparency, etc.) may have to be included, once the reconstruction, including ghost cleaning, has been carried out.

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The normalized variance, which is approximately constant in the FCFOV for optimum or pure random masks, and whose relative value increases outside the FCFOV going towards the edges, is computed accordingly [Here X2 = X · X.]: V =

(G+ )2 ⋆ (D · W 2 ) + Bal 2 · ((G− )2 ⋆ (D · W 2 )) A2

(2)

since the cross-terms G+ · G− vanish. Here it is assumed that the variance in the detector image is just given by the detector image itself (assumption of Poisson noise and not processing of the image); however if it is not the case, the D array in this last expression shall be substituted by the estimated detector image variance. The signal to noise image is given by the ratio √S and is used to search for significant excesses. The deconvolution procedure V can be explicitly expressed by discrete summations over sky and detector indices of the type given in section “Coding and Decoding: The Case of Optimum Systems” for Sij (Goldwurm et al. 2003). Different normalizations may be applied in the reconstruction (Skinner and Ponman 1994); for example, one can normalize in order to have in the sky image the total number of counts in the input detector image. However the basic properties of the reconstructed sky image do not change. In particular with the presence of a detector background, there are more unknowns than measurements, and therefore reconstructed sky pixels are correlated. It is possible to show (Skinner and Ponman 1994) that, at least for optimum masks, the level of correlation is of the order of 1/N (where N is again the number of elements in the basic pattern). Clearly if binning is introduced, then the level of correlation increases, depending on the reconstruction algorithm employed as discussed below. All the previous calculations can be performed in an efficient and fast way using the discrete fast Fourier transform algorithm because all operations involved are either element-by-element products or summations or array correlations for which we can use the correlation theorem [For which A ⋆ B = I F T (F T (A) · F T (B)) where FT is the Fourier transform, IFT is the inverse Fourier transform, and the bar indicates complex conjugate.].

Detector Binning and Resolution: Fine, Delta, and Weighted Decoding We have until now implicitly assumed to have a detector of infinite spatial resolution and data digitization for which images are recorded in detector elements (pixels) with the same shape and pitch as the mask elements and that sources are located in the center of a sky pixel, allowing for perfect detector recording of the projected mask shadow. These approximations are of course not verified in a real system, which implies a degradation of the imaging performance. Recorded photons are either collected in discrete detector elements (for pixelated detectors) or recorded

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by a continuous detector (like an Anger camera) subject to a localization error described by the detector point spread function (PSF) and where the measured positions are digitally recorded in discrete steps (pixels). In both cases we will have detector pixels with a finite detector spatial resolution characterized by the detector pixel size d or the σD of a Gaussian describing the detector PSF and the digitization. Pixels may have sizes and pitches different from those of the mask elements, but for a good recording of the mask shadow, resolution and digital pixels must be equal or smaller than the mask element size; otherwise the shadow boundary is poorly measured, and there is a large loss of sensitivity and in source localization. One can define the resolution parameter r as the ratio r = m/d in each direction of the linear sizes of the mask element and the detector pixel (where pixel size means pixel pitch, since the physical pixel may be smaller with some dead area around it). Fenimore and Cannon (1981) considered the case of r integer in both directions and showed that the same procedure of cross-correlation reconstruction can be carried out just by binning the array M with the same pixel grid as the detector, which will give the rebinned mask M R ; by assigning to all its pixels corresponding to one given mask element the value of that element, defining G accordingly (G = 2 · M R − 1, for a = 0.5); and then by carrying out the correlation over all pixels. So, for example, for r × r detector pixels (square geometry) per mask element, each element of the mask is divided in r × r mask pixels. To each of them, one assigns the value of the element and then carries out the G-definition and correlations accordingly. This is the fine cross-correlation deconvolution. Another way, when building the decoding array G, is to assign the value of the mask element to one pixel from the r × r ones that bin this mask element, while the others are set to the aperture a. For a URA (a = 0.5), the G array has +1 or −1 for one pixel per mask element, and the others are set to 0 (and do not intervene in the correlation). This is the so-called delta-decoding (Fenimore 1980; Fenimore and Cannon 1981). This implies that the reconstructed adjacent r × r sky pixels are built using different pixels of the detector, and therefore they are statistically independent. Of course a delta-decoding reconstruction can be transformed in fine decoded image by convolving the delta-decoded image with a r × r box-function of 1s. The delta-decoding also allows one to use the FHT in the case of detector binning finer than the mask element (if M is a Hadamard array, the rebinned array M R build for the fine decoding is not) (Fenimore and Weston 1981). As discussed above, FHT is not relevant anymore as the FFT can do the job, but the relative independence of delta-decoded sky image pixel over sizes of the SPSF peak was found useful in order to apply standard methods of chi-square fitting directly on the reconstructed sky images including parameter uncertainty estimations (Goldwurm 1995). When there is a non-integer number of pixels per mask element, which is a typical, and sometimes desirable [The exact integer ratio, when pixels are surrounded by dead zones, leads to incompressible localization uncertainty, given by the angle subtended by the dead area, for source positions for which mask element borders are projected within the dead zones.] condition of pixelated detectors,

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Fig. 7 IBIS images showing the sky reconstruction process from data of the Cygnus region. From left/top to right/bottom: binned corrected detector image (130×134 pixels) including dead zones (D C ), associated efficiency image (W ), rebinned MURA mask on a detector pixel grid (233×233 pixels) (M R ), decoded intensity sky image (S) (358×362 pixels), associated variance (V ), and final SNR sky image after cleaning of coding noise of the two detected sources (Cyg X-1 and Cyg X-3)

then the mask is rebinned by projecting the M array on a regular grid with same pixel pitch as in the detector and by assigning to the mask pixels the fraction of open element area projected in the pixel. The same decoding array definition and correlation operation given above (Eqs. 1–2 and all associated definitions) are then applied using the rebinned mask array M R at the place of M. M R can take (for non-integer r) fractional values between 0 and 1, and the decoding G array also can have different fractional values accordingly. Weighing the inverse correlation using a filtered mask describing the not-integer binning or the finite detector resolution optimizes the SNR of point sources (Cook et al. 1984; Goldwurm 1995; Bouchet et al. 2001) and is usually implemented (weighted decoding) even if this implies a further smearing of the source peak. Figure 7 shows some of the image arrays involved in the weighted sky reconstruction process described above and applied to IBIS data of a Cygnus region observation (Goldwurm et al. 2003).

Image Analysis Following the prescriptions given above, one obtains a reconstructed sky in the EXFOV of the instrument, composed of an intensity and a variance image. They are “correlation” images; each sky image pixel value is built by a linear operation on all, or part of, the detector pixels. Sky image pixels are therefore highly correlated

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in particular within an area of one mask element. Statistical properties of these images are different from standard astronomical images and their analysis, including fine derivation of source parameters, error estimation, the various steps to reduce systematic noise from background, or source coding noise, and final combination of cleaned images in large mosaics must take into account their characteristics.

Significance of Detection The reconstructed and normalized sky image shall be searched for significant peaks by looking for excesses over the average value that should be, by construction (and neglecting the effect of non uniform background), close to zero. This is done by searching for relevant peaks in the SNR image. In the absence of systematic effects, the distribution of this SNR image shall follow the standard normal distribution. Deviations from such distribution indicates residual systematic effects or presence of sources and their ghosts (Fig. 8 left). Excesses in signal to noise larger than a certain threshold are considered as sources. However the concept of significance level in such a decoded image where each sky pixel is built by correlating all, or part of, the pixels of the detector image needs to be carefully considered. If we are interested to know if one or few sources at given specified positions are detected, then we can use the standard rule of the 3 sigma excess that will give a 99.7% probability that the detected excess at that precise position under test is not a background fluctuation. If, instead, we search all over the whole image for a significant excess, then the confidence level must take into account that we perform a large number of trials (in fact different linear combinations of nearly the same data set) to search for such excess. Assuming standard normal distribution for the noise fluctuations, the probability that an excess (in σ ) larger than α is produced by noise is

Confidence level of detection (%)

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Fig. 8 Left: SNR distribution of a CMI (IBIS/ISGRI) reconstructed sky image without sources before (red) and after (blue) correction of some systematic effects, compared to the expected normal distribution (dashed line). (Reproduced with permission from Krivonos et al. 2010, © ESO). Right: Variation of the confidence level of detection (in %), for no a priori knowledge of source position, as function of number of sky pixels in a CMI sky image for different SNR levels of detection

48 Coded Mask Instruments for Gamma-Ray Astronomy

1 P (α) = √ 2π



+∞ α

e

−x 2 2

1635

  α 1 dx = erf c √ 2 2

The confidence level of a detection (not a noise fluctuation) is then 1 − P (α) in a single trial. Assuming that we have N independent measurements, then the confidence level for such excess to be a source will be reduced to [1 − P (α)]N ∼ 1 − NP (α)

for N P (α) ≪ 1

For a given confidence level and N , the value of α is found from this relation. Curves of α as a function of N can be calculated (see Fig. 8 right and Caroli et al. 1987), and it is found that to have a confidence level of 99% for number of pixels N=104 − 105 , the excess must be in the range 4.5–6.0. For coded mask however, it is difficult to evaluate N , since it does not simply correspond to the number of pixels in the sky reconstructed image, unless this refers to the FCFOV of an optimum system with one detector pixel per mask element. The reason is that in general sky pixels are not fully independent and are highly correlated over areas of the size of the typical SPSF. The best way to evaluate the threshold is therefore through simulations. A value of 5.5–6.5 σ is typically assumed for a secure (may be conservative) source detection threshold in reconstructed images of 200–300 pixel linear size.

System Point Spread Function An isolated significant excess in the deconvolved sky image may indicate the presence of a point-like source, which will be characterized by the System Point Spread Function (SPSF), that is, the spatial response to an isolated bright point source of the overall imaging system, including the deconvolution process (Fig. 9). The SPSF includes a possibly shift-invariant, main peak, proportional to the source intensity, and usually non-shift-invariant, side-lobes of the coding noise, also proportional to the source intensity. For a perfect cyclic optimum coded mask system, the main peak is shift invariant, and the side-lobes are flat within the FCFOV for a source in the FCFOV, but large side-lobes appear in the PCFOV (ghosts) along with a diffuse moderate coding noise, and when the source is in the PCFOV, the width of the main peak may vary depending on the mask pattern, and side-lobes, including the main ghosts, appear all over the field. In random masks, side-lobes are distributed all over the image including in the FCFOV, even for sources in the FCFOV, but, generally, with low amplitude and without the strong ghosts typical of cyclic systems. For a pixelated detector and a sky reconstruction based on the weighted crosscorrelation, the SPSF can be described by a peak function correlated with a set of positive and negative delta functions of different amplitudes (what we will call here the correlation function) that take into account the mask pattern and the decoding operation based on correlation (see, e.g., Fenimore 1980). A positive δ-function of maximum amplitude of this set is of course positioned at the source location and will provide the main peak of the SPSF at the source position. The other positive

A. Goldwurm and A. Gros

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Fig. 9 IBIS/ISGRI SPSF from data of a point source observation. Left: Source peak in the center of the FCFOV of a decoded sky image. Color code highlights the, rather low, coding noise particularly affecting (given the symmetry of the MURA mask) the image axes centered on the source. Right: Source profiles in a decoded image along the 2 axis (black lines) and the Gaussian model, approximation of the SPSF, that best fits the excess (red lines). (From Gros et al. 2012)

and negative deltas, convolved with the peak function, describe the coding noise spread over the image (including ghosts). Assuming from hereon a square geometry with square mask elements of linear dimension m and square detector pixels of linear dimension d (extension to rectangular geometry is trivial, and analog, less trivial, relations can be given for the hexagonal one), the peak function Q is given by the normalized  correlation of four 2-d box functions [A 1-d box function is given

1 for |z| ≤ p/2 .], two of mask element width m (x, y) = m (x) · by p (z) = 0 elsewhere



m (y) and two of pixel width d (x, y) = d (x) · d (y) Q(x, y) = Q(x) · Q(y)

where Q(x) =

m (x) ⋆



m (x) ⋆ d (x) ⋆ 2 d m

d (x)

This function, a blurred square pyramidal function for square geometry, can be expressed analytically. The 1-d analytical function Q that composes it has a peak value (at zero lag) given by the simple equation Q(0) = 1 −

1 3r

(3)

where, as usual, r is the ratio r = m/d. This quantity, which corresponds to the term coding power in Skinner (1995), is important because it appears in the expression of the error estimate for the source flux and location.

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The 2-d function Q can be also √ conveniently approximated by a 2-d Gaussian function with FWHM width of r 2 + 1 along the two axes (Fig. 9 right). For a continuous detector, the SPSF (where now pixel is the data discrete sampling step) is the function above but further convolved with the detector PSF. The explicit formulae of the SPSF for such a system, where the detector PSF is approximated by a Gaussian, were given in the description of SIGMA/GRANAT data analysis (Goldwurm 1995; Bouchet et al. 2001). The use of the SPSF in the analysis of CMI data is important because in general both the detector resolution and the sampling in discrete pixels are finite. Then the discrete images produced by the correlations, with the same steps of the data sampling, do not provide the full information, unless the resolution is exactly given by the sampling, pixels are in integer number per mask element, and the source is exactly located at the center of a sky-projected pixel in order to project a shadow exactly sampled by the detector pixels. Of course an artificial finer sampling can be introduced in the correlation analysis, but this implies rebinning of data with alteration of their statistical properties and increase in computing time for deconvolution (dominant part of the overall processing), and finally the precision may not be adequate to the different level of SNR of the sources, where the brightest ones may be located with higher accuracy than the artificial oversampling used. Therefore, in order to evaluate source parameters, and in particular the position of the source, in a finer way than provided by the sky images with the sampling equivalent to the detector pixels, a practical method is to perform a chi-square fit of the detected excess in the deconvolved sky image with the continuous SPSF peak analytical formula or its Gaussian approximation (see Fig. 9 right). The procedure can also be used to disentangle partially overlapping sources (Bélanger et al. 2006). Once the fine position of the source is determined, a model of the projected image on the detector can be computed and used to evaluate the source flux, subtract the source contribution or its coding noise, and perform simultaneous fit with other sources and background models to extract spectra and light curves. Even though the fit, in the deconvolved image, of the source peak with the model of the SPSF peak will provide a reasonable estimate of the source parameters, the error calculation cannot be performed in the standard way directly using the chisquare value of the best fit and its variation around the minimum, because pixels are too much correlated. Nevertheless formulae for the expected error in source flux and source localization can be derived from the formalism of chi-square estimation in the detector space and can be used to provide uncertainties, after some calibration on real data that will account for residual systematic biases.

Flux and Location Errors One can show that the correlation reconstruction for a single point-like source in condition of dominant Gaussian spatially flat background noise is equivalent to the minimum chi-square determination of source flux and position in the detector image space, where one can determine the errors, using the minimum chi-square paradigm. Using the notations used above for the SPSF and introducing the terms t for integration time, A for detector geometrical area, b (in cts/s/cm2 ) for a background

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count rate, and s0 (in cts/s/cm2 ) for the considered source count rate, both integrated within an energy band, we define σCR =



b A·t

SNRCR =

s0 σCR

fI (x, y) =

SP SF (x, y) −a N ·a

where fI is called the image function and is linked, as shown, to the shape of the SPSF, and N is the average number of mask elements in the detector area A (N = A/m2 ) (and in the basic pattern for an optimum system). σCR and SNRCR are, respectively, the minimum error and maximal signal to noise from purely statistical noise given by the measured count rates in case perfect reconstruction can be achieved and for a mask aperture of 1 (i.e., no mask, where all the area A is used for the measure) with the idealistic assumption that a measurement of the background is available (in the same observation time t). Using the minimum chi-square method applied to the detector image compared to a source shadow-gram model, one obtains, from the inversion of the Hessian matrix of the chi-square function, the expression for source flux and position errors, expressed as 1 σ at 68.3% confidence level in one parameter, which are related to the image function and to its second partial derivatives (Cook et al. 1984; Finger 1988; in’t Zand et al. 1994). The flux error is given by

σS = σCR



1 1 = σCR a · fI (0, 0) Q(0)



1 a(1 − a · fM )

(4)

where the mask function fM is 1 for optimal masks and, in average, for random masks and is given by a more complex relation for the general case, which involves the cross-correlation of the mask pattern. The SNR is then SNR = SNRCR · Q(0) ·



a(1 − a · fM )

(5)

The location error along one direction also can be expressed by an analytical expression and involves the second derivative of the image function:   1 1 d   = KX · σX = ·  2   ∂ f (0,0) SNRCR SNR I a ·  ∂x  2

(6)

For optimal masks (URA, MURA, etc.) with a = 0.5 as well as for random masks in average, the following formula for the constant Kx holds approximately: KX =



r · Q(0) 2

(7)

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The error here, as for the flux, is given at 1 σ along one axis direction. The fact that Eqs. 6–7 hold for both URAs and random masks does not mean that these mask types always have the same localization capability as their signal to noise is not the same if the aperture is different. These expressions are equivalent to those reported in Cook et al. (1984) and Finger (1988) and can be extended to the case of√continuous detectors by replacing the pixel linear dimension d with the value 2 3σD ≈ 1.5wD where σD is the detector spatial resolution in σ and wD in FWHM 1 [Following Skinner (1995) the numerical factor comes from the fact that √ is the 2 3 rms uncertainty in a variable which is known to plus or minus half a pixel.]. A more complicated expression, involving properly computed fM and its second partial derivatives, can be obtained for general (or not-so-random) masks. We do not show it explicitly here because it is too cumbersome, but it has been used to identify which quasi-random masks that cannot be purely random in order to make them self-supporting have optimal sensitivity-location accuracy pairs.

Non-uniform Background and Detector Response In gamma-ray astronomy, the background is generally dominant over the source contribution. Its statistical noise, spatial structure, and time variability are therefore important problems for any kind of instrument working in this energy range. CMI, unlike non-imaging instruments, allow measurement of the background simultaneously with the sources, limiting the problems linked to its time variability. However if the background is not flat over the detector plane, its inherent subtraction during image deconvolution does not work properly. In fact any spatial modulation is even magnified by the decoding procedure (Laudet and Roques 1988). Therefore the non-uniform background shall be corrected before decoding as well as any nonuniform spatial detector response which may affect both the background and the source contributions. Using an estimation of the detector spatial efficiency E for the given observation (spatial efficiency variations due to noisy pixels, dead times, or other time-varying effects) and of the detector non-uniformity U (quantum efficiency spatial variation depending on energy), along with a measure (e.g., from empty field observations already corrected for both E and U ) or a model of the background shape B, a correction of the detector image D affected by non-uniformity can be given by DC =

D −b·B E·U

and use then this corrected image D C to reconstruct the sky (Eqs. 1–2). The background normalization factor b can be computed from the ratio of the averages of the input detector and background images or from their relative exposure times. If one can neglect the variance of both B and b and assuming the Poisson distribution in each detector pixel, the variance of the corrected image can be approximated by σD2 C =

D E2 · U 2

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This implies that in the computation for the sky variance (Eq. 2), this detector variance shall be used instead of simply the detector image D C . Of course the details of the procedures, including other different, more sophisticated correction techniques, to account for spatial modulations not due to the mask, depend on the instrument properties, observing conditions, and calibration data (see, e.g., Goldwurm et al. 2003; Segreto et al. 2010). In general extensive ground and in-flight calibrations, including empty-field observations, will be needed in order to get the best models of the background and of the instrument response. One typical contribution to a non-uniform background is the CXB, dominant at low energies, and whose contribution on the detector plane, despite its isotropic character, becomes significantly non-uniform for large FOVs. In fact the CXB is viewed by each detector pixel through all the instrument opening with different solid angles, dependent on the instrument geometry (mask holes, shield, collimator, supporting structures, etc.). An example of such effect expected on the ECLAIRs detector plane is shown in Fig. 10, which also illustrates the noise that this effect produces in the decoded sky image if not properly corrected before reconstruction. Below we discuss the further modulation of the CXB produced when the Earth enters the instrument FOV. Other observational conditions can also be very important in this regard. For satellite orbits that intersect the radiation belts or the South Atlantic Anomaly, parts of the satellite, instrument, and the detector itself may be activated during the passage through this cloud of high-energy particles. The non-uniform distribution of the material in or around the detector may produce an additional non-flat timevarying background remnant that will spoil the images. A careful study of these effects is often required in order to introduce proper corrections in the analysis.

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Fig. 10 Non-uniform CXB in ECLAIRs. Left: Simulation of the CXB intensity (counts/pix) on the ECLAIRs detector during one orbit. Right: Decoded sky SNR map of the detector image (left), when two bright sources (SNR > 60) are also added in the simulation and no correction for the non-uniform background is performed. The sources can be barely seen in spite of their high SNR

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Overall Analysis Procedure, Iterative Cleaning, and Mosaics Once the raw data, possibly in event list form, are calibrated and binned in detector images, along with their weighting array, and then background, non-uniformity, and efficiency are corrected, the decoding can be performed by applying Eqs. 1–2 and prescriptions given in previous sections in order to derive preliminary sky images. Point sources are then searched throughout them by looking for SNR significant peaks. The detected source is finely located by fitting the peak of the SPSF function to the detected excess. A localization error can be associated (Eqs. 6–7) from the source SNR which allows to select the potential candidates for the identification. Iterative cleaning of coding noise from detected sources is performed in order to search for the weaker objects. This is done by modeling each source and subtracting its contribution, either in the detector image, which then must be decoded to look again for new sources, or directly in the deconvolved one. Typically the procedure is iterative, starting with the most significant source in the field and going on to the weaker sources, one by one, until no excess is found above the established detection threshold. Few iterations can be implemented, by restarting the procedure with the source fluxes corrected by the contamination from all other sources, for a deeper search. For close sources with overlapping main peaks, a simultaneous fit of their SPSFs may have to be implemented. A catalog is usually employed to identify, and even to facilitate the search, of the sources. This iterative cleaning procedure has been sometimes called Iterative Removal Of Sources (IROS) (Hammersley et al. 1992; Goldwurm et al. 2003), the most important element of which is the proper estimation of the source contribution in the recorded image which depends on a well-calibrated model of the instrument. As for the background correction, very often the source modelling is not perfect, and the ghost cleaning procedure leaves systematic effects which may dominate the noise in the images of large exposure times or on large sets of combined data. One way to smear out background and source residual systematic noise is to combine reconstructed images from different pointing directions and orientations. Overlapping cleaned sky images can be combined, after a normalization accounting for off-axis losses, in sky mosaics by a proper roto-translation to a common grid frame and then a weighted sum using the inverse of variance as the weight. While this is a standard procedure in astronomy imaging, here again one has to remember that we are treating correlation images and that the combined variance shall be computed including the co-variance term. The combination of images may take different forms depending on the scope of the mosaics (e.g., preserve source flux estimation versus reducing source peak smearing) (Skinner et al. 1987b; Goldwurm et al. 2003). A schematic picture of the overall analysis procedure using the IBIS images as example is shown in Fig. 11 (see also the procedures described by Segreto et al. 2010 and Krivonos et al. 2010).

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UBC Det Ima

CALIBRATED Events

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Cleaned Sky Image

Fig. 11 Simplified scheme of an overall image analysis procedure for CMI data including selection and binning of corrected/calibrated events, background and non-uniformity correction, decoding using the mask pattern, an IROS cleaning procedure on detected sources, and finally image mosaic, illustrated using the IBIS images (Goldwurm et al. 2003)

Coded Mask System Performances From the error estimations one can determine the expected CMI performance as function of instrument parameters and design. It is usually evaluated in terms of sensitivity, angular resolution, localization accuracy, field of view, and shape of SPSF. We already discussed the FOV in Section “Definitions and Main Properties” and the SPSF in Section “System Point Spread Function”.

Sensitivity and Imaging Efficiency The sensitivity of a coded mask system is given by the minimum point-like source flux that can be detected above a certain significance level nσ . The lower the minimum flux, the higher the sensitivity of the instrument. This minimum flux can be derived as function of the CMI parameters from the flux error estimation of Eq. 4. Let ε be the detector efficiency (we neglect here energy redistribution) and τo and τc , respectively, the transparencies of the open

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and closed mask elements, all dependent on the energy E of the incident radiation; then for given observation conditions and detector and mask parameters, with symbol meaning as in previous sections, assuming Gaussian statistics and neglecting systematic effects (see Skinner 2008 for different hypothesis), the continuum sensitivity FS , in units of ph/cm2 /s/keV, of a coded aperture system, on-axis and in the energy interval ΔE around E (keV), is given by

FS = n2σ ·

[(1 − a) · τo + a · τc ] +



[(1 − a) · τo + a · τc ]2 +

4·t·b·A(τo −τc )2 ·a·(1−a) n2σ

2 · ε · A · t · ΔE · (τo − τc )2 · a · (1 − a)

(8)

In the case of dominant background, the same relation holds with the term [(1 − a) · τo + a · τc ] at the numerator set to zero. Equation 8 can be solved toward nσ for a given source flux FS providing the upper signal to noise (SNR) limit attainable on-axis for that exposure or toward time t to have the observation exposure needed to reach the desired detection significance nσ for a given source flux FS . This formula, and the analogous ones for SNR and exposure, usually found in the literature (e.g., Carter et al. 1982; Skinner 2008), neglects both the mask pattern and the finite spatial resolution of the detector. Therefore it approaches the case for optimum or pure random mask systems with infinite resolution or with integer resolution parameter r and the source exactly located in the center of a sky pixel, that is, when detector pixels are all either fully illuminated or fully obscured for that source. This is in fact the most favorable configuration and gives the highest sensitivity, but in the general case, one must take into account the effect of the finite detector spatial resolution which is dependent on source position in the FOV. This gives an additional loss in the SNR due to imaging, which, averaged over source location within a pixel, is given by the term Q(0) of the SPSF, which depends on the resolution parameter r through Eq. 3. We therefore define the imaging efficiency as εI = Q(0) = 1 − 3r1 . The formula of Eq. 8 for the sensitivity can be used as it is also when including an average imaging loss over a pixel size, if one replaces everywhere the value nσ with nσ I = nεσI . In the same way, the SNR derived from Eq. 8 will be reduced to an imaging SNR by a factor given by the imaging efficiency, i.e., SNRI = SNR · εI . This formula, modified with the imaging efficiency, corresponds to Eq. 5 for the SNR discussed in the section “Flux and Location Errors” and approximates well the sensitivity within the FCFOV when the source position is known and the flux evaluation is performed by fitting the SPSF at the source position, or, which is the same, by correlating with a rebinned mask shifted at the exact source position. If one wants to include in the calculation the fact that the source position is not known (e.g., to establish the detection capability of unknown sources in the images), then an additional loss shall be included which takes into account that the deconvolution is performed in integer steps (sky pixels) usually not matching the source position (the phasing error of Fenimore and Weston 1981). If the source location is not

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in the center of a pixel, its peak will be spread over the surrounding pixels in the reconstructed image, and the SNR for the source will appear lower. In this case the prescriptions given above hold, but the expression for the imaging efficiency shall be replaced by the integral over 1 pixel of the SPSF peak, which can be approximated 1 by εI ≈ 1 − 2.1r for pixelated detector and square geometry (Goldwurm et al. 2001). For example, for the IBIS/ISGRI system (r = 2.4), the average (over a pixel) imaging efficiency is εI = 0.86 for known source location (fit of detected peak) and 0.80 for unknown location (peak in the image). The sensitivity formula, and its extensions for different hypothesis, can also be used to determine the optimum open fraction a of the mask (Fenimore 1978; Skinner 2008). One can easily see that for dominant background (b ≫ s) the SNR is optimized for a = 0.5. However if b is not dominant or if the sky component of the background is relevant, or in other applications like nuclear medicine (Accorsi et al. 2001), open fractions lower than 0.5 are optimal. As discussed by in’t Zand et al. (1994) and Skinner (2008) however, the optimum value varies slowly with parameters and remains generally close to 0.4–0.5. Other elements of the CM imaging system have an influence on the sensitivity. They are the used deconvolution procedure, the background shape and its correction, the source position knowledge, and of course the numerous systematic effects that may be present and some mentioned in the subsection on “real systems.” Also a decrease of the sensitivity with the increase of the source distance from the optical axis is present due to reduction of mask modulation, the vignetting effect of the mask thickness, and the possible variation of open and closed mask element transparency with the incident angle. In this case the additional sensitivity loss dependence on source direction angle shall be integrated in the term of the detector efficiency ε in Eq. 8, which then becomes dependent on energy but also on the source direction angle θ , that is, ε = ε(E, θ ).

Angular Resolution The separating power of a CMI system is basically determined by the angle subtended at the detector of one mask element. However the finite detector spatial resolution also affects the resolution. For a weighted cross-correlation sky reconstruction (Eqs. 1–2), the resulting width of the on-axis SPSF peak in one direction, which gives the angular resolution (AR) in units of sky pixels, is well approximated, with the usual meaning of resolution parameter r, for square geometry and a pixelated detector, by AR(F W H M) =



r2 + 1

(9)

To obtain the angular resolution in angular units (radians) on-axis, one has to take the arc-tangent of this value divided by the mask to detector distance H (Table 1).

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Fig. 12 IBIS/ISGRI imaging performance from INTEGRAL early data. (Reproduced with permission from Gros et al. 2003, © ESO). Left: FWHM of the fitted Gaussian to the SPSF along the two central sky image axes: constant at ≈2.6 pix in the FCFOV, it changes wildly in the PCFOV. The upper horizontal line gives the average value in the FCFOV (delimited by 2 vertical lines), the lower one the size of a mask element (2.43 pix). Right: PSLE radius at 90% c.l. from measured offsets of known sources at different signal to noises compared to prediction (solid line). Data are well fitted by a 1/SNR function plus a constant (dashed line)

Of course the angle subtended by a pixel varies along the FOV because of projection effects, and that shall be considered for the off-axis values. Moreover the separating power may vary along the FOV and particularly in the PCFOV because the coding noise may deform the shape of the SPSF main peak while vignetting effect of mask thickness will reduce its width. Figure 12 left shows the fitted width (in pixel units) of the IBIS SPSF, along the two image axes passing by the image center. The width is consistent with the AR value of Eq. 9 and of Table 1 within the FCFOV but changes wildly in the PCFOV (Gros et al. 2003). In any case the SPSF width of a system can be evaluated at any location in the image, and the fitting procedure applied to detected sources can either use the fixed computed value or let the width be a free parameter.

Point Source Localization Accuracy An essential characteristic of an imaging system is the quality of the localization of detected sources. As we have seen in the analysis section, the fine localization of a detected point-like source within the pixels around the significant peak excess shall be derived by a fitting procedure. This is usually implemented as a fit of the source peak in the decoded sky image with a function that describes (Goldwurm 1995; Bouchet et al. 2001) or approximates (e.g., a bi-dimensional Gaussian function) (Goldwurm et al. 2003; Gros et al. 2003) the SPSF, but can in principle (with a more complex procedure which for each tested location models and compares to data the shadow-gram of the studied source) be performed on the detector image. For this last implementation,

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formal errors can be derived and can be related to the SPSF and the source strength. As discussed above the uncertainty on the location is inversely proportional to the significance of the source. The typical procedure is then to express the location error radius for a given confidence level, as a function of the source SNR. Once the function is defined and calibrated for a given system, the error to be associated to the fitted position of a source is derived from its SNR. Using the relation for the location error σx (1-σ error along one direction) of Eqs. 6–7 and assuming that the joint distribution of errors in both directions is bi-variate normal and that they are uncorrelated, one can apply the Rayleigh distribution to obtain and relate to the system parameters (including r), the 90% √ confidence level error radius as P SLE(SN R) = 2 · ln10 · σx (SN R). The error can be expressed in angular units by taking the arc-tangent of the value divided by the mask to detector separation H , with the usual caveat that off-axis projection effects shall be considered. In Skinner (2008) the location error was rather approximated with the expression for the angular resolution (Eq. 9) divided by the SNR, while in Caroli et al. (1987) with the angle subtended by the PSD spatial resolution divided by the SNR. A more accurate and, for optimum or random masks, formally correct approximation with the explicit dependence on r is in fact P SLE(SN R) ≈ arctan

√

ln10 d · · SNR H



1 r− 3



(10)

which gives the 90% c.l. angular error radius of the estimation of a location of an on-axis source with signal to noise SNR. The SNR to use in the above expression is the imaging SNRI for a SPSF fit at the source location. If one wants to use the SNR measured in the images (in average affected by sampling), the value that should be used is the average estimation SNRI for unknown location, in which case the constant of Eq. 10 changes. In any case the PSLE expression above is valid for ideal conditions and shall be considered only as a lower limit obtainable for a given system geometry. In real systems, the non-perfect geometry, systematic effects, and the way to measure the SNR induce generally larger errors in the location than predicted by Eq. 10 and can even change the expected 1/SNR trend. In fact the PSLE will generally tend to a constant value greater than 0 for high SNR, which at the minimum includes the finite attitude accuracy. The PSLE curve as function of SNR is therefore always calibrated with simulations or directly on the data using known sources (Fig. 12). Reducing systematic effects and improving analysis techniques shall lead the calibrated curve to approach the theoretical one. Figure 12 shows the measured offsets of known sources with IBIS compared to the predicted error (Gros et al. 2003). The SNR used to plot the data was the SNR measured in the images, and the theoretical curve is then plotted with a specific constant. Even though the data roughly follow the 1/SNR trend, systematic effects prevent the system to reach the “ideal” performance even at large SNR.

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Sensitivity Versus Localization Accuracy In the design of CMI, it is often important to make a trade-off between sensitivity and localization power. Figure 13 shows the variation of the sensitivity (in terms of the inverse of the flux error σS of Eq. 4) and of the location accuracy (given here by the inverse of the location error σX of Eq. 6) with the resolution parameter r. In the left panel, different r values are obtained maintaining mask element (and mask pattern) fixed and varying the detector pixel size for two types of masks. The formulae correctly predict the performance evaluated through simulations, also shown in the plot: for a fixed mask element size (and then angular resolution), increasing detector resolution improves both sensitivity and accuracy. The cases considered are in condition of dominant background; thus the performance parameters with a 30% aperture mask are slightly worse than those for a 50% aperture.

Fig. 13 Theoretical, computed with full complex formulae, and simulated CMI performance as function of the resolution parameter r = m/d assuming dominant background. Left: Variation of sensitivity (solid line) and location accuracy (dashed) with r for two types of masks, an optimum system with a replicated 95×95 MURA of 53×53 basic pattern (blue) and a random mask of same dimensions and 30% aperture (green). Variation of r is obtained maintaining fixed m (and the mask pattern) and decreasing d (with d < m). Computed curves are compared to simulations, shown by data points and their error bars with the same color code. Right: Normalized accuracy versus normalized sensitivity curves for different r, where r is varied by fixing detector resolution d and varying m for the same masks of left panel (green, blue) plus a random mask with the same dimensions and a = 0.4 (violet). Curves for random masks are obtained by computing, and averaging, error values of a large sample of patterns. Dots give the specific values for integer r, while gray crosses those from the approximate formulae that neglect mask pattern (Eq. 5, 6, and 7). The cyan cross indicates the reference value for IBIS/ISGRI (r = 2.4) in the MURA curve (blue). The red curve is for an optimized quasi-random (auto-sustained) mask of a = 0.4 and dimensions 46×46, which is the pattern chosen for ECLAIRs whose performance is positioned in this plot by the brown cross at r = 2.5. Both sensitivity and accuracy depend on the configuration of the system, and therefore values for different systems are not directly comparable. For example, localization accuracy of IBIS/ISGRI is much higher than for ECLAIRs, because sky pixels are 5′ wide while for ECLAIRs are 30′ wide, even if their accuracy values appear identical in this plot

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In the right panel, the location accuracy is plotted versus sensitivity for different values of r where its variation is obtained by fixing the value of d and varying m. The apparent incoherence with the left panel plot (where accuracy increases with r) is due to the different way r is varied. Clearly by increasing m, which determine the angular resolution, the location accuracy decreases from its maximum at r=1, in contrast to the sensitivity which increases with r. As discussed in Skinner (2008), often the trade-off values of r are set in the range 1.5–3 in order to have, for given detector resolution d, better sensitivity at moderate expenses of positional precision. This opposite trend (for a fixed and finite detector spatial resolution) comes from the fact that localization is determined from a measure on the detector of the position of the boundary between transparent and opaque mask elements; therefore the larger the total perimeter of mask holes (which is maximized for given a when holes are small and are isolated), the better the measure of the source position. On the other hand, signal to noise is optimum when total mask hole perimeter is minimum (i.e., when open elements are large and agglomerated) which reduces the blurring that occurs at the boundary between open and closed mask elements. The above considerations explain not only the dependence on r but also the one on the element distribution (mask pattern). In Fig. 13 right, the curve for the specific quasi-random pattern of ECLAIRs (see section on SVOM) is also plotted. Considering this kind of prediction, the r value for ECLAIRs was finally fixed to 2.5, to reach the desired localization accuracy with the highest possible sensitivity. The formulae of Eqs. 4, 5, 6, and 7, as in general those published before, do not include the terms related to the mask pattern and do not predict the performances precisely other than for optimum systems or, in average, for fully random masks. But these terms can be computed using the mask auto-correlation in particular to select patterns which have best sensitivity/accuracy pair for given science objectives, as was done for ECLAIRs. Indeed, by comparing the values at integer r, its pattern appears better in both sensitivity and localization accuracy than the comparable 40% aperture random mask.

Coded Mask Instruments for High-Energy Astronomy The development of coded mask imaging systems has been, from the beginning, linked to the prospect of employing these devices in high-energy astronomy. We review here the implementation of CMI to this field from the first rocket experiments to the missions presently in operation or expected in the close future. Even if not exhaustive, this summary provides a chronological panorama of CMI in astronomy which illustrates the topics discussed above and recalls the main achievements obtained in imaging the gamma-ray sky with these devices (for a complete list of hard X-ray (>10 keV) experiments including CMI, see Cavallari and Frontera 2017). Specific subsections are dedicated to three major experiments successfully flown, or to be launched soon, on space missions, a representative set of CMI, with different and complementary characteristics. SIGMA, the first gamma-ray CMI

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on a satellite, featured an Anger-type gamma-camera with a continuous spatial resolution depending on energy. Thanks to its imaging capability in the hard Xray range, it became the black hole hunter of the 1990s and provided the first 20-arcmin resolution images of the Galactic bulge at energies above 30 keV, and its success opened the way to the INTEGRAL mission. IBIS, presently operating on INTEGRAL, is the most performing gamma-ray imager ever flown, reaching, for the brightest sources, better than 20′′ location accuracy at 100 keV over a large FOV. It still provides, along with the BAT/Swift experiment, some of the most crucial results in the gamma-ray domain. ECLAIRs/SVOM is the future CMI to be mounted on an autonomously re-pointing platform dedicated to time domain astronomy. The quasirandom mask, optimized to push the threshold at low energies, shall open to the community the efficient detection of cosmological gamma-ray bursts (GRB).

First Experiments on Rockets and Balloons The CMI concept was first applied to high-energy astronomy with instruments mounted on sounding rockets or on stratospheric balloons. Following the first ideas on coded aperture imaging, several such projects were initiated mainly by American, English, and Italian groups. The first experiment that actually probed the CM concept in astronomy was SL1501 (Proctor et al. 1978), built by a UK laboratory and launched on a British Skylark sounding rocket in 1976. Composed of a position sensitive proportional counter (PSPC) and a rectangular 93×11 Hadamard mask, both of the same dimensions (box-type), delimited by the diameter of the rocket, it provided in the few minute flight the first X-ray (2–10 keV) images of the Galactic Center (GC) with an angular resolution of 2.5′ ×21′ (the higher resolution side purposely oriented along the Galactic plane) in a square 3.8◦ FOV (Proctor et al. 1979). SL1501 data were combined with those of Ariel V space mission in order to establish the activity of the X-ray sources of the region, and together they even permitted to detect and localize some GC X-ray bursts. A balloon-borne CMI which was highly successful was the US Gamma-Ray Imaging Payload (GRIP) experiment (Althouse et al. 1985) that flew several times between 1988 and 1995 from Australia. Composed of an NaI(Tl) Anger camera working between 30 keV and 10 MeV coupled to a rotating mask (Cook et al. 1984) of about 2000 elements disposed on multiple repetition of a 127 HURA basic pattern (Fig. 6), this telescope imaged a FOV of 14◦ with 1.1◦ angular resolution and provided some of the first high-quality images of the Galactic Center at energies higher than 30 keV, in particular confirming the results obtained by SIGMA in the same period (Cook et al. 1991). GRIP also detected and located gammaray emission from SN1997a, confirming the discovery from the Kvant Roentgen observatory. Another American balloon experiment, EXITE2 (Lum et al. 1994), based on a phoswich (NaI/CsI) detector but coupled to a fixed rectangular URA, with a collimator that limited the FOV to the 4.5◦ FCFOV, flew several times between

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1993 and 2001 (after a preliminary 1988–1989 flight) giving some results on hard point sources. This project was a technological preparation for a more ambitious CMI space mission, EXIST, not yet included in the US space program. The American Directional Gamma-Ray (DGT) experiment deserves to be mentioned because it aimed to push the CM technique to high energies (Dunphi et al. 1989). Using a set of 35 BGO scintillation crystals working in the range from 150 keV to 10 MeV coupled to a 2-,cm-thick lead mask with 13×9 elements disposed as a replicated 7×5 URA basic pattern, it covered a FCFOV of 23◦ ×15◦ with a 3.8◦ angular resolution. The instrument suffered by a large non-uniform background which limited its performances. Nevertheless DGT could probe the CM concept at high energies with the detection of Crab nebula and the black holes (BH) Cyg X-1 and Cyg X-3 above 300 keV during a 30-hr balloon flight from Palestine (Texas) in 1984 (McConnel et al. 1989). These experiments and several others, only conceived, failed, or operated but for short periods, probed the coded aperture imaging concept and paved the way to the implementation of CMI in space missions.

Coded Mask Instruments on Satellites Table 2 reports the list of the fully 2-d imaging coded mask instruments successfully launched on, or securely planned for, an astronomy satellite mission. Other CMI with 1-d only design (or two 1-d systems disposed orthogonal to each other) were launched on space missions, and some provided relevant results mainly as (all-sky) monitors of point-like sources. These were Gamma-1 on Gamma (URSS-Fr), XRT on Tenma (Japan), ASM on Rossi XTE (US), WXM on HETE2 (US), and SuperAgile on AGILE (Italy); none of them is presently in operation. A 1-d coded mask all-sky monitor system presently in operation is the SSM on the Indian ASTROSAT mission (Singh et al. 2014). We will not describe them, as they are not, fully, imaging systems, even if the 1-d CMI concept, particularly when coupling orthogonal systems that give locations along the two axes, is an interesting one and has certain advantages for which it is still considered for some future missions. The first successful CMI flown on a space mission was the UK XRT experiment, launched as part of Spacelab 2 (SL2) on board the NASA Space Shuttle Challenger for an 8-day flight in August 1985 (Skinner et al. 1988; Willmore et al. 1992). Two modules were included, equipped with the same multi-wire proportional counter working in the 2.5–25 keV range but with two Hadamard masks of different basic pattern, 31×29 for the coarse one and 129×127 for the fine one, and different mask element size which allowed for, respectively, coarse and high resolutions over the same 6.8◦ -wide FOV. Remarkable results were obtained from XRT/SL2, which provided in particular the first GC images with few arcmin resolution at energies >10 keV (Fig. 14 left) (Skinner et al. 1987a). Other XRT results concerned galaxy clusters, X-ray binaries (XRB), and the Vela supernova remnant.

Satellite Challenger SL2 MIR Kvant GRANAT GRANAT SAX INTEGRAL INTEGRAL INTEGRAL Swift ASTROSAT SVOM

Detector type PSPC PSPC Anger PSPC PSPC CdTe CsI HPGe MGC CdZnTe CdZnTe CdTe

Mask type Hadamard Hadamard URA URA Triadic MURA HURA HURA Random Hadamard Random

Notes: [ ] foreseen at the time of writing (Jul 2022) a Second module

CMI XRT TTM SIGMA ART-P WFC IBIS SPI JEM-X BAT CZTI ECLAIRs

Table 2 Coded mask instruments on satellites Pattern or order 129×127a 255×257 31×29 43×41 256×256 53×53 127 22501 54000 17×15 46×46

Energy (keV) 2.5–25 2–32 30–1300 4–30 2–30 15–10000 20–15000 3–35 15–150 20–200 4–150

Ang. Res. (FWHM) 3′ –12′ 1.8′ 15′ 6′ 5′ 12′ 2.5◦ 3.3′ 17′ 17′ 90′

Field of View (at ZR) 6.8◦ 15.8◦ 20◦ 1.8◦ 40◦ 30◦ 45◦ 13.2◦ 120◦ ×85◦ 11.8◦ 90◦

Operations (years) 1985 1987–1999 1989–1997 1989–1993 1996–2002 2002-[2025] 2002-[2025] 2002-[2025] 2004-[2025] 2015-[....] [2024-2029]

Reference (Willmore et al. 1992) (Brinkman et al. 1985) (Paul et al. 1991) (Sunyaev et al. 1990) (Jager et al. 1997) (Ubertini et al. 2003) (Vedrenne et al. 2003) (Lund et al. 2003) (Barthelmy et al. 2005) (Bhalerao et al. 2017) (Godet et al. 2014)

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The following CMI in space was the Coded Mask Imaging Spectrometer telescope (COMIS/TTM) (Brinkman et al. 1985) flown on the Kvant module of the soviet MIR station as part of the Roentgen Observatory which included three other non-imaging experiments. The instrument, built by Dutch and UK laboratories, used again a Hadamard mask (Fig. 6) coupled to a PSPC in a simple system (in’t Zand 1992). It operated at different times between 1987 and 1999 and provided interesting hard X-ray images of the Galactic Center and upper limits of the famous SN1987a in the LMC (Sunyaev et al. 1987). In spite of the progress obtained in the UK and US, it was finally France that built the first soft gamma-ray CMI to fly on a satellite, SIGMA. It was launched in 1989 on the Soviet satellite GRANAT along with few other experiments: the Russian ART-S and CMI ART-P, the Danish rotating collimator monitor Watch, and the French Phebus burst detector. SIGMA spectacular results firmly established the superiority of CM imaging over collimation, on/off chopping, or Earth occultation techniques for gamma-ray astronomy. SIGMA is described in Section “SIGMA on GRANAT: The First Gamma-Ray Coded Mask Instrument on a Satellite.” Soon after SIGMA, the Dutch Wide Field Camera (WFC) (Jager et al. 1997) working in X-rays up to 30 keV was launched in 1996 on the Italian space mission Beppo-SAX (Boella et al. 1997). This instrument was based on a pseudo-random mask, with a pattern called “triadic residues,” with low open fraction (33%), more adapted to the X-ray domain than URAs, arranged in a simple system configuration which provided a 40◦ ×40◦ PCFOV (in’t Zand et al. 1994). Two such cameras

Fig. 14 Left: Image of the Galactic Center obtained by the XRT/SL2 instrument in the 3–30 keV band. (Reproduced by permission from Skinner et al. 1987a, © Springer Nature 1987). Right: Detection of GRB960720 by WFC/SAX. (Reproduced with permission from Piro et al. 1998, © ESO). Top: 3D shadow picture of the WFC 40◦ ×40◦ FOV of the observation showing the GRB peak along with the one from Cyg X-1. Bottom: maps around the GRB before during and after the ≈30 s of the burst

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were disposed orthogonal to each other and to the optical axis of the other SAX instruments and particularly of the X-ray mirror telescope. The WFC allowed the discovery of the first X-ray afterglow of a GRB (Costa et al. 1997) when the satellite could re-point its X-ray mirrors on the transient source positioned with arcmin precision (Fig. 14 right). This was a crucial astrophysical discovery which allowed the community, with follow-up optical observations, to establish that GRBs are extra-galactic events, which now we know are connected to explosion or coalescence of stars in external galaxies. The heritage of SIGMA allowed Europe to maintain and consolidate the advantage in CMI. In fact France, Germany, and Italy took the lead of the development of the two main instruments of the INTEGRAL Mission, both based on coded aperture techniques. The International Gamma-Ray Astrophysical Laboratory (Winkler et al. 2003) of the European Space Agency (ESA) with participation of Russia and the US was launched on the 17th October 2002 from Baikonour by a Proton rocket on a very eccentric orbit, which allows long uninterrupted observations of the sky, about 3 days before entry in the radiation belts. The platform carries four co-axial instruments, the two main gamma-ray CMI, the imager IBIS, and the high-resolution spectrometer SPI, plus the coded mask X-ray monitor JEM-X and the optical telescope OMC. INTEGRAL performs observations in dithering mode where a set of pointing of ≈30 min are carried out along a grid of directions about 2◦ apart around the target source. Data are sent to ground in real time which allows fast analysis and reaction in the case of detection of transient events. The spectrometrer on INTEGRAL (Vedrenne et al. 2003) working in the range 20 keV–8 MeV is composed of 19 individual cooled Germanium detectors of hexagonal shape with 3.2 cm side disposed in an hexagonal array 1.7 m below a thick tungsten non-replicated and non-rotating HURA mask of order 127, with hexagonal elements of the size of the Ge crystals. The very high spectral resolution (2.5 keV at 1.33 MeV) of the 6-cm-thick Ge detectors allows study of gamma-ray lines with moderate imaging capabilities (2.5◦ resolution over a 16◦ FCFOV and a 30◦ half coded EXFOV) thanks to the CM system and the dithering mode which permits a better correction of the background. The SPI CsI anti-coincidence system is by itself a large area detector that is presently used also for the search of GRB events outside the FOV of the CMI. The Danish JEM-X monitor (Lund et al. 2003) working in the range 3–30 keV is also a CMI. Composed of two identical modules with the same non-cyclic fixed HURA of more than 20,000 elements with 25% aperture but rotated by 180◦ in order to have different ghost distribution and highpressure Microstrip Gas Chamber (MGC) detectors, it provides 3′ angular resolution images over a 7◦ FWHM FOV. IBIS is certainly the core of the CM imaging capabilities of INTEGRAL and is described in Section “IBIS on INTEGRAL: The Most Performant Gamma-Ray Coded Mask Instrument.” INTEGRAL provides the community with a large amount of excellent astrophysical results and crucial discoveries, in particular with the mapping of the 511 keV line of the Galaxy; the measurements of gamma-ray lines from SNR and close supernovae (SN); the detection and study of GRBs and BH sources in binary systems and in active galactic nuclei (AGN), of all variety of neutron star (NS)

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systems; and the detailed imaging of the GC region. The mission is still operating today (Kuulkers et al. 2021) with many important results obtained each year, the most recent ones in the domain of time domain astronomy (see, e.g., Ferrigno et al. 2021 and references therein). Meanwhile, on the side of the high-energy time domain astronomy, Beppo [Beppo-SAX, the Italian satellite for X-ray astronomy was named in honor of Giuseppe Occhialini, the eclectic and visionary Italian physicist, to whom we owe, in addition to other things, the strong involvement of Europe in astrophysical space programs.] had, once more, showed the way. The future of this domain would reside on agile spacecrafts with capability of fast (therefore autonomous) re-pointing and a set of multi-wavelength instrumentation, including a large field imaging instrument at high energies, based on coded mask technique, and high-resolution mirror-based telescopes at low energies. Too late to implement these features in INTEGRAL, the US did not miss the opportunity by developing in collaboration with UK and Italy the Neil Gehrels Swift mission (Gehrels et al. 2004), dedicated to GRBs and the transient sky. Using a platform conceived for the military “star-wars” program, with unprecedented, and still unequalled, capability of fast (tens of seconds) autonomous re-pointing, this mission has provided since its launch in 2004 exceptional results in the domain of GRB science (Gehrels and Razzaque 2013) but also of the variable and transient high-energy sky (Gehrels and Cannizzo 2015). Many of these are based on the Burst Alert Telescope (BAT) (Barthelmy et al. 2005) a large coded mask instrument which is still in operation along with the two narrow-field telescopes of the mission, one for X-rays (XRT) and one for ultraviolet-optical frequencies (UVOT). BAT (Fig. 15) is the instrument that detects and localizes the GRB and triggers the platform re-pointing. It is composed of an array of 32,768 individual square CdZnTe semiconductor detectors, for a total area of 5240 cm2 , coupled to a large random mask with a “D” shape and a 50% aperture, made of about 52,000 elements, each of 1 mm thickness and dimensions 5×5 mm2 with a resolution ratio r = 1.2 with respect to the detector pixels. The mask is set at 1 m from the detection plane, and it is connected to the detector by a graded-Z shield that reduces the background. BAT provides a resolution of about 20′ over a huge FOV of 1.4 sr (half coded), a location accuracy of 1′ –4′ , and a good sensitivity in the range 15–150 keV. Ground BAT data analysis is described in Tueller et al. (2010), Segreto et al. (2010), Baumgartner et al. (2013), Oh et al. (2018), and it is quite similar to the standard one described above. Figure 16 left shows the BAT reconstructed image of the Galactic Center from which one can appreciate the imaging capability of this CMI and can compare it to the IBIS one. A specific feature of the instrument is that a BAT data analysis is continuously performed on board in near real time thanks to an image processor which allows the detection and position of GRBs within 12 s from their start and the rapid triggering of the platform re-pointing to the computed location. BAT performances are the key of the large success of the mission. The instrument detects and positions about 100 GRBs per year allowing the following red-shift determination for about 1/3 of them. It provides excellent results on many different variable hard X-ray sources, both Galactic and extra-galactic, like AGNs,

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Fig. 15 Left: Scheme of the BAT CM instrument on board the Swift satellite. (Credit NASA, https://swift.gsfc.nasa.gov/about_swift/bat_desc.html). Right: Assembly of the BAT coded mask, characterized by a “D” shape and a random distribution of elements. (Reproduced by permission from Barthelmy et al. 2005, © Springer Nature 2005)

Fig. 16 Left: Reconstructed image of the Galactic Center from BAT data. (Reproduced with permission from Baumgartner et al. 2013, © AAS). Right: The BAT/Swift catalogue of sources (>15 keV) detected in the first 105 months of operations. (Reproduced with permission from Oh et al. 2018, © AAS)

magnetars, different types of binaries, and others (Gehrels and Cannizzo 2015), for example, it allowed the discovery in 2011 of the first tidal disruption event with a relativistic jet (Burrows et al. 2011). More than 1600 non-GRB hard X-ray sources have been detected by BAT/Swift in the first 105 months of operations (Oh et al. 2018) (Fig. 16 right). The most recent launch of a coded aperture instrument on a space mission is the Cadmium Zinc Telluride Imager (CZTI) (Bhalerao et al. 2017) of the Indian ASTROSAT (Singh et al. 2014) mission in operation since 2015. The CZTI is composed of four identical and co-axial modules disposed 2×2 on the platform. The modules are based on a mask composed of 4×4 arrays, each one following a Hadamard pattern built (in different way) from the same 255 PN sequence, and then coupled to a pixelated CdZnTe detector in a “simple system” configuration. Its overall parameters are given in Table 2, but for more complete and recent reports about the in-flight calibrations and performance of the instrument, see Vibhute

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et al. (2021). Important results have been obtained on transient sources, pulsars, and polarization measurements.

SIGMA on GRANAT: The First Gamma-Ray Coded Mask Instrument on a Satellite SIGMA (Système d’Imagerie Gamma à Masque Aléatoire) is the first gammaray coded mask telescope flown on a satellite (Paul et al. 1991) and provided extraordinary discoveries and results in the domain of black hole astrophysics. Launched on the 1st December 1989 from Baikonour (URSS) by a Proton rocket on the three-axis stabilized Soviet GRANAT satellite, it operated in pure pointing mode till 1995 and then mainly in scanning mode for a couple of years more. A schematic view of SIGMA is given in Fig. 17 where its coded mask is also shown, with its characteristic URA pattern, after the instrument was mounted on the platform. Made of a NaI(Tl) Anger camera, composed of 1.25-cm-thick circular scintillating crystal viewed by 61 photo-multipliers, surrounded by a CsI(Tl) anti-coincidence system, and set at 2.5 m from a 1.5-cm-thick tungsten coded mask, SIGMA could provide images in the 35 keV–1.3 MeV range with angular resolution of 20′ –13′ in a FCFOV of 4.7◦ ×4.3◦ and a half-coded EXFOV of 11.5◦ ×10.9◦ with an onaxis 40–120 keV 3σ sensitivity of the order of 100 mCrabs in 1-day observation. The rectangular mask of 53×49 elements was a replicated 31×29 URA (and not a random mask as implied by the instrument acronym), and the events, detected in the

Fig. 17 The SIGMA/GRANAT coded mask instrument. Left: Scheme of the SIGMA telescope. (Reproduced with permission from Bouchet et al. 2001, © AAS). Right: SIGMA, with its URA tungsten coded mask, mounted on the GRANAT spacecraft. (Credit CEA/IRFU)

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central rectangular 725 cm2 area of the NaI crystal corresponding to the URA basic pattern, were coded in 124×116 pixel detector images and in 95 energy channels. Data analysis and calibration of SIGMA are reported in Goldwurm (1995) and Bouchet et al. (2001) and references therein. A specific feature of the decoding process was the use of the efficiency array to take into account the drifts of the platform (Goldwurm 1995) for the extension of the sky image reconstruction to the PCFOV of the instrument. Another important element was that the continuous spatial resolution of the gamma camera varied with energy (see Fig. 19) and time, and therefore it had to be monitored and modelled along the mission (Bouchet et al. 2001) in order to optimize the analysis of the data. The SIGMA long and repeated observations of the Galactic Bulge (Fig. 18), allowed by the fact that its imaging capabilities could be fully exploited over its huge PCFOV, clarified the situation of the high-energy emission from this very active and variable region by showing in particular that the central degrees at energies >20 keV are fully dominated by the source 1E 1740.7–2942, not particularly bright at low energies, that was soon after identified as the first persistent Galactic BH micro-quasar displaying extended radio jets. They also led to the discovery of the other persistent X-ray BH binary GRS 1758–258 (Mandrou et al. 1991) of the bulge and second identified micro-quasar of the Galaxy (too close to the NS XRB GX5-1 to be studied by previous non-imaging instruments), to a measure of the weakness of the central massive black hole Sgr A∗ at high energies, and to the detection of several other BH and NS X-ray persistent and transient bulge sources (Goldwurm et al. 1994). Again thanks to its huge FOV and imaging capabilities, SIGMA was very efficient in discovering Galactic BH X-ray transients (or X-ray novae) which are particularly hard sources. It detected and positioned seven of them in its 6 years of nominal operations, and between them is the other famous BH

Fig. 18 The Galactic Bulge and Galactic Center observed with SIGMA/GRANAT (Goldwurm et al. 1994). Left: The mosaic of the 40–80 keV sky images reconstructed from SIGMA data from observations of the GC in 1990–1994. Right: Zoom in the central GC region, dominated by the bright micro-quasar 1E1740.7–2942. Very weak emission is present at the position of the SMBH Sgr A*

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35 – 50 keV

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Fig. 19 SIGMA Observation of Nova Muscae 91 in January 1991 (Goldwurm et al. 1992). Left: Sky image sectors around the source in different energy bands which show the large variation of the width of the SPSF due to the changes in the gamma-camera spatial resolution with energy, along with the reappearance of a significant excess in the band around 500 keV. Right: Source spectrum, derived from the deconvolved images, which shows the presence of a high-energy feature

micro-quasar GRS 1915+105 that was the first specimen to reveal super-luminal radio jets. An important result was the detection, in the BH X-ray Nova Muscae 91, of a weak and transient feature around 511 keV (Fig. 19), the energy of the electron-positron annihilation line (Goldwurm et al. 1992). These results showed how well-designed CMI can provide also high-quality spectra and light curves of gamma-ray sources. SIGMA detected, in its 12 Ms 1990–1997 survey, a total of about 35 sources including 14 BH candidates, 10 XRB, 5 AGN, 2 pulsars, and 9 new sources (Revnivtsev et al. 2004b). SIGMA data were complemented at low energies by those of the ART-P coded mask hard X-ray telescope (Sunyaev et al. 1990) which had four identical modules made of a PSPC coupled to a replicated URA mask and providing 6′ angular resolution over less than 2◦ FOV. ART-P’s most relevant results were the hard Xray images of the GC that complemented nicely those of SIGMA (Pavlinsky et al. 1994) and revealed a diffuse emission consistent with the molecular clouds of the region and interpreted as scattering by the clouds of high-energy emission emitted elsewhere. Initially used to put limits on the activity of Sgr A*, the detected emission was later recognized as a signal of the Galactic SMBH past activity and was coupled to the measurements of the molecular cloud Sgr B2 with IBIS/INTEGRAL to constrain the Sgr A* ancient outbursts (Revnivtsev et al. 2004a).

IBIS on INTEGRAL: The Most Performant Gamma-Ray Coded Mask Instrument The main gamma-ray imaging device on INTEGRAL (Fig. 20 left) is the Imager on board the INTEGRAL satellite, a hard X-ray/soft gamma-ray coded mask telescope (Ubertini et al. 2003) developed mainly by Italy and France. IBIS is composed of a

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Fig. 20 IBIS/INTEGRAL coded mask instrument. Left: Artistic view of the INTEGRAL satellite, where the characteristic MURA and HURA patterns of the IBIS and SPI masks are visible. (Credit ESA). Right: The ISGRI detection plane composed of 8 modules of 2048 CdTe detectors integrated in the IBIS instrument. (Reproduced with permission from Lebrun et al. 2003, © ESO)

replicated MURA mask of 95×95, 1.6-cm-thick tungsten square elements (see the pattern in Fig. 6) with 50% open fraction coupled to two position sensitive detectors, the Integral Soft Gamma-Ray Imager (ISGRI) and the Pixellated Imaging Caesium Iodide Telescope (PICsIT), both of the same dimension of the central MURA basic pattern of 53×53 elements. ISGRI (Lebrun et al. 2003) is made of 128×128 individual 2-mm-thick cadmium telluride (CdTe) semiconductor square detectors each of dimensions 4×4 mm2 (for a total area of 2600 cm2 ) (Fig. 20 right), works in the range 15 keV–1000 MeV, and is placed 3.2 m below the mask. The overall IBIS/ISGRI sensitivity is of the order of a mCrab for 1 Ms exposure at 80 keV with typical spectral resolution of 7% (FWHM). PICsIT (Di Cocco et al. 2003) is placed 10 cm below ISGRI and is composed of 64×64 CsI bars, each exposing a collecting area 4 times of an ISGRI pixel and working in the range 175 keV–10 MeV. The detector planes are surrounded by an active anti-coincidence system of BGO blocks, and an absorbing tube connects the unit with the mask allowing for reduction of un-modulated sky radiation. Data of both instruments are recorded, transmitted, and analyzed independently, but coincident events from the two detector layers are combined to provide the so-called Compton mode data which are particularly useful to study polarimetry properties of the incident radiation. In the following we will refer to the IBIS/ISGRI system only, given that it provides the best imaging performances of the telescope, and we will neglect the Compton mode. IBIS has provided the most precise images of the GC (Fig. 21 left) at >20 keV before the recent extension of the grazing incidence technique to 70–80 keV with NuSTAR, and it is still the best imager that can cover such large FOV (>2◦ ) at high energies. The most recent and remarkable discoveries of this telescope have been the detection of emission of a close supernova (SN2014j) in the Na lines and the identification of a magnetar flare (Fig. 21 right) with a fast radio burst (FRB) (Mereghetti et al. 2020).

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Fig. 21 IBIS/INTEGRAL results. Left: Image of the Galactic Center (2.5◦ ×1.5◦ ) in the 20– 40 keV from the mosaic of 5 Ms of observations of the field. (Reproduced with permission from Bélanger et al. 2006, © AAS). Right: IBIS detection of the magnetar SGR 1935+2154 flares coincident with a FRB (Mereghetti et al. 2020): sky image, source location, and light curve (blue) compared to the radio bursts (red) (INTEGRAL POM 07/2020, credits: S. Mereghetti and ESA)

IBIS Data Analysis and Imaging Performance The IBIS coded mask system and the standard analysis procedures of the data are described in Goldwurm et al. (2003) and Gros et al. (2003), but see also Krivonos et al. (2010) for sky surveys at high energies and Renaud et al. (2006) for analysis of extended sources. The instrument analysis software is integrated in the Integral Science Data Center (ISDC) (Courvoisier et al. 2003) through which it is distributed to users as Off-line Scientific Analysis (OSA) packages. After 20 years of operations, the instrument is still providing excellent data, and several new features have been integrated in the analysis procedures (Kuulkers et al. 2021). We have already largely used characteristics and data from this system in order to illustrate CMI design, analysis, and performance concepts: in Table 1 for imaging design/performance, in Fig. 6 for the mask pattern, in Fig. 7 for decoding process, in Fig. 8 for distribution of peaks in reconstructed image, in Figs. 9 and 12 for the resulting SPSF and PSLE, and in Fig. 11 for the overall analysis process. Indeed IBIS represents a typical CMI with a cyclic optimum (MURA) mask coupled to a pixelated detector. The detector spatial resolution is just given by the geometrical dimension of the square pixels, independent from energy. CdTe square pixels have size of 4 mm, but the pitch between them is 4.6 mm with 0.6 mm of dead area. The mask elements are not integer number of pixel pitch also in order to avoid ambiguity in source position due to the dead zones. This does introduce a non-perfect coding even for sources in the FCFOV; however other factors break the perfect coding, and noise is anyway introduced. Imaging performances were studied on different data sets of bright and weak known point-like sources along the years (Gros et al. 2003, 2012; Scaringi et al. 2010). The FCFOV is 8◦ ×8◦ , the halfcoded EXFOV 19◦ ×19◦ , and the zero-response one 29◦ ×29◦ . The detector pixel pitch (and therefore the reconstructed sky pixel for the decoding process described

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above) subtends an angle of 5′ on the sky, while the mask element an angle of 12′ . With a ratio mask element to pixel pitch of 2.43, IBIS is expected to have an average image efficiency (at source location) of 86%; an angular resolution, for weighted reconstruction, of 13′ FWHM in the FCFOV; and a localization better than 0.5′ at SNR > 30. The width of the SPFS however varies wildly along the PCFOV due to the secondary lobes as shown in Fig. 12 left (Gros et al. 2003). The localization error as measured at the beginning of the mission (Fig. 12 right) (Gros et al. 2003), even if it followed well the expected 1/SNR trend and reached values of less than 1 arcmin at SNR > 30, was not as good as the theoretical curve and stalled at a constant level of 20′′ even for very high SNR. With the improvement of the analysis software and the reduction of systematic effects, the PSLE was significantly reduced (Scaringi et al. 2010; Gros et al. 2012) and reaches now about 40′′ at SNR 30. Figure 22 reports the PSLE as a function of the source SNR obtained at later stages of the mission. Systematic effects like pixel on/off, absorption by different detector structures, mask vignetting, and absorption by mask elements including screws and glue and in the mask support honeycomb structure have been studied along the years. All shall be accurately accounted for in source modelling. In fact while the MURA optimum system provides clean and narrow SPSF in the FCFOV, it also creates strong ghosts and coding noise in particular along the image axis passing through the source position, which must be removed in order to search for weaker excesses. An iterative algorithm of search, modelling, and removal of sources is implemented in OSA (Fig. 11) in order to clean the images before summing them in sky mosaics (Fig. 23).

Fig. 22 IBIS/ISGRI imaging performance: recent determination of the PSLE. Left: PSLE vs SNR in FCFOV and PCFOV compared to early measurements (Scaringi et al. 2010). (Credit: IBIS Observer’s Manual, 2017, ESA SOC). Right: Recent PSLE measurements (dots) and derived curves (red, orange, yellow) using refined analysis, compared to previous results and theoretical trend (violet) (Gros et al. 2012)

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Fig. 23 IBIS/ISGRI imaging performance: mosaic in the Cygnus Galactic region after the decoding, analysis, cleaning, roto-translation, and sum of several individual sky images (Goldwurm et al. 2003)

ECLAIRs on SVOM: The Next Coded Mask Instrument in Space The Chinese-French SVOM (Space-based multi-band astronomical Variable Object Monitor) space mission (Wei et al. 2016; Cordier et al. 2015), planned, today, for a launch in 2023–2024, is a multi-wavelength observatory dedicated to the astrophysics of GRBs and of the high-energy variable sky. Between the four instruments of the payload, the hard X-ray coded mask imager ECLAIRs (Godet et al. 2014) (Fig. 24), operating in the 4–150 keV energy range, will autonomously detect onboard GRBs and other high-energy transients providing their localization to the ground (through a fast VHF system) and triggering on board, under certain criteria, the slew of the platform in order to point in few minutes the SVOM narrowfield telescopes working in X-rays (Micro X-ray channel plate Telescope, MXT) and in the optical (VT) toward the event. The ECLAIRs detection plane is made of 6400 pixels of Schottky type CdTe (4×4 mm2 , 1 mm thick) for a total geometrical area (including dead zones) of ≈1300 cm2 . A 54×54 cm2 coded mask with 40% open fraction is located 46 cm above the detection plane to observe a FOV of 2 sr (zero coded) with an angular resolution of 90 arcmin (FWHM). A passive lateral Pb/Al/Cu-layer shield blocks radiation and particles coming from outside the aperture. Sky images will be reconstructed in maps of 199×199 square pixels with angular size ranging from 34′ on-axis down to 20′ at the edges of the FOV. ECLAIRs provides a sensitive area of ≈400 cm2 , a point source localization error better than 12′ for 90% of the sources at the detection limit, and is expected to detect each year about 70 GRBs, several nonGRB extra-galactic transients, dozens of AGNs, and hundreds of Galactic X-ray

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Fig. 24 The ECLAIRs/SVOM coded mask instrument. Left: A scheme of the instrument showing the different elements. (From Godet et al. 2014). Right: The ECLAIRs Mask mounted on the instrument at the CNES premises. (Credit CTS/CNES)

transients and persistent sources. Its low energy threshold of 4 keV will open to SVOM the realm of extra-galactic soft X-ray transients, such as X-Ray flashes or SN shock breakouts, which are still poorly explored, and in particular will allow the detection and study of cosmological GRBs whose emission peak is red-shifted in the X-ray band. The 46×46 square mask elements have linear size 2.53 times the detector pixel pitch, and their distribution follows an optimized quasi-random pattern chosen by requiring connection between elements in order to allow the mask to be autosustained. Thousands of quasi-random patterns of this kind with a 40% aperture, which optimizes performance at these energies, were generated and studied, using the formulae of error estimation for general masks (mentioned but not explicitly given in the section “Flux and Location Errors”), in order to select the one presenting the best compromise between sensitivity and source localization for the GRB science, compatible with the mechanical criteria. The performance as function of the resolution parameter r for the specific chosen mask pattern is shown in Fig. 13 right along with the relative values, at the selected resolution factor which was chosen in order to optimize the system for the scientific objectives of the mission. For the chosen design, the predicted imaging performances are shown in Fig. 25. Left panel shows the peak of the SPSF that, given the non-optimum system based on a quasi-random mask, does present relevant side-lobes even in the center of the FCFOV. Once the source is detected and positioned, the lobes must be cleaned by an IROS procedure in order to search for weaker sources. Right panel shows the localization error curve from simulations of sources at different SNR. The accuracy is expected to be within half the size of the VT FOV (≈26′ ) in order to always have the event within both the optical and the X-ray telescope FOVs after the slew of the platform to the ECLAIRs measured GRB position.

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Fig. 25 ECLAIRs/SVOM imaging performances. Left: Central part of the SPSF for on-axis position. Lobes close to the central source peak are present. Right: Expected PSLE radius at 90% c.l. versus the source signal to noise. Source offsets from true positions obtained from simulations are indicated by black dots and the fitted PSLE, with 1/SNR trend, by the solid line. (From Godet et al. 2014)

The actual mask, integrated in the ECLAIRs instrument, is shown in Fig. 24 right. It is composed by a Ti-Ta-Ti sandwich with the tantalum providing the main absorbing power and the titanium the mechanical strength. A central opaque cross, of width 1.4 times the mask element size, is added, along with fine titanium supporting structures running along the mask elements on the side which avoids vignetting of off-axis sources, to make the overall structure resistant to the expected vibration amplitudes of the launch. The design of the ECLAIRs mask has been optimized in this way in order to allow the instrument to be sensitive at energies as low as 4 keV. That requires to have a solid self-sustained mask without a support structure that would absorb the radiation passing through the mask open elements. The multi-layer thermal coating insulation that envelops the telescope in order to protect the camera from light and micro-meteoroids will stop however X-rays below 3–4 keV and determines the low-energy threshold of the instrument. One particular feature of the SVOM mission is that the general program observations, during which data on other sources are collected while waiting to detect GRB events, will be scheduled giving priority to an attitude law that optimizes the search of GRB. SVOM will generally point opposite to the sun, toward the Earth night, so that detected GRB can be rapidly observed with ground-based observatories, and also, to reduce noise, will avoid the bright Galactic plane and rather observe the sky Galactic poles. These constraints and the low Earth orbit of the satellite (≈650 km) will lead to a frequent and variable occultation of the instrument FOVs by the Earth. ECLAIRs will then often experience partial Earth occultation of its large FOV during which the CXB will be modulated in a variable way during the ≈90 min orbit. Figure 26 shows a simulation of the expected spatial modulation on the detector by this effect, the impact on the imaging performance, and the expected correction results. Given the uncertainties of the CXB model and the additional components of

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Fig. 26 Effect of CXB modulation by partial Earth occultation of the ECLAIRs FOV. From left to right and top to bottom: Simulated detector image of the Earth-modulated CXB in 20 s exposure (during which the Earth can be considered stable in the FOV). Configuration of Earth occultation of ECLAIRs FOV considered in the simulation. Decoded SNR sky image of the simulated detector image and including two not-obscured sources when background is not corrected: large modulation is present, and the sources are not easily detected. Decoded SNR sky image when proper model of CXB modulated by the Earth is used for the background correction: the reconstructed image is flat, and the two sources are detected as the highest peaks

Earth albedo and reflection, the background correction of ECLAIRs images affected by the Earth in its FOV in real conditions will certainly be challenging. However CMI have been proven to be robust and effective imaging systems, and new exciting results are expected from this novel coded mask-based high-energy mission, dedicated to the transient sky, that will be launched soon.

Summary and Conclusions In this review we have described the concept of coded mask instrument for gamma-ray astronomy, discussed the mask patterns, and introduced definitions and terminology useful to understand the large literature on the subject. We have illustrated the correlation analysis procedure to apply to the data of standard CM

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systems, along with some practical recipes for the analysis. We have provided the formulae to evaluate errors and performance of the systems from their design parameters and illustrated them with data, simulations, or calculations for some of the CMI presently in operation or in preparation. Finally we have described the historical development of the field and the main CMI implementations in space missions and recalled some of the important results obtained by these devices in imaging the soft gamma-ray sky. Even if focusing techniques, with their power to reduce background and to reach arcsec scale angular resolutions, are more and more extended to high energies and are definitely performing well in exploring the most dense sky regions like the Galactic center, they are limited to narrow fields, and CMI remain the best options for the simultaneous monitoring of large sky regions. Since the X-/gamma-ray sky is dominated by compact objects which are, most of the time, very variable and even transient, these surveys are crucial to explore this realm, especially in the new era of time-domain and multi-messenger astronomy. Indeed rapid localization at moderate resolutions of high-energy electromagnetic counterparts of gravitational wave or neutrino burst events, which have large positional uncertainties, can trigger the set of high-resolution observations with narrow-field instruments which finally lead to identification of the events. This is what happened for the very first identified GW source (GW170817), and this is the strategy envisaged for the next multi-messenger campaigns of observations. The reaction time for the follow-up of fast transients is obviously very important; therefore the way to go is to couple imaging wide-field monitors with a multiwavelength set of space or/and ground-based narrow-field telescopes with fast autonomous capability to point the sky positions provided by the monitors. This strategy first implemented by Swift and ready to be used by SVOM is still based on CMI. Another technique that is emerging to design large field of view X-ray telescopes is the so-called lobster-eye or micro-pore optics (MPO). The concept, taken from the optical system of the eyes of crustaceans, is to use grazing reflection by the walls of many, very small channels to concentrate X-rays toward the focal plane PSD. By disposing a wide micro-channel plate with a large number of micro-holes with very polished and flat reflecting walls over a properly curved surface, a focusing system with a large FOV can be obtained. MPO is used for the MXT of SVOM (Götz et al. 2014) that will obtain X-ray images with arcmin angular resolution over 1◦ FOV, but larger systems are now being developed, e.g., for the Einstein Probe mission (Yuan et al. 2018). However MPO technique is for now limited to low X-ray energies, and projects for future high-energy missions dedicated to variable sky still plan to implement coded mask wide-field cameras, as, for example, the set of orthogonal 1-d cameras in the Chinese-European eXTP (enhanced X-ray Timing and Polarimetry) mission (Zhang et al. 2019a), or the two full 2-d cameras of the XGIS (X-Gamma ray Imaging Spectrometer) instrument (Labanti et al. 2020) of the Theseus (Transient High-Energy Sky and Early Universe Surveyor) (Amati et al. 2021) project, proposed recently to ESA for a medium size mission (M7) of the Cosmic Vision

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program. This last instrument based on a random mask coupled to Silicon Drift Detectors features a combined ZR-EXFOV of 117◦ ×77◦ , an AR of 120′ , and a localization accuracy of 15′ at SNR = 7 in the 2–150 keV range. A rather complex CMI devoted to soft gamma-rays is also proposed for a future NASA explorer mission, GECCO, an observatory working in the 50 KeV–10 MeV range that combines coded mask imaging at low energies and a Compton mode system for the high energies (Orlando et al. 2021). A specific feature of this CMI is its capability of deploying after launch a mast, which can extend the mask to any distance from the detector up to 20 m, in order to reach the desired imaging performances by tuning this system parameter (H in Table 1). In conclusion, coded mask instruments are very efficient devices to carry out imaging surveys of the hard X-ray/soft gamma-ray sky over large fields of view with moderate angular resolution and localization power and are still considered for future missions dedicated to the time-domain astronomy, for which lighter and more agile systems are now designed. While several such instruments are still presently in operation on INTEGRAL, Swift, and ASTROSAT, the next CMI to fly soon is ECLAIRs, on the SVOM multi-wavelength mission, which pushes the technique to cover a large energy band from X to hard X-rays and is expected to provide exceptional results on GRB and the transient sky science.

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48 Coded Mask Instruments for Gamma-Ray Astronomy M. Revnivtsev et al., AstL 30, 527 [A81] (2004b) J.P. Roques, App. Opt. 26(18), 3862 (1987) S. Scaringi et al., A&A 516, A75 (2010) A. Segreto et al., A&A 510, A47 (2010) M.R. Sims et al., SSI 5, 109 (1980) K.P. Singh et al., SPIE 9144, 91441S (2014) G.K. Skinner, Exp. Astron. 6, 2 (1995) G.K. Skinner, App. Opt. 47(15), 2739 (2008) G.K. Skinner et al., Nature 330, 544 (1987a) G.K. Skinner et al., ASS 136, 337 (1987b) G.K. Skinner et al., ApL&C 27, 199 (1988) G.K. Skinner, T.J. Ponman, MNRAS 267, 518 (1994) R.A. Sunyaev et al., Nature 330, 227 (1987) R.A. Sunyaev et al., AdSpR 10(2), 233 (1990) T. Takahashi et al., SPIE 9144, 25 (2014) J. Tueller et al., ApJS 186, 378 (2010) P. Ubertini et al., A&A 411, L131 (2003) G. Vedrenne et al., A&A 411, L63 (2003) A. Vibhute et al., J. Astrophys. Astron. 42, 76 (2021) J. Wei et al., SVOM White Paper, arXiv:1610:06892 (2016) R. Willingale et al., NIMS 221, 60 (1984) A.P. Willmore et al., MNRAS 258, 621 (1992) C. Winkler et al., A&A 411, L1 (2003) W. Yuan et al., SPIE 10699, 25 (2018) S.-N. Zhang et al., Sci. China Phys. Mech. Astron. 62(2), 029502 (2019a) R. Zhang et al., NIMS 934, 41 (2019b)

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Enrico Virgilli, Hubert Halloin, and Gerry Skinner

Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Laue Lenses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Laue Lenses Basic Principles: Bragg’s Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Crystal Diffraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Focusing Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Laue Lens Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Technological Challenges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Examples of Laue Lens Projects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Fresnel Lenses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Focal Length Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Effective Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Chromatic Aberration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Detector Issues for Focused Gamma Rays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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E. Virgilli () Istituto Nazionale di Astrofisica INAF-OAS, Bologna, Italy e-mail: [email protected] H. Halloin Université de Paris, CNRS, Astroparticule et Cosmologie, Paris, France e-mail: [email protected] G. Skinner University of Birmingham, Birmingham, UK e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2024 C. Bambi, A. Santangelo (eds.), Handbook of X-ray and Gamma-ray Astrophysics, https://doi.org/10.1007/978-981-19-6960-7_45

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Abstract

The low-energy gamma-ray domain is an important window for the study of the high-energy Universe. Here matter can be observed in extreme physical conditions and during powerful explosive events. However, observing gamma rays from faint sources is extremely challenging with current instrumentation. With techniques used at present, collecting more signal requires larger detectors, leading to an increase in instrumental background. For the leap in sensitivity that is required for future gamma-ray missions, use must be made of flux concentrating telescopes. Fortunately, gamma-ray optics such as Laue or Fresnel lenses, based on diffraction, make this possible. Laue lenses work with moderate focal lengths (tens to a few hundreds of meters), but provide only rudimentary imaging capabilities. On the other hand, Fresnel lenses offer extremely good imaging, but with a very small field of view and a requirement for focal lengths ∼108 m. This chapter presents the basic concepts of these optics and describes their working principles, their main properties, and some feasibility studies already conducted. Keywords

Laue lenses · Fresnel lenses · Focusing optics · Hard X-ray astronomy · Diffraction

Introduction The “low-energy” gamma-ray band from ∼100 keV to a few tens of MeV is of crucial importance in the understanding of many astrophysical processes. It is the band in which many astrophysical systems emit most of their energy. It also contains the majority of gamma-ray lines from the decay of radioactive nuclei associated with synthesis of the chemical elements and also the 511 keV line tracing the annihilation of positrons. However, observations at these energies are constrained in ways that those at lower and higher energies are not. At lower energies, grazing incidence optics enable true focusing of the incoming radiation, forming images, and concentrating power from compact sources onto a small detector area. At higher energies, the pair production process allows the direction of the incoming photon to be deduced. However, in the low-energy gamma-ray band grazing, incidence optics are impractical (the graze angles are extremely small), and the dominant Compton interaction process provides only limited directional information. Detector background due to particle interactions and to photons from outside the region of interest is a major problem in gamma-ray astronomy. A large collecting area is essential because the fluxes are low, but unless a means is found to concentrate the radiation, this implies a large detector and hence a lot of background. Shielding helps, but it is imperfect, and the materials in the shield themselves

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produce additional background. If the flux from a large collecting area A can be concentrated with efficiency η onto a small area Ad of detector, then √ for backgrounddominated observations there is an advantage in sensitivity of ηA/Ad compared with a “direct-view” instrument of area A having the same background per unit area, energy band, and observation time. At energies where grazing incidence optics are not viable, only two technologies are available for concentrating gamma rays. Both use diffraction. Laue lenses use diffraction from arrays of crystals, while Fresnel lenses utilize diffraction from manufactured structures. Both type of lens can provide a high degree of concentration of flux from a compact on-axis source. Fresnel lenses provides true imaging, albeit with chromatic aberrations, whereas the Laue lens is a “singlereflection” optic, where the off-axis aberrations are severe. MeV astrophysics is now eagerly waiting for the launch of NASA’s COSI mission (Tomsick et al. 2019) which is scheduled for 2025. This will be a survey mission with a large field of view and, consequently, a relatively high background. Nevertheless, COSI is expected to be a factor of 10 more sensitive than Comptel the pioneering instrument for the MeV gamma-ray range (Schoenfelder 1993). A focusing telescope using the techniques discussed here may improve the sensitivity for the study of individual sources by another large factor, allowing studies not possible with scanning, high-background, instruments. Laue lenses and Fresnel lenses are discussed separately.

Laue Lenses The concept of a Laue telescope is shown in Fig. 1. The essential element is a “Laue Lens” containing a large number of high-quality crystals. Each crystal must be correctly oriented to diffract radiation in a narrow spectral range from a distant source towards a detector located at a common focus behind the lens. The crystals are used in the Laue mode (transmission) since the very small diffraction angles make it impractical to rely on surface reflections. Excellent reviews of previous work on this topic can be found in Frontera and Von Ballmoos (2010) and Smither (2014). The term “Laue lens” is actually a misnomer, and it would be more correct to refer to a Laue-mirror. Such a “lens” relies on the mirror reflection of gamma rays from the lattice planes in the crystals. The reflective power of the electrons bound in atoms in a single lattice plane is very small, but the power increases with the square of the number of planes – or electrons – acting coherently.

Laue Lenses Basic Principles: Bragg’s Law The requirement for coherent diffraction is both the strength and the weakness of Laue lenses. It provides for the possibility of high reflectivity, but at the same time,

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Fig. 1 A gamma-ray lens, based on diffraction From crystals in the Laue (transmission) geometry. Crystal tiles are oriented in order to diffract the radiation towards the common focus. In this drawing, five concentric rings of crystals are shown as an example. Crystals can be arranged over a spherical cap, but the lens can also be planar and other radial distributions are possible. Crystals at the same radius from the axis will have the same orientation with respect to the incident radiation, but the orientation will change with radius

it imposes a strict dependence of the diffraction angle, θB , on the wavelength, λ, (or the energy, E) of the radiation. This dependence is expressed by Bragg’s law: sin θB = n

λ 2dhkl

with : n = 1, 2, 3, ...

(1)

where n is the diffraction order, dhkl is the spacing of the crystal lattice planes, and λ is the wavelength of the gamma rays. The first order (n = 1) contributions are by far the most significant. For energies which concern us here, the Bragg angles are always small (≃1◦ ), so we can set tan θ = sin θ = θ . In the following, we shall often prefer to speak in terms of energy, E, rather than wavelength. Bragg’s law then takes the form sin θB = n

hc , 2dhkl E

(2)

where h is Planck’s constant and c the velocity of light. (λ(Å) = 12.39/E (keV)). From the Bragg equation for first diffraction order, with simple geometrical considerations, it can be shown that there is a relation between the distance ri at which the crystal is positioned with respect to the Laue lens axis and the diffracted energy Ei : Ei =

hcF , dhkl ri

where F is the focal length of the Laue lens.

(3)

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Equation 3 shows that for a given focal length, if crystals with a fixed dhkl are used, those placed closer to the lens axis are dedicated to the highest energies, while those positioned further away from the axis diffract the lower energies. Consequently, at a given focal length, there is a direct link between the energy band of a Laue lens and its spatial extent, rin to rout . For a narrow band Laue lens, with the whole surface optimized for a single energy, it would be necessary to arrange that dhkl varies in the radial direction such that dhkl ri is constant (an analogous condition will be seen when the zone widths of Fresnel lenses are discussed in section “Fresnel Lenses”).

Crystal Diffraction Ideal and Mosaic Crystals Before going into details of the calculation of diffraction efficiencies, it is useful to introduce a distinction between “ideal” and “mosaic” crystals. In ideal (defect free) crystals, the crystalline pattern is continuous over macroscopic distances. Examples of such crystals are the highly perfect silicon and germanium crystals now commercially available, thanks to their great commercial interest and the consequent intense development effort. “Mosaic crystals” on the other hand are described by a very successful theoretical model introduced by Darwin (1914, 1922) a century ago. Darwin modeled imperfect crystals as composed of a large number of small “crystallite” blocks, individually having a perfect crystal structure but slightly misaligned one to another. The spread of the deviations, ω, of the orientation of a lattice plane in one block from the mean for the entire mosaic crystal is described by means of a probability distribution Ω ′ (ω), the so-called mosaic distribution function. Darwin’s model has been very useful and quantitatively describes many aspects of real crystals. The mosaic distribution function, Ω ′ can be found experimentally for a given crystal through observation of the ‘rocking curve’, which is the measured reflectivity as function of angle for an incident beam of parallel, monochromatic gamma rays when a crystal is scanned through the angle corresponding to a Braggreflection. The crystal sample should be thin enough that the reflectivity is never close to the saturation value. Examples of measured rocking curves are shown in Fig. 2. For good quality crystals, the mosaic distribution can be well approximated by a Gaussian function. Its width, as observed through the rocking curve, is called the mosaic width of the crystal. Mosaic widths are specified as angular quantities, characterized by either the Full Width at Half Maximum (FWHM) or the standard deviation, σθ , of the rocking curve. Rocking curves are measured at constant diffraction angle, hence constant energy. For Laue lens design where the source direction is the fixed quantity, what is often of interest is the mosaic distribution as a function of the energy offset from the energy, EB , corresponding to the Bragg angle. If the standard deviation of the distribution as a function of energy is σE , then the two quantities are related by

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20

Absolute reflectivity %

Niob (110)

Tantal (110)

MoIybdenum (110)

16

12

8 FWHM 2.70’

FWHM 1.05’

FWHM 1.35’ 4

0 Rocling angle

Fig. 2 Measured rocking curves (at 412 keV) for a few metal crystals having different degrees of mosaicity. The small number triplets shown along with the element names are the “Miller indices” (see Zachariasen 1945) identifying the lattice planes used for diffraction (Reprinted from Lund 1992)

σθ σE = EB θB

(4)

To be useful in a Laue telescope, the rocking curve for each crystal should possess a single, narrow peak. Unless great care is taken in the growth of crystals, the mosaic distribution may not be well behaved, and the rocking curves may be broad or exhibit multi-peaked structures.

Diffraction Efficiency According to Schneider (1981), the crystal reflectivity, ν(E), for mosaic crystals of macroscopic thickness in the Laue-case can be calculated from ν(E) =

1 −µ(E)t e (1 − e−Ω(E−E0 )R(E)t ). 2

(5)

Here µ(E) is the linear attenuation coefficient for photons of energy E, and t is the crystal thickness. Ω(E − E0 ) is the mosaic distribution as function of energy, and R(E) is the specific reflectivity (reflectivity per unit thickness). E0 is defined as the energy where Ω is at its maximum. In the following, we shall assume that the mosaic distribution Ω has a Gaussian shape: Ω(E − E0 ) = √ We then get for the peak reflectivity:

1 2π σ

e−(E−E0 )

2 /2σ 2

.

(6)

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ν(E0 ) =

R(E )t 1 −µ(E0 )t −√ 0 e (1 − e 2π σ ). 2

(7)

The value of the crystal thickness which maximizes the peak reflectivity is ln (1 + α) µ(E0 )α

(8)

R(E0 ) 1 √ µ(E0 ) 2π σ

(9)

tmax = with α=

and the corresponding peak reflectivity is νm (E0 ) =

1+α 1 α(1 + α)− α . 2

(10)

Note that the specific reflectivity, R, and the attenuation coefficient, µ, are characteristic of a particular material and set of crystalline planes, whereas the mosaic width, σ , depends on the method of manufacture and subsequent treatment of the crystals. It is therefore reasonable to start by seeking crystals that maximize the value of R/µ and leave the choice of the mosaic width to the detailed lens design. The specific reflectivity is given by R(E) = 2re2

λ3  Fstruct (x) 2 −2Bx 2 e sin(2θB ) V

(11)

with x = sin(θB )/λ. Here re is the classical electron radius, V is the volume of the unit cell, and Fstruct is the “structure factor” for the crystal unit cell. The structure factor depends on the crystal structure type (e.g., body centered cubic, face centered cubic), on the atoms, and on the choice of lattice planes involved, described by the Miller indices (h,k,l). The exponential factor describes the reduction in the diffraction intensity due to the thermal motion of the diffracting atoms. Considering only crystals of the pure elements, Eq. 11 can be rewritten as R(E) ∝ E −2 a −5/3 (f1 (x, Z))2 e−2Bn

2 /2d 2

,

(12)

where a is the atomic volume, d is the interplanar distance of the diffracting planes, f1 (x, Z) is the atomic form factor, and n is the diffraction order. Here use has been made of the approximations sin(2θB ) ∼ 2 sin(θB ) and x ∼ n/2d. The linear attenuation coefficient, µ(E), can be expressed as a function of the total atomic cross section, κ(E), and the atomic volume: µ(E) =

κ(E) a

(13)

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thus R f1 (x, Z)2 −Bn2 /2d 2 ∝ E −2 a −2/3 e . µ κ(E)

(14)

Since at high energies both f1 (x, Z) and κ(E) are roughly proportional to Z, it is clear that for gamma-ray energies a high atomic number and a small atomic volume (a high atomic density) are important for maximizing R/µ. For energies below ∼100 keV, photoelectric absorption may rule out the use of crystals of the heaviest elements for Laue lenses. The atomic density of crystals of the pure elements varies systematically with the atomic number, Z, as illustrated in Fig. 3. The most suitable elements for Laue lens crystals are found near the peaks in this plot, that is, near Z = 13 (Al), Z = 29 (Ni, Cu,), Z = 45 (Mo, Ru, Rh Ag) or Z = 76 (Ta, W, Os, Ir, Pt, Au). The atomic form factors are tabulated in the literature (International Tables for X-ray Crystallography 1977), and software for their calculation is publicly available (del Rio and Dejus 1997). The thermal factor, B, turns out to be anti-correlated with the atomic density, thereby strengthening somewhat the case for a high atomic density (Warren 1969).

ATOMIC DENSITY x 1022cm-3

10

5

0 0

10

20

30

40

50

60

70

80

90

ATOMIC NUMBER

Fig. 3 The Atomic Density as function of the Atomic Number, Z. (Reprinted from Lund 1992)

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Extinction Effects In the above derivation of the diffraction efficiencies, only the attenuation by incoherent scattering processes was explicitly considered in equation 13. However, losses due to coherent effects also occur. These are termed “extinction effects” (Chandrasekhar 1960). One type of extinction loss is due to the diffraction process itself and occurs in both mosaic and perfect crystals. Photons are removed from both the incoming beam and from the diffracted beam by diffraction. (The diffracted beam is a mirror image of the incoming beam with respect to the lattice planes and fulfills the Bragg condition just as well). This dynamic interaction is termed “secondary extinction” and accounts for the factor 12 in Eq. 5. A more subtle extinction effect, which is only present if phase coherence is maintained through multiple diffractions, is termed the “primary extinction.” Every diffraction instance is associated with a phase shift of π/2. Consequently, after two coherent diffraction processes, the photon has accumulated a phase shift of π and destructively interferes with the incoming beam. In the same way, three coherent diffraction processes will cause destructive interference in the diffracted beam. This effect only occurs in perfect crystals or in mosaic crystals in which the size of the crystallites is large enough that there is a significant probability of multiple successive coherent scatterings. The critical dimension here is the “extinction length” (see Zachariasen 1945) which can be estimated as text ≈

1 V . r0 Fstruct (x)λ

(15)

The extinction length for the Cu(111) reflection at 412 keV is 66 µm (Schneider 1981). As text is proportional to the energy, it will be at the lower gamma-ray energies that extinction effects may become noticeable. For Laue lenses, it is important to find or develop crystals in which the defect density is high enough to keep the crystallite size below text at the lowest energies where the crystals are to be used.

Focusing Elements Classical Perfect Crystals Perfect crystals, where the ideal lattice extends over macroscopic dimensions, are not particularly suitable for the use of Laue lenses in Astrophysics because they are too selective regarding the photon energy, even for Laue lenses intended for narrow line studies. Perfect crystals diffract with high efficiency, but only for an extremely narrow range of energy/angle combinations. For example, at 511 keV a perfect germanium crystal will have an angular width of the diffraction peak (the “Darwin width”) of only 0.25 arc-seconds. This should be compared to the Bragg angle, which at this energy is 750 arc-seconds, i.e., about one part in 3000.

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The corresponding energy bandwidth is then only 0.14 keV! Thus, perfect crystals are not preferred for observations of astrophysical sources.

Classical Mosaic Crystals Fortunately, perfect crystals are not the norm. Most artificial crystals grow as mosaic crystals. According to the Darwin model, such crystals can be viewed as an ensembles of perfect micro-crystals with some spread of their angular alignments. Photons of a specific energy may traverse hundreds of randomly oriented crystallites with little interaction and still be strongly diffracted by a single crystallite oriented correctly for this energy. Mosaic crystals generally perform much better than perfect crystals in the context of Laue lenses. The internal disorder, the mosaic width, may be controlled to some extent during the crystal growth or by subsequent treatment. Mosaic widths of some arc-minutes can be obtained with relative ease for a range of crystal types. For the lenses described further, a mosaic width of about 0.5 arcminutes is typical. Such values can be obtained, but this has required substantial development effort (Courtois et al. 2005). Copper crystals, in particular, have attracted interest because of the need for large size, high quality, Copper crystal for use in low-energy neutron diffraction. It must be kept in mind that Bragg’s law is always strictly valid, even for mosaic crystals. As illustrated in Fig. 4a, after diffraction from a mosaic crystal a polychromatic beam of parallel gamma rays with a spread of energies will emerge as a rainbow-colored fan. Its angular width will be twice the angular mosaic width of the crystal. Even if the crystal is oriented so that the central ray of the emerging beam hits the detector, the extreme rays of the fan may miss it.

Fig. 4 Different crystal options proposed for Laue lenses. Flat mosaic crystals (a) produce a chromatic effect that is evident if the mosaicity is large compared with the angular size of the crystals. Longitudinally bent crystals (b) can in principle reach higher diffraction efficiencies than mosaic crystals. However, they are complex to manufacture. A transverse bent perfect crystal (c) can offer almost achromatic focusing at the expense of the effective area, as the geometric area corresponding to a given energy is a fraction of the total surface of the crystal. In this case, the passband of a crystal depends on its curvature

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At a given energy, the radiation diffracted from a flat mosaic crystal forms in the detector plane a projected image of the crystal. It is important to note that this projected image does not move if the crystal tilt is changed. Its position is fixed by Bragg’s law, and it onlychanges in intensity.

Crystals with Curved Lattice Planes As well as perfect and mosaic crystals, a third group has attracted interest as potential diffractive elements for Laue lenses. These are perfect crystals with curved lattice planes. The curvature of the lattice planes has two remarkable effects: (i) the secondary extinction may be suppressed and (ii) the energy passband is not constrained anymore to the Darwin width but will be defined by the total range of lattice direction, i.e., in principle something under our control. If the lattice curvature is correctly chosen relative to the photon energy, secondary extinction may be suppressed, and the diffraction efficiency can approach 100% – ignoring incoherent absorption, which is always present. Different methods to create such lattice curvature have been proposed and experimentally demonstrated. One involves imposing a thermal gradient on the crystal along its thickness, such that the hot side expands and the cold side contracts. This method is very convenient in the laboratory because both the degree of bending (the bending radius) and the “sign” of the bending can be changed with minimal change in the experimental set up (Smither et al. 2005). Unfortunately, this method cannot be used in space due to the significant power dissipation required to maintain the thermal gradient. A second method relies on specific pairs of elements (or compounds) which can form perfect crystals across a range of component fractions. Stable, curved lattice planes exist in these binary crystals in the regions where a composition gradient is present (Abrosimov 2005). Silicon/germanium composition-gradient crystals have been proposed for the “MAX” Laue lens described in section “The MAX Project (2006)”. A further bending method relies on externally applied mechanical forces to bend the crystals. Mechanically, bent crystals are used in several applications in laboratory experiments including monochromators. However, the mass of the structures necessary to maintain the bending forces is unlikely to be acceptable for a space experiment. Controlled permanent bending of silicon and germanium wafers by surface scratching has been developed by the Institute of Materials for Electronics and Magnetism, (IMEM-CNR) in Parma (Buffagni et al. 2012) in connection with the Italian Laue project (Virgilli et al. 2014). The lapping procedure introduces defects in a superficial layer of a few microns, providing a high compressive stress resulting in a convex surface on the worked side. In such transversally bent crystals, the orientation of the diffraction planes with respect to the incident radiation continuously changes in the direction of the curvature of the crystal. If the bending radius is equal to twice the focal length of the lens, the effect is to produce achromatic focusing as illustrated in Fig. 4.

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A spectrum of finite extent may be focused into an area which is considerably smaller than the crystal cross-section. In this way, the overall Point Source Response Function (PSF) of a Laue lens can be narrower than achievable with flat crystals of the same size. Transversally, bent crystals were studied in the Laue project in which a number of different aspects of the Laue lens technology were faced, from the production of suitable crystals to the definition of an accurate and fast method for their alignment. It was demonstrated through simulations and experimental tests (Virgilli et al. 2013) that a transversally bent crystal focuses a fraction of the radiation arriving on its surface into an area which, depending on mosaicity, can be smaller than the cross section of the crystal itself. For some crystals and crystallographic orientations, if an external (primary) curvature is imposed through external forces, a secondary curvature may arise. This effect is a result of crystalline anisotropy. It has been termed quasi-mosaicity (Ivanov et al. 2005) and leads to an increased diffraction efficiency and angular acceptance (Camattari et al. 2011). A promising manufacturing technology for bent crystals which may overcome some of the limitations of flat crystal diffraction optics is based on the so-called silicon pore optics (SPO) (Bavdaz et al. 2012). This is a bonding technology for silicon wafers which is being developed for the ESA Athena mission. It has made possible the development of novel units for focusing gamma-rays called silicon Laue components (SiLCs (Ackermann et al. 2013; Girou et al. 2017)). These components are being developed at the COSINE company (the Netherlands) in collaboration with the University of California at Berkeley. They are self-standing silicon diffracting elements which can focus in both the radial and the azimuthal directions. SiLCs consist of a stack of thin Silicon wafers with a small wedge angle between adjacent plates such that the diffracted rays from all the plates converge at a common focus. The incidence angle of the radiation is small so the radiation passes through only one plate. The wafer angle with respect to the optical axis of the telescope is selected such that the mean angle enables diffraction at energy E, and the overall range of wedge angles between the wafers dictates the energy bandpass around the centroid E. As can be seen in Fig. 5, the curvature of the wafers allows focusing in the orthoradial direction.

Laue Lens Optimization The response of a Laue lens is strongly energy dependent. For a given focal length and crystal plane spacing, the area diffracting a particular energy passband is inversely proportional to E. Furthermore, the diffraction efficiency of the crystals adopted for realizing these optics decreases with energy. These two reasons, combined with the fact that the gamma-ray emission of astrophysical sources typically decreases with energy according to a power law, make observations at high energies even more challenging. The dependence of the effective area on energy is a geometric effect and can be mitigated only at particular energies in narrow passband Laue lenses. The decrease in diffraction efficiency with energy can be mitigated by choosing crystals to maximize the reflectivity.

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Fig. 5 Sketch of the principle at the basis of the SILCs elements developed at Cosine Measurement System (The Netherlands). A polychromatic beam is focused in two directions. (Published with permission of the authors and adapted from Cosine Measurement Systems Cosine Measurement Systems 2022)

A number of parameters can be tuned in the optimization of a Laue lens. They are mainly related to the crystals properties (mosaicity, crystal material, diffraction planes, crystallite size, crystal thickness), or to the overall lens structure (lens diameter, focal length, inner and outer radius, geometrical configuration). The optimization is complex and depends on the Laue lens requirements (lens bandwidth, point spread function extension, total weight of the lens). The main factors involved in the optimization are described in the following sections.

Crystal Selection As discussed in section “Diffraction Efficiency”, crystals with high atomic density and high atomic number are generally preferable as Laue lens elements except at the lowest energies where photoelectric absorption may render their use less attractive. The technical difficulties involved in the fabrication and handling of crystals of the different chemical elements are also important factors. These difficulties vary significantly among the elements. The mechanical properties of the crystals are an important issue, for example, silicon and germanium are quite hard and rugged, whereas copper, silver, and gold crystals are soft and require special care in treatment and handling. As already observed in section “Extinction Effects”, the crystallite thickness plays an important role in the reflectivity optimization. For given values of the mosaicity and crystal thickness, the highest reflectivity is obtained for a crystallite size much smaller than the extinction length of the radiation. At the energies of interest, this thickness must be of the order of few µm. The crystal mosaicity also has a primary role in the Laue lens optimization. The higher the mosaicity, the larger the integrated reflectivity, and thus the effective the area, but the broader the

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signal on the focal plane detector. These two effects act in opposite senses in the optimization of the sensitivity. The crystal thickness is also an important factor for the optimization of the crystal reflectivity and therefore for the maximization of the Laue lens sensitivity. Equation 8 provides the thickness that maximizes the reflectivity for a given material and for fixed diffraction planes. As the best thickness is also a function of energy, it is expected that, depending on the adopted geometry, crystals dedicated to high energy are thicker than those used to diffract low energies. It must be also taken into account that the choice of the thickness maximizing the reflectivity would often lead to a mass unacceptable for a satellite-borne experiment. A trade-off between lens throughput and mass is then necessary.

Narrow- and Broadband Laue Lenses Depending on the scientific goal to be tackled, Laue lens can be designed, or adjusted, with two different optimizations: lenses for a broad energy passband (e.g., 100 keV–1 MeV) or those configured to achieve a high sensitivity over one or more limited range(s) of energy. The latter can be valuable for studying gamma-ray lines, or narrow-band radiation. Relevant energies of interest might be the 511 keV e+/e− annihilation energy or the 800–900 keV energy range for its importance in Supernova emission. The two classes of Laue lenses need different optimizations and dispositions of the crystals over the available geometric area. For a narrow energy passband, Laue lens as many as possible of the crystals should be tuned to the same energy. According to Eq. 3, the d-spacing of the crystals should ideally increase in proportion to their radial distance from the focal axis in order keep the diffracted energy fixed. The energy range of a broadband Laue lens follows from Eq. 3. With the focal length and d-spacing of the crystalline diffraction planes both fixed, the energy range will be from Emin =

hc F hc F to Emax = , dhkl Rmax dhkl Rmin

where the radial extent of the lens is Rmin to Rmax . If the inner and outer radii are fixed, the simultaneous use of different materials, and thus of different dhkl , would allow enlarging the Laue lens energy passband compared with a single-material Laue lens. Equivalently, for a given energy passband and focal length, the use of multi-material crystals would allow a more compact lens.

Tunable Laue Lens A classical Laue lens with fixed inner/outer radius and focal length has a passband which is uniquely defined by the d-spacing of the crystals used. The red curve in Fig. 6 shows the effective area of an example 100 m focal length Laue lens configured to cover a 300–800 keV energy passband. If all of the crystals could be retuned for different focal lengths, the Laue less could be made sensitive to different passbands. Furthermore, as shown in Fig. 6,

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Fig. 6 The effective area of a single Laue lens which is tunable for different energy passbands. The adjustment of the lens to a different band involves changing both the focal length and the orientation of each crystal. When the focal length increases from 50 to 400 m, the integrated effective area increases and the passband becomes larger. Note that the detector size assumed throughout is matched to the 100 m focal length configuration. (Figure reprinted with permission and adapted from Lund 2020)

the larger the focal length, the broader the passband and the higher the integrated effective area. The adjustment in orbit is not trivial – both the orientation of thousands of crystals and the lens to detector separation must be changed and verified. The former requires thousands of actuators and a sophisticated optical system. An innovative mechanism for the adjustment of the orientation of a crystal, along with an optical system for monitoring alignment of each one, has nevertheless been proposed (Lund 2021a,b). The mechanism is based on a miniature piezo-actuator coupled with a tilt pedestal and does not require power once a crystal has been correctly oriented. It is assumed that the lens and detector are on separate spacecraft that can be maneuvered to adjust their separation.

Multiple Layer Laue Lenses A possible way to increase the flux collection from a lens is to use two or more layers of crystals covering the same area. For instance, two layers of crystals can be used, one on each side of the lens structure. In order to focus at the same position, crystals placed at the same radius but in different layers must diffract at the same angle, so different crystals or Bragg planes must be used to diffract different energies.

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Fig. 7 Blue line: effective area of a single layer of Ag(111) crystals with optimized thickness. Black line: effective area of a Laue lens made with two layers of crystals Ag(111) and Ag(200) whose thickness has been reduced with respect to the optimized thickness in order to save mass. In spite of the thickness reduction, the effective area increases by about 65% and the overall mass is reduced by ∼10%. Both effective areas are obtained with 100 m long focal length, crystals with 0.5 arcmin mosaicity, and detector diameter of 5 cm. (Figure taken and adapted with permission from Lund 2021a)

In a simulation (Lund 2021a), two layers of thin crystals made with Ag(111) and Ag(200) increased the effective area by about 65% (see Fig. 7). A third layer did not further increase the lens throughput. It must be stressed that with multiple layers, the diffracted radiation from any one layer will be attenuated by all of the other layers. The number of layers maximizing the effective area will depend on the crystals parameters (thickness, mosaicity, diffraction efficiency).

Flux Concentration and Imaging Properties of Laue Lenses The sensitivity of a telescope using a Laue lens depends on the effective area over which flux is collected, but because observations will almost always be background limited, it is also a function of the extent to which the collected flux is concentrated into a compact region in the detector plane. For a given lens design, the collecting area at a particular energy is just the sum of the areas of the crystals multiplied by their reflecting efficiency at that energy. Obviously, only those crystals for which the incidence angle is close to the Bragg angle need be considered. In practice, this means that the only crystals that contribute are those with centers that fall inside an annulus whose width depends on the extent, ∆θ , of the rocking curve. For broadband lenses, the incidence angle is a simple inverse function of radius from the axis. Consequently, crystals at the center of the band will contribute most, with the response decreasing towards the edges

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of the annulus. Making the small angle approximation θ = r/2F , the width of the annulus is given by ∆r =

∆θ = 2F ∆θ. dθ/dr

(16)

As the radius of the annulus is also proportional to F , this means that its area is proportional to F 2 . Because each crystal simply changes the direction of the incoming parallel beam, it will illuminate a region in the detector plane identical in size and shape to the profile it presents to the incoming radiation. This immediately means that the focal spot can never be smaller than the size of the crystals. Moreover, crystals that are not at the center of the illuminating annulus will have a “footprint” in the detector plane that is offset from the instrument axis by a corresponding distance. Thus to a good approximation, the radial form of the on-axis PSF of a broadband Laue lens is the convolution of the (scaled) rocking curve and a flat-topped function corresponding to the crystal size (The azimuthal extent of the crystals has been ignored and it is assumed that the crystals are smoothly distributed in radius). As is usual with telescopes, other things being equal, the best signal-to-noise ratio will be obtained with a compact PSF. • In circumstances where use of smaller crystals is feasible and would lead to a significantly narrower PSF, then choosing them will always offer an advantage. • If the PSF width is dominated by the rocking curve width, the situation is more complex. Decreasing the mosaicity will then narrow the PSF but also decrease the area of the diffracting annulus, reducing the advantage to be gained. • Lastly, because of the F 2 dependence of the area of lens over which crystals diffract a given energy, a wider PSF can actually provide an advantage if it is the result of an increased focal length – although the signal will be spread over a detector area proportional to F 2 , the uncertainty due to background only increases as F . This of course assumes that such a design is feasible given the cost and mass of the larger lens and detector. The above discussion concerns the response to an on-axis source. As Laue lenses are single reflection optics, they do not fulfill the Abbe sine condition, and therefore, for off-axis sources, they are subject to coma. The aberrations are very severe as illustrated in Fig. 8. The integrated flux is a little affected by off-axis pointing, but importantly the image is smeared over a larger area, and thus the signal-to-noise ratio of the signal is significantly reduced.

Technological Challenges The development of Laue lenses presents several technological challenges. These can be divided into two categories. The first is associated with the search for, and

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Fig. 8 On- and off-axis images of a point source calculated for the lens of the gamma-ray imager proposal (see section “GRI: The Gamma-Ray Imager (2007)”), based on copper crystals and 100 m focal length. The image aberrations are typical for single-reflection devices

production of, suitable materials and components. Highly reproducible crystals with high reflectivity are needed, as are thin, rigid, and low Z substrates and structures to minimize the absorption. The second category is related to the required accuracy of positioning and alignment, both for the mounting of the crystals in the Laue lens and for the alignment of the lens with respect to the focal plane detector. Some of the main issues that are being faced in studies and development of Laue lenses are described further.

I. Production of Proper Crystals and Substrate In order to cover a competitive geometric area, a Laue lens must contain a large number of crystal tiles. The production of a large quantities of crystals having the optimal properties for providing a reflectivity that is as high as possible is still problematic. Crystal growth has been described as an art as well as a science.

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Advanced technologies present their own problems. For instance, it has been shown that bent crystals reduce the width of the PSF compared with flat crystals, but the advantages depend on very accurate control of the curvature.

II a. Crystal Mounting Methods and Accuracy In a Laue lens, it obviously important that each crystal is properly oriented. It is useful to consider three angles describing the orientation of a generic crystal: • (i) A rotation α about an axis parallel to the instrument axis. If there is an error in α, diffraction will occur with the expected efficiency, but the photons will arrive in the focal plane displaced by a distance R∆α, where R is the distance of the crystal from the instrument axis. This displacement should be kept small compared with the spatial scale of the PSF. • (ii) A rotation φ about an axis normal to the diffracting crystal planes. To first order an error in φ will not have any effect on efficiency or imaging. • (iii) A rotation θ about an axis in the plane of the crystal plane and orthogonal to the instrument axis. If θ does not have the intended value, then the energy at which the reflectivity is highest will change. For any given energy, the position in the focal plane where photons of a given energy are arrived will not be altered. However, the number of photons diffracted by the crystal may either increase or decrease depending on the energy considered. The probable effect is a spreading of the PSF as a result of enhancing the response of crystals that are not at the optimum radius for diffracting photons of a given energy towards the center of the focal spot, at the expense of that of those that are. To avoid such spreading, errors in θ should be kept much smaller than the rocking curve width. The most obvious mounting method is to use adhesives to bond the crystals to a supporting structure at their proper position and orientation. However, due to glue deformation during the polymerization phases, it has not proven easy to maintain the necessary precision (Barrière et al. 2014; Virgilli et al. 2015). The amount of misalignment that is introduced depends on the type of adhesive used and on the polymerization process (two components epoxy adhesive, UV curable, thermal polymerization, etc.). In the CLAIRE experiment, the effects of uncertainties in the bonding process were avoided by the use of a manual adjustment mechanism (Section: “The CLAIRE Balloon Project (2001)”), but this technique is probably not appropriate for space instrumentation.

II b. Laue Lens Alignment Because the MeV sky is poorly known at present, the issue of how to verify the correct alignment of gamma-ray diffraction instruments after launch and during operations is important. It is therefore suggested that some optical means of verifying the shape of the large-scale structure of the lens should be incorporated from the start of the project.

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One possible way is to install mirror reflectors on the lens structure, the orientation of which can be monitored, perhaps from a separate detector spacecraft. If the attachment technique for these mirrors is similar to that used for the Laue crystals, the long-term stability of the mirror alignment will also give some confidence in the stability of the crystal mounting.

Examples of Laue Lens Projects In this section, we will review the Laue lens experiments that have been realized or proposed from the early 2000s until the present. The CLAIRE project is the only Laue lens instrument that has actually flown. Other experiments have been realized in the laboratory as R&D projects and were directed to the advancement of welldefined aspects of the Laue lens technology (mainly crystal production and tiles alignment). Studies have been conducted of several possible space missions based on Laue lenses.

The CLAIRE Balloon Project (2001) A pioneering proof-of-principle Laue telescope, CLAIRE, was built and successfully flown as a balloon payload by the Toulouse group in 2001 and 2002 (Laporte et al. 2000; Halloin et al. 2004). The balloon payload is shown in Fig. 9 during flight preparations.

Fig. 9 The CLAIRE telescope during preparation for the 2001 balloon launch. The instrument features, in addition to the Laue lens, a 3×3-array of cooled germanium detectors, and a pointing platform for the lens. The total weight of the payload was less than 500 kg. (Published with permission from von Ballmoos et al. 2004)

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Fig. 10 Detail of the CLAIRE lens with 659 Ge/Si crystals mounted on adjustable lamellae on a titanium frame

The CLAIRE experiment is an example of a narrow energy passband instrument. It was designed for focusing photons with energy ∼170 keV, with a passband of ∼4 keV at a focal distance of 2.8 m. The lens (Fig. 10) consisted of 659 germanium/silicon mosaic crystals arranged in 8 concentric rings providing a collecting area of 511 cm2 and a field of view (FOV) of 90 arcseconds. The mosaicity of the crystals selected was in the range 60 to 120 arc-seconds, leading to an angular resolution for the instrument of 25–30 arcseconds. Two crystal sizes were used: 10 × 10 mm2 and 7 ×10 mm2 . The crystals focused the radiation onto a germanium detector with 9 elements, each 15 × 15 × 40 mm3 , having an equivalent volume for background noise of 18 cm3 . The fine-tuning of the lens utilized a mechanical system capable of tilting each crystal tile until the correct diffracted energy was detected. The crystals were mounted via flexible lamellae on a rigid titanium frame. The tuning of the individual crystals was done manually with adjustment screws. Due to the finite distance (14 m) of the X-ray source during the crystal tuning phase, the gamma-ray energy used was lowered from 170 to 122 keV. Moreover, also due to the finite source distance used for the crystals alignment, only a limited fraction of each crystal was effectively diffracting at the tuning energy, their subtended angle (about 150 arc-seconds, as seen from the source) being much larger than the crystal mosaicity. The performance of the complete lens was verified using a powerful industrial X-ray source at a distance of 200 m (hence a diffracted energy of 165.4 keV). Seen from a distance of 200 m, each crystal subtended an angle of about 10 arc-seconds, i.e., significantly less than the crystal mosaic width. The CLAIRE lens was flown twice on balloon campaigns in 2000 and 2001. In both flights, the target source was the Crab Nebula. The observed diffracted signal

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at 170 keV was found to be consistent with that expected from the Crab Nebula given the lens peak efficiency, estimated at about 8% from ground measurements (von Ballmoos et al. 2005).

The MAX Project (2006) Following up on the successful CLAIRE project, the French Space Agency, CNES, embarked on the study of a project, “MAX,” for a satellite mission with a Laue lens. MAX was planned as a medium-sized, formation-flying project with separate lens and detector spacecrafts launched together by a single launcher. The scientific aims were (i) the study of supernovae type 1a (through observations of the gamma-lines at 812 and 847 keV), (ii) a search for localized sources of electron-positron annihilation radiation at 511 keV, and (iii) a search for 478 keV line emission from 7 Be-decay associated with novae. These objectives could be met by a Laue lens with two energy Passbands: 460–530 and 800–900 keV. The left panel of Fig. 11 shows the lens proposed for MAX which would contain nearly 8000 crystal tiles 15 × 15 mm2 with a mosaic spread of 30 arc-seconds. The total mass of the Laue crystals was expected to be 115 kg. A focal length of 86 m was foreseen. The predicted response of the MAX lens is shown in the right panel of Fig. 11. In the end, however, CNES decided not to continue the development of MAX. GRI: The Gamma-Ray Imager (2007) The Gamma-Ray Imager (GRI) mission concept was developed by an international consortium and proposed to the European Space Agency in response to the “Cosmic Vision 2015–2025” plan. GRI consisted of two coaligned telescopes each with a focal length of 100 m: a hard X-ray multilayer telescope working from 20 up to 250 keV and a Laue lens with a broad passband 220 keV – 1.3 MeV. The low-energy limit of the GRI Laue lens was driven by the anticipated upper limit of the multilayer technology. The NuSTAR mission has demonstrated the capability of multilayer

Fig. 11 Left panel: The proposed MAX lens layout. Note the two crystal groups corresponding to the two energy bands of the lens. A stable structural octagon supports both. Right panel: The simulated response of the MAX Laue lens. More detailed analysis of the response using Monte Carlo techniques indicated that only about half of the photons collected by the lens are sufficiently well focused to be of use during background limited observations. (From Barriere et al. 2006)

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telescopes of focusing photons up to 70–80 keV. Further developments are expected to allow multilayers to be used up to 200/300 keV. The two optics were proposed to share a single solid-state detector using cadmium zinc telluride (CZT) crystals which are attractive as they can be used without cooling. Thanks to the 3-d capability of pixellated CZT, GRI could also be exploited for hard X-/soft gamma-ray polarimetry. Due to the long focal length, a two spacecraft, formation flying mission was proposed. With these features, GRI was expected to achieve 30 arcsec angular resolution with a field of view of 5 arcmin. Unfortunately, the mission was not selected by CNES or ESA for further assessment.

ASTENA: An Advanced Surveyor of Transient Events and Nuclear Astrophysics (2019) Within the European AHEAD project (integrated Activities in the High Energy Astrophysics Domain) (Natalucci and Piro 2018), a mission was conceived to address some of the current issues in high-energy astrophysics: a high sensitivity survey of transient events and the exploitation of the potential of gamma-ray observations for Nuclear Astrophysics (Fig. 12). This mission concept, named ASTENA (Advanced Surveyor of Transient Events and Nuclear Astrophysics) (Frontera et al. 2019; Guidorzi et al. 2019), has been proposed to the European Space Agency in response to the call “Voyage 2050”. It consists of a Wide Field Monitor, with both spectroscopic and imaging capabilities (WFM-IS), and a Narrow Field Telescope (NFT) based on a broad energy passband (60–700 keV) Laue lens with a field of view of about 4 arcmin and with an angular

Fig. 12 The ASTENA mission concept in its folded configuration at launch (left) and in the operative configuration (right) in which the WFM-IS array and the NFT focal plane detector are unfolded

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resolution of ∼30 arcsec. The Laue telescope exploits bent tiles of Si and Ge using the (111) reflecting planes. The tiles have dimensions of 30 × 10 mm2 in size (the longer dimension being in the focusing direction) and a bending curvature radius of 40 m. The focal length of the lens is 20 m. The crystals are arranged in 18 rings, with an outer diameter of ∼3 m that gives an outstanding geometric area of about 7 m2 . The focal plane detector consists of four layers of CZT drift strip detectors (Kuvvetli and Budtz-Jorgensen 2005) each layer having a cross section of 80 × 80 mm2 and thickness of 20 mm.

Fresnel Lenses Fresnel lenses have been extensively discussed and studied for use in astronomy at X-ray energies (e.g., Dewey et al. 1996; Skinner 2004; Gorenstein 2004; Braig and Predehl 2006; Gorenstein et al. 2008; Braig and Predehl 2012; Braig and Zizak 2018) and missions exploiting them in that band have been proposed (Skinner et al. 2008; Dennis et al. 2012; Krizmanic et al. 2020). For a review see Skinner (2010). The circumstances in which such lenses offer diffraction limited resolution are discussed in ⊲ “Diffraction-Limited Optics and Techniques”. Although the idea of Fresnel lenses for gamma rays was introduced at least as far back as 2001 (Skinner 2001, 2002). When their potential for micro-arc-second imaging was pointed out, the idea has rested largely dormant. It will be seen further that the main reason for this is the extremely long focal lengths of such lenses. A secondary reason is that although they offer effective areas far greater than any other technique, with a simple lens the bandwidth over which this is achieved is narrow because of chromatic aberration. However, if those difficulties can be overcome, gamma-ray Fresnel lenses offer some unique possibilities. Like Laue lenses, Fresnel lenses provide a way of concentrating incoming gamma rays onto a small, and hence low background, detector. A gamma-ray Fresnel lens could focus the flux incident on an aperture that could be many square meters into a millimeter scale spot with close to 100% efficiency. Moreover, such a lens would also provide true imaging in the sense that there is a one-to-one correspondence between incident direction and positions in a focal plane. At photon energies above the limits of grazing energy optics, no other technique can do this. Finally, the imaging can be diffraction-limited, which in the gamma-ray band with a meter scale aperture means sub-micro-arcsecond resolution. What is more, even if missions employing them present challenges, gamma-ray Fresnel lenses are, per se, low-technology items. A conventional refractive lens, operating, for example, in the visible band, focuses radiation by introducing a radius-dependent delay such that radiation from different parts of the lens arrives at the focal spot with the same phase (Fig. 13a). A Fresnel lens (Strictly the term used should be “Phase Fresnel Lens” as the shorter form can also be used for stepped lenses in which coherence is not maintained between steps) (Fig. 13b) achieves the same phase-matching by taking advantage of the fact that the phase of the incoming radiation never needs to be changed by more than 2π . Consequently the maximum thickness of the lens can be reduced to that necessary to produce a phase change of 2π , a thickness termed here t2π . It is

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Fig. 13 (a) A conventional refractive lens for visible radiation (b) An equivalent Fresnel lens (c) A gamma-ray Fresnel lens (d) A gamma-ray Phase Zone Plate

usual to write the complex refractive index as n = 1 − δ − iβ where for gamma rays both δ and β are small and positive. The imaginary component describes absorption and does not affect the phase so t2π = λ/δ where λ is the wavelength. The fact that δ is positive for gamma rays means that a converging lens has a concave profile and a Fresnel lens has the form illustrated in Fig. 13c. It is a more efficient form of a ‘Phase Zone Plate’ (Fig. 13d) in which the thickness profile has just two levels differing in phase shift by π . The parameter δ is given in terms of the atomic scattering factor f1 (x, Z) discussed in section “Crystal Diffraction” by δ=

re λ 2 na f1 (x, Z) 2π

(17)

where re is the classical electron radius and na is the atomic density. For lenses of the type considered here, x is essentially zero. Well above all absorption edges, f1 approaches the atomic number Z and so is constant. Thus, δ is proportional to λ2 or inversely proportional to the square of the photon energy E. In principle in the region of the 1.022 MeV threshold for pair production in the nuclear electric field and above, Delbrück scattering should be taken into consideration. Early reports of an unexpectedly large contribution to δ from this effect (Habs et al. 2012) turned out to be mistaken (Habs et al. 2017) but did lead to experimental confirmations of predicted gamma-ray refractive indices at energies up to 2 MeV (Günther et al. 2017; Kawasaki et al. 2017). Like those from Delbrück

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scattering, contributions from nuclear resonant scattering will also be negligible in most circumstances. Although δ is extremely small at gamma-ray energies, the wavelength is also extremely short, for example, 1.24 pico-metres at 1 MeV. Using δ from Eq. 17 results in the following expression for t2π in terms of some example parameters t2π

 −1  −1  E ρ Z λ mm. = = 2.98 δ A 1 MeV 1g cm−3

(18)

Noting that for materials of interest Z/A is in the range 0.4 to 0.5, this means that a gamma-ray Fresnel lens need have a thickness only of the order of millimeters. The period of the sawtooth profile where it is lowest at the edge of the lens is a crucial parameter. Again in terms of example parameters, for a lens of diameter d and focal length F , the minimum period is given by pmin

  −1   F d −1 E F = 2λ = 2.48 mm. d 1 MeV 1m 109 m

(19)

The difficulties lie in the F term. For reasonable values of pmin , extremely long focal lengths are required. pmin is an important parameter in another respect. The PSF will be an Airy function with a FWHM of 1.03λ/d, so the focal spot size using this measure will be given by w = 1.03

Fλ = 0.501pmin d

(20)

That is to say, the size of the focal spot is about half the period at the periphery of the lens. The corresponding angular resolution is w/F and is given in micro-arcseconds (µ′′ ) by ∆θd = 0.263



E 1 MeV

−1 

d 1m

−1

.

(21)

Thus, gamma-ray Fresnel lenses have the potential to form images with an angular resolution better than available in any other waveband and would be capable of resolving, for example, structures on the scale of the event horizons of extra-galactic massive black holes.

Construction If the full potential of a Fresnel lens is to be realized, then Eq. 20 implies that pmin should be larger than the detector spatial resolution and so should be of the order of millimeters or more. Except at energies above 1 MeV, the required thickness is also of the order of millimeters (Fig. 14a) so high aspect ratios are not then needed.

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Fig. 14 (a) The thickness of some example materials needed to produce a 2π phase shift, plotted as a function of energy. (b) The mean absorption of a lens having as its maximum thickness that is shown in (a). Absorption in any supporting substrate is not taken into account

Almost any convenient material can be used – the nuclei only serve to hold in place the cloud of electrons that produces the phase shifts! Dense materials have the advantage of minimizing thickness but also tend to be of higher Z and hence more lossy at low and high energies. Over much of the gamma-ray band all reasonably low Z materials have similarly low losses (Fig. 14b). Because the refractive index is so close to unity, dimensional tolerances are relatively slack. Using the Maréchal formula (Mahajan 1982), if the rms errors in the profile are kept within 3.5% of the maximum lens thickness (assumed to be t2π), the loss in Strehl ratio (on-axis intensity) will be less than 5%. If the lens is assembled from segments, then the precision needed in their alignment is only at a similar level. Thus, a range of constructional technologies can be considered, including diamond point turning, vapor-phase deposition, photo-chemical etching, and 3-d printing.

The Focal Length Problem As argued above, if the best possible angular resolution is sought, then detector consideration drives one to a pmin ∼ mm. When this is coupled with a requirement for a reasonable collecting area, Eq. 19 implies a focal length of the order of

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105 –106 km. This sort of focal length clearly demands formation flying of two spacecraft, one carrying the lens and the other a focal plane detector. Minimizing station-keeping propulsion requirement suggests locations near to a Sun-Earth Lagrangian point. The line of sight from detector to lens must be controlled with sufficient accuracy to keep the image on the detector, so the precision needed depends on the size of the detector. This could be from a few cm up to perhaps 1 m. Changes in the direction of that line of sight need to be determined with an accuracy corresponding to the angular resolution aimed for, which could be sub-micro-arcsecond. Detailed studies have been performed of missions with requirements that meet all of these requirements separately. Not all are met together in any single study, but on the other hand, the complexity of the instrumentation and spacecraft was in each case much greater than that for a gamma-ray Fresnel telescope. New Worlds Observer requires a 50 m star shade and a 4 m visible-light diffractionlimited telescope to be separated by 8 × 104 km (Cash et al. 2009). The transverse position of the telescope must be maintained to within a few cm. The MAXIM Xray interferometer mission calls for a fleet of 26 spacecraft distributed over an area 1 km in diameter to be separated from a detector craft 2 × 104 km away (Cash 2003, 2005). The requirement for a diffraction-limited gamma-ray Fresnel lens mission to track changes in the orientation of the configuration in inertial space at the submicro-arcsecond level are similar to the corresponding requirement for MAXIM, though only two spacecraft are needed. MAXIM studies envisaged a “super star tracker”. Such a device could locate a beacon on the lens spacecraft relative to a stellar reference frame. In terms of separation distance, the requirement for ∼106 km separation can be compared with the needs of the LISA gravitational wave mission (Joffre et al. 2021) for which three spacecraft must each be separated from the others by 2.5 × 106 km, though in this case it is the rate of change of inter-spacecraft distance that requires strict monitoring rather than the orientation.

Effective Area The focusing efficiency of a gamma-ray Fresnel lens will depend on the fraction of incoming radiation that passes unabsorbed through the lens and on the efficiency with which that radiation is concentrated into a focal spot. In Fig. 14b, the mean transmissio