Infrared Methodology and Technology 2881245900, 9782881245909

Table of contents :
Cover
Half Title
Series
Title
Copyright
Contents
Preface to the Series
Preface
Part 1
Chapter 1 Need and Necessity of NDT
Chapter 2 Theoretical Aspects of the Infrared Radiation
Chapter 3 Instrumentation for the Infrared
Chapter 4 Dedicated Image Processing for Thermographic Non-Destructive Testing
Part 2
Chapter 5 Infrared Techniques for Materials Analysis and Nondestructive Testing
Chapter 6 Infrared Techniques in Buildings and Structures: Operation and Maintenance
Chapter 7 Infrared Techniques for Printed Circuit Board (PCB) Evaluation
Chapter 8 Infrared Techniques for Electric Utilities
Chapter 9 Infrared Techniques in the Nuclear Power Industry
Chapter 10 Infrared Techniques for Real-Time Weld Quality Control
Chapter 11 Infrared Techniques for Military Applications
Chapter 12 Infrared Techniques in the Aerospace Industry
Chapter 13 Utilization and Application of Infrared Techniques in Forest Fire Detection and Suppression Operations
Chapter 14 Medical Applications of Infrared Thermography
Chapter 15 Bibliographical Survey of Thermal NDT and Related Fields
About the Contributors
Index

Citation preview

INFRARED METHODOLOGY AND TECHNOLOGY

Nondestructive Testing Monographs and Tracts

A series edited by Warren J. McGonnagle, Elmhurst, Illinois Editorial Advisory Committee Richard A. Beatty, Office of Quality Assurance, Mail Stop 201 ESH/QA, Argonne National Laboratory, 9700 South Cass Avenue, Argonne, Illinois 60439, USA J.C. Domanus, Riso National Laboratory, Postboks 49, DK-4000 Roskilde, Denmark Tau-Chao Fan, Division of Materials Science and Engineering, Faculty of Engineering and Technology, World Open University, Post Office Box 955, Palos Verdes Estates, California 90274, USA Edvard Heiberg, James Frank Institute, University of Chicago, 5640 South Ellis Avenue, Chicago, Illinois 60637, USA Zhang Jiajen, Mechanical Engineering Department, Tsinghua University, Peking, Peoples Republic of China W. Lord, Iowa State University, 351 Durham Center, Ames, Iowa 50011, USA Xavier P.V. Maldague, Department of Electrical Engineering, Université Laval, Quebec G1K 7P4, Canada Amos Notea, Quantitative Nondestructive Evaluation Laboratory, Technion-Israel Institute of

Technology, Technion City, Haifa 32 000, Israel Dennis N. Poffenroth, Industrial and Electrical Safety Division, Safety and Health Technology Center, United States Department of Labor, Post Office Box 25367, Denver, Colorado 80225, USA James F. Shackelford, Department of Mechanical Engineering, University of California, Davis, Davis, California 95616, USA Roderick K. Stanley, Baker Hughes Veteo Services, Post Office Box 7631, Houston, Texas 772707631, USA Bruce Suprenant, Department of Civil Engineering and Architectural Engineering, Box 428, University of Colorado, Boulder, Colorado 80309, USA William Ulbricht, 2533 Albermarle Court, Richland, Washington 99352, USA James W. Wagner, Johns Hopkins University, Maryland Hall 102, Baltimore, Maryland 21218, USA Gary L. Workman, University of Alabama at Huntsville, Huntsville, Alabama 35899, USA

Volume 1 Microwave Nondestructive Testing Methods Alfred J. Bahr Volume 2 Acoustic Emission Edited by James R. Matthews Volume 3 Electromagnetic Method of Nondestructive Testing Edited by William Lord Volume 4 Automated Nondestructive Testing Edited by Warren J. McGonnagle Volume 5 Nondestructive Evaluation for Aerospace Requirements Edited by Gary L. Workman Volume 6 Basic Acoustic Emission Ian G. Scott Volume 7 Infrared Methodology and Technology Edited by Xavier P.V. Maldague This book is part of a series. The publisher will accept continuation orders which may be cancelled at any time and which provide for automatic billing and shipping of each title in the series upon publication. Please write for details.

INFRARED METHODOLOGY AND TECHNOLOGY

Edited by

Xavier P.V. Maldague Department of Electrical Engineering Universite Laval Quebec, Canada

Boca Raton London New York

CRC Press is an imprint of the Taylor & Francis Group, an informa business

First published 1994 by Gordon and Breach Publishers Published 2018 by CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 1994 by Taylor & Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group, an Informa business

No claim to original U.S. Government works ISBN 13: 978-2-88124-590-9 (pbk) ISBN 13: 978-1-138-45589-4 (hbk) This book contains information obtained from authentic and highly regarded sources. Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the validity of all materials or the consequences of their use. The authors and publishers have attempted to trace the copyright holders of all material reproduced in this publication and apologize to copyright holders if permission to publish in this form has not been obtained. If any copyright material has not been acknowledged please write and let us know so we may rectify in any future reprint. Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced, transmitted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any information storage or retrieval system, without written permission from the publishers. For permission to photocopy or use material electronically from this work, please accesswww.copyright.com(http://www.copyright.com/) or contact the Copyright Clearance Center, Inc. (CCC), 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400. CCC is a not-for-profit organization that provides licenses and registration for a variety of users. For organizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged. Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com Library of Congress Cataloging-in-Publication Data

Infrared methodology and technology / edited by Xavier P.V. Maldague. p. cm. - (Nondestructive testing monographs and tracts, ISSN 0730-7152 ; v. 7) Includes bibliographical references. ISBN 2-88124-590-0 1. Infrared testing. 2. Thermography. I. Maldague, Xavier. II. Series. TA417.5.154 1992 a621.36'12-dc20 92-43489

DOI: 10.1201/9781003420200

CIP

Contents Preface to the Series ....................................... vii Preface ..................................................

ix

PARTl Chapter 1

Need and Necessity of NOT J. Boogaard .................................

3

Chapter 2

Theoretical Aspects of the Infrared Radiation J.L. Beaudoin and C. Bissieux ..................

9

Chapter 3 Chapter 4

Instrumentation for the Infrared

X.P.V. Maldague... ...........................

53

Dedicated Image Processing for Thermographic Non-Destructive Testing E. Grinzato.................................. 103

PART2 Chapter 5

Infrared Techniques for Materials Analysis and Nondestructive Testing V. Vavilov ................................... 131

Chapter 6

Infrared Techniques in Buildings and Structures: Operation and Maintenance s.A. Ljungberg ............................... 211

Chapter 7

Infrared Techniques for Printed Circuit Board (PCB) Evaluation D. Dumpert ................................. 253

Chapter 8

Infrared Techniques for Electric Utilities T.L. Hurley .................................. 265

Chapter 9

Infrared Techniques in the Nuclear Power Industry R.J. Lewak .................................. 319

vi Chapter 10

CONTENTS Infrared Techniques for Real-Time Weld Quality Control S. Nagarajan and B.A. Chin

367

Chapter 11

Infrared Techniques for Military Applications R.N. Strickland

397

Chapter 12

Infrared Techniques in the Aerospace Industry D.D. Burleigh

429

Chapter 13

Utilization and Application of Infrared Techniques in Forest Fire Detection and Suppression Operations R. Young

453

Medical Applications of Infrared Thermography R.B. Traycoff

469

Bibliographical Survey of Thermal NDT and Related Fields X.P.V Maldague

483

Chapter 14

Chapter 15

About the Contributors

509

Index

519

Preface to the Series This series concentrates on the methods of, and techniques in, nondestructive testing (NDT) and will publish information and data obtained from applications, experimentation and theory; improved methodology; instrumentation modification and developments; application of the methodology to new and different problems or problem areas, and analysis, discussion and evaluation of standard methodology. Each volume may be devoted to one method or subject or may contain papers on a number of methods. Members of the Editorial Board will assist in the selection of the subject matter, as well as in the evaluation of manuscripts submitted for publication in the series. We believe that these monographs and tracts will help advance the science, engineering and technology of NDT and stimulate its application to industrial problems, thus helping to ensure the quality, reliability and safety of industrial materials, components and systems. Some of the volumes will also be useful in seminars and courses in NDT materials and related areas. Comments concerning this series are welcome. Warren J. McGonnagle

Preface It gives me great pleasure to be writing this preface. Infrared thermography is a rather new technique used for inspection, evaluation (nondestructive testing [NDT]) and assessment in a wide variety of applications. Considering its relatively new development and the variety of applications, the idea for a book on infrared techniques has been around for sometime in the infrared community. The support and advice of Dr. McGonnagle back in September of 1990 initiated the whole process. First, a table of contents was devised and collaboration was sought within the infrared community. The response from industries, institutes and universities was enthusiastic, including authors from many countries (Canada, France, Italy, Sweden, Netherlands, USA, Russia) who have various infrared background experience. In fact, this broad source of interests is one of the strong points of this book. The book is divided into two parts. Part 1 is more fundamental. The field of infrared technology with associated theory and experimental considerations is presented herein. The second part is devoted to a wide variety of applications of infrared techniques. Although a very broad span of applications is covered, we believe some subjects are still missing, though perhaps not directly related to NDT, such as applications in astronomy. Nevertheless, Part 2 of the book is quite representative of the ongoing work as well as of the new research activities within the infrared community. The book starts with an introduction to the NDT field: its goals and its necessity in our technological and global economic era. This text (chapter 1) was written by J. Boogaard (Netherlands). Chapter 2 by J.L. Beaudoin and C. Bissieux (France) then follows with a presentation of the infrared radiation theory. These fundamental aspects are the basis behind the burden of the infrared activities we experience nowadays, especially with annual conferences devoted to the subject such as the Society of Photo-Optical Instrumentation Engineers Thermosense conferences (which will be in their sixteenth year in 1994). In chapter 3, by X.P.V. Maldague (Canada), updated information is given on experimental set-up configurations for infrared NDT. This chap-

X

PREFACE

ter also includes some historical background as well as a review of infrared detectors. We feel this is an important subject to cover, since detectors (and related information) are really at the heart of any measurement. Knowledge of detector behavior allows one to better understand the limitations of the infrared NDT techniques presented in the other chapters. Chapter 4, written by E. Grinzato (Italy), deals with image processing. Although the first infrared experiments in the sixties were generally done only with a scope screen, the computer is now an integral part of infrared NDT. It allows image enhancement, complex algorithm computations, archiving and many other tasks that permit extraction of more quantitative and accurate information. Part 2 of the book begins with chapter 5 by V. Vavilov (Russia). This chapter combines heat transfer theory, signal processing and decision making. This is another essential pillar of the book, where the fundamentals of infrared NDT techniques and methods are presented. Chapter 6 by S.À. Ljungberg (Sweden) covers an important area of application for infrared NDT: the building industry. This chapter presents a detailed study of how infrared NDT is applied in this context, for energy saving, and for assessment and refurbishing programs of manmade constructions. Chapter 7 by D. Dumpert (USA) concerns another field of deployment of infrared testing in the case of printed circuit boards (PCBs) inspection. This contribution explains the techniques and methods used to spot faulty PCBs through hot spot detection and reference techniques. The next two chapters are devoted to energy generation and distribution activities. Chapter 8 by T.L. Hurley (USA) presents a review of passive applications of infrared for electric utilities. Infrared is much used in electric power plants, since through predictive maintenance it allows avoiding costly power shortage and catastrophic failure. In chapter 9, by R.J. Lewak (Canada), infrared NDT is presented in the more specific context of the nuclear power industry. This is a relatively new sphere of interest for infrared testing, which, for instance, can be deployed for inspection of fiberglass reinforced plastics and rubber, the measurement of corrosion in piping or the degradation of cable insulation. Main advantages of infrared techniques in this case are the swift mode of operation and non-contact deployment which prevent human exposition to harmful radiation. Chapter 10 by S. Nagarajan and B.A. Chin (USA) introduces the infrared applications in welding. High energy is released in the welding process: consequently, temperature distribution measured by infrared

PREFACE

xi

equipment permits quality control and quantitative evaluation of welds, as well as control of the welding process. Chapter 11 by R.N. Strickland (USA) brings us to one of the most important applications of the infrared in terms of invested dollars: the military. In this chapter, attention is given to target signature recognition, which is a major issue for both defensive and offensive deployment. One obvious but important advantage of infrared testing, in this case, is the difficulty of concealing warm bodies or hot gas exhaust either at night or during foggy weather: this opens the door to infrared detection and interpretation followed by tactical actions. In chapter 12, by D.D. Burleigh (USA), we stay in the aerospace industry but away from the battlefield. Presentation is given about the use of infrared NDT for the specific inspection of aerospace components (i.e., graphite epoxy components, and thrust structure of launch vehicles) or for the thermal mapping of aerodynamically heated structures. The next two chapters present perhaps less publicized applications of infrared NDT. They concern forest fire detection and medicine. Forest fire detection is becoming more and more important with the unprecedented occurrence of droughts, which now afflict forest lands more regularly, as a consequence of global climate warming. Early detection of fires originating from lightning or human related causes, such as vandalism, allows saving thousands of forest acres. This serious issue is covered by R. Young (Canada) in Chapter 13. Medicine is another area where infrared thermography should find important developments in the future, especially because of its non-invasiveness, which suppresses concerns physicians and patients have been having about safety. The ability of infrared thermography to record temperature patterns on the body makes it a useful, although still controversial, diagnostic tool. R.B. Traycoff (USA) brings us this interesting subject in chapter 14. Chapter 15 by X.P.V. Maldague (Canada) is different from the other chapters as it is a bibliographical survey. It is hoped that this extensive bibliography can help readers who want to delve into specific subjects related to infrared technology. This book is the result of a tight collaboration between all the authors, especially in regard to the restricted time schedule. Following the text, short biographies and photos of the authors are grouped together. This was found important to help keep a personal contact with the reader (comments will be highly appreciated). Finally, I would like to express my deep gratitude to all the individuals who helped the dream of this book come

xii

PREFACE

true. In addition to all the authors and their respective support staff, I especially thank Dr. McGonnagle, editor-in-chief of the Nondestructive Testing Monographs and Tracts series. In concluding this preface, I would like to cite a nice passage from Le Petit Prince {The Little Prince) by Antoine de Saint-Exupéry. While talking to the Little Prince, the Fox said: "We only see correctly with the heart. The essential is invisible for the eyes." In the case of infrared, I consider this play on words particularly meaningful and I hope this book, through its pedagogic nature, will help promote infrared thermography as a wellestablished NDT tool. XavierPV. Maldague

— M ^ s o l i d ~ a f l u i d ) ,

where h (Wm~ 2 K _1 ) is the convection coefficient, and Tsoiid is the temperature of the solid surface. In the literature, the convection coefficients are most often obtained from correlations implying dimensionless numbers according to well-established use: • Niisselt number Nu links convection coefficient h, the thermal conductivity of the fluid (fc), and length D characteristic for the device under consideration (the diameter of a cylindrical pipe, the length of a plane plate, etc.): Nu = h D/k. • Reynolds number Re characterizes the nature (laminar or turbulent) of the flow in the case of forced convection. If U is the fluid velocity and v (m 2 s _1 ) is kinematic viscosity, then the Reynolds number is expressed as follows: Rc =

UD/v.

• In the case of free convection, the Reynolds number is replaced by the Grashof number (Gr), which is representative of the causes of buoyancy (temperature gradient 0

Theoretical Aspects of Infrared Radiation

13

between the solid surface and the fluid at rest, and the local acceleration due to gravity g (g = 9.8 ms~ 2 )): Gr =

g/39D*/v2)

where ¡3 is the expansion coefficient of the fluid. For a perfect gas, (3 = i/r. • Prandtl number Pr is the ratio of the kinematic viscosity (y) of the fluid to its thermal diffusivity a (Pr = v/a). The simplest correlations giving the values of Nu usually have the following form: forced convection: Nu = bRem Pr n , free convection: Nu = 6Gr m Pr n , where 6, m, and n are numerical coefficients. In most common situations, h values range from 2 to 200 Wm~ 2 K _ 1 in gases and from 100 to 2000 Wm~ 2 K _ 1 in liquids. Apart from the two references cited above [6,11], some more elaborate results can be found in specialized treatises such as Kays [12]. Example 1. A flat plate of length L = 10 cm and width w = 8 cm is maintained at a uniform temperature (Tp = 80° C). Atmospheric air at 20°C flows over the plate, parallel to L, at velocity U = 15 ms" 1 . The properties of the air at 50° C are: v = 17.5 x 10" 6 m 2 s _ 1 ; Re = UL/v =

k = 0.028 W m " 1 ^ 1 ;

Pr = 0.7,

(15 m s - 1 * 0.1m)/(17.5 x l O ^ m V 1 ) = 85714.

Thus, the flow is laminar (Re < 500,000) and the relevant correlation is [6] Nu = 0.66Re£-5Pr0'3 = 0.66 * 85714 1/2 * 0.7 1 / 3 = 171.6. The convection coefficient is given by: h = Nu k/L = 171.6 * 0.028 W H I ^ K ^ / C U m = 48 W m ^ K " 1 . The cooling rate of the plate is expressed as $ = Ah(Tp-Tñniá) = (0.1m * 0.08 m) * 48 W m ^ K - 1 * (20-80) K = - 2 3 watts.

14

J. L. Beaudoin and C. Bissieux

Example 2. Evaluate convection coefficient h in case of free convection of atmospheric air at 20° C along a vertical plate of height H = 3 m. The plate is maintained at temperature Tp = 10°C. The properties of the air at 15°C are: k = 0.025Wm^K" 1 ; Pr = 0.71; /? = 1/288K" 1 .

t/ = 15xl0-em2s'1]

First we have to calculate the Grashof number: Gr =

gp0Hs/v2

= 9.8 ms~ 2 * 288" 1 K" 1 * 10 K * 3 3 m 3 /(15 x 10" 6 m V 1 ) 2 = 4.10 10 . One relevant correlation is: Nu = O.lSGr^Pr 1 / 3 = 398.5. Thus, h = Nu • k/H = 398.5 * 0.025 W m ^ K - 1 ^ m = 3.3 W m ^ K " 1 . 2.3. Introduction to Radiation Energy transfer by radiation is a common experience. Each of us has felt warm and comfortable near an open fire. On the contrary, the discomfort originating from the proximity of a cold window pane in winter (apart from air leakage!) is well known. As the main topic of this chapter, radiative energy transfer will be more developed than conductive and convective transfer in subsequent sections. At this point, our only purpose is to give a brief overview of the relevant physical phenomena. The intimate nature of radiation was established by Maxwell as electromagnetic waves, ranging from X-rays to microwaves via visible light and the infrared. The behavior of the electromagnetic waves is described by a set of mathematical relations called Maxwell's equations [13,14]. In a vacuum, the simplest solution is a monochromatic plane wave: E = Eo cos 2ir(vt -

z/\o),

where E0 is amplitude, v is frequency, z represents the distance from the origin of the coordinate axis, and Ao is the wavelength in a vacuum. At any instant, the wave amplitude is spatially periodic, and the wavelength is equal to this period. The wavelengths of radiation visible to the human

Theoretical Aspects of Infrared Radiation

15

eye range from 0.4 to 0.8 p,m\ the infrared domain extends up to 100 /xm. If we introduce the velocity (c) of an electromagnetic wave in a vacuum, we find that Ao = c/u. When the wave must propagate in a material, things are much more involved. On a microscopic scale, it is clear that the electric and magnetic fields of the wave do interact with the free or bounded electric charges of matter and force them into vibrations at the same frequency. As we are only interested here in the macroscopic aspect of things, Maxwell's equations are still usable, provided that we introduce a new macroscopic parameter, the complex refractive index: n — n — jfc, where n is the refractive index, and k is the extinction index. Frequency v remains unchanged in the material, whereas the wavelength and the wave velocity become A = Ao/n and v = c/n. We should mention the frequent use by spectroscopists of wavenumber a instead of the wavelength (a = 1/A). The wavenumber is commonly expressed in c m - 1 . The expression of a plane monochromatic wave propagating along the z axis becomes E = Eo exp -(27T k z/Xo) cos27r(i4 — nz/Ao). The exponential term represents progressive attenuation of the amplitude as long as the wave travels deeper into the medium, according to the value of extinction index k. The absorption coefficient for energy (K) (often expressed in m _ 1 or cm - 1 ) is related to k: K =

4irk/\0.

Various processes may be responsible for emission of radiation: collision of particles in electrical discharges (discharge lamps, TV screen phosphors), excitation by light beams (UV excitation or so-called "black light"), and heating of matter (incandescent bulbs and infrared sources). Among these processes, only the latter relates to thermal radiation. A medium is said to emit thermal radiation when the interactions between its constituent particles are strong enough to keep their energy distribution in statistical equilibrium. This equilibrium is mathematically

16

J. L. Beaudoin and C. Bissieux

described by a function of the local temperature, such as the MaxwellBoltzmann distribution. We then say that the medium is at local thermodynamic equilibrium. For example, in an electric wire heated by the Joule effect, the unceasing collisions between electrons and atoms produce this statistical equilibrium. This is not the case in the rarefied atmosphere of a discharge lamp, where the electric arc is able to establish a particular energy distribution related to its strength. At local thermodynamic equilibrium, the mathematical expression for the spectral distribution of radiation is the product of a universal expression dependent only on temperature, Planck*s law, and a quantity specific of the material, its emissivity. In fact, any medium that has been set to temperature T (higher than absolute zero) has become an energy reservoir and is thus able to release some energy toward its environment through "thermal" radiation. Energy exchanges via thermal radiation are always occurring, contributing to thermal equilibrium between objects and their environment. 3. FUNDAMENTALS OF RADIATION 3.1. Radiometric Quantities Some quantities must be defined in order to quantify the radiation leaving or reaching a surface. First, two categories of terms are considered: • Total quantities deal with energy summed over the whole spectrum. • Spectral or monochromatic quantities characterize the energy contained in a narrow interval of wavelength; they will be written with subscript A. Using the same approach taken for the other modes of heat transfer, the radiant flux or radiant power $, expressed in watts, is the time rate of radiant energy. The radiant flux per unit area (over all directions of space) is still defined by

and is thus expressed in Wm~ 2 . If the energy is emitted by the surface, then this quantity is called emitting power M (or the radiant emittance of the surface). If the energy is received by the surface, then it is called irradiance E (¿clairement in French). If the energy is leaving the surface, due to whatever physical cause (emitted plus reflected plus eventually transmitted), then it is called radiosity J.

Theoretical Aspects of Infrared Radiation

17

So M, E, and J appear as varieties of the same physical species ip\ they are introduced to describe more precisely radiative exchanges around a surface element. In order to quantify the flux passing through small surface áA within small solid angle dfi around a direction making angle 9 with the normal to the surface, we now introduce radiance L {luminance in French), expressed inWm~ 2 sr _1 :

This quantity appears to be fundamental, because any imaging system, such as our eyes or the detector in an infrared camera, responds proportionally to it. No varieties of radiance are usually introduced, and so we must specify whether a radiance is emitted or received or reflected or even transmitted by a surface. Without any specification, the radiance of a surface is understood to be derived from the radiosity. Of less utility is a quantity called radiant intensity (denoted I), which has the same purpose as radiance L but with no reference to the value of the emitting area: Intensity is mainly used to characterize point sources, but care must be taken in the frequent use of the word "intensity" for radiance in many texts. Historically, characterization of light flux was accomplished by visual methods. Another set of characteristics linked to human eye sensitivity (maximum around 0.55 micrometers) is known as (visual) photometric quantities. They are expressed in exotic units such as, e.g., nit, candela, and stilb. Conversion to (energetic) radiometric quantities is only possible for visible light and is in no way straightforward. 3.2. Blackbody Radiation The basic laws of thermal radiation describe emission of an ideal emitting material, usually known as a blackbody. This emission, the physical laws of which are thoroughly settled, actually exists inside an isothermal closed cavity, whatever the nature of its walls. Emission of this completely closed isothermal cavity would be impossible to observe. If a small aperture is made in one of the cavity walls, we obtain a device called a laboratory blackbody. Geometrical calculations show that its actual emission is very close to that of the ideal blackbody.

18

J. L. Beaudoin and C. Bissieux

Surface element àA of a blackbody (total absorber and best emitter) emits flux d$ in a vacuum hemisphere. Its total emitting power, denoted M° (Wm -2 ), summed over the whole spectral range is given by the Stefan-Boltzmann law:

where

Total radiance L° (Wm 2sr *) is given by

since the blackbody radiation is isotropic or lambertian in this case. This means that radiance is independent of emitting direction. Planck's law gives spectral repartition of the flux emitted by the blackbody in a vacuum (where À « AQ, very close to that emitted in air):

with Ci = 2nhc2 = 3.742 x 10" 16 Wm2 and C2 = hc/k = 1.4388 x 10~ 2 mK, and M® is the spectral (or monochromatic) emissive power of the blackbody. We deduce its spectral radiance L^ as follows:

At a given blackbody temperature, we can thus compute M°, M°, L°, and L°. M j represents a maximum value at wavelength Am given by Wien's law: Corresponding value M° m follows this law:

Theoretical Aspects of Infrared Radiation

19

When the temperature of the blackbody increases, its thermal emission will contain more and more energy at shorter wavelengths; thus, whitehot is hotter than red-hot. Objects at temperatures under 500° C are not actually perceptible to the eye because their thermal emission lies mainly in the infrared. As a rule of thumb, one should remember that a blackbody emission becomes visible (in a dark room) when its temperature reaches 550°C. We wish to point out that more than 95% of the emitted energy lies in a spectral domain between 0.5 and 5 Am (one order of magnitude in wavelength). For a blackbody at room temperature, Am is 2898/293 « 10 /¿m, and most of the energy is emitted between 5 and 50 /xm in the infrared. At 550° C, Am = 2898/823 « 3.5 ¿xm, and most of the emission still lies in the infrared, but the human eye, a very sensitive detector, sees the tiny emission at the limit between red and infrared. If the solar surface is supposed to radiate like a blackbody at 5800 K, its emission peaks at around 0.5 ¡im and essentially lies between 0.25 and 2.5 /¿m. Aside from this shift toward shorter wavelengths, one should never forget that a hot blackbody always emits more than a cold one, at any wavelength! 4. RADIATIVE PROPERTIES OF MATERIALS 4.1. Definition of the Emissivities A blackbody is an ideal radiator which emits as much radiant energy as possible. The emissive power of a real material is then defined by comparison with that of a blackbody at the same temperature, the ratio being called the emissivity of the material. In order to characterize the angular and spectral dependences of the emitting behavior of the real material, we must define four parameters: • total (hemispherical) emissivity:

• directional (total) emissivity:

• spectral (hemispherical) emissivity:

J. L. Beaudoin and C. Bissieux

20

FIGURE 1. Emitting power M. spectral directional emissivity:

The adjectives between brackets are usually not mentioned. The radiances under consideration here are strictly emitted ones. According to these definitions, the four ratios are obviously equal to unity for a blackbody (which is the reference) and comprised between zero and unity for real materials. They are related by the spatial integral relation between emissive power and radiance:

leading to integral relations that allow us to determine the three first emissivities given a knowledge of e'x. The latter is thus the fundamental parameter, which describes most completely the emissive ability of a real material, versus wavelength and emissive direction. Note that the knowledge of e'x or e\ can be restricted to the interval (0.5Am; 5Am), since L\ is negligible outside this range.

Theoretical Aspects of Infrared Radiation

21

It is frequently assumed for simplicity that the surfaces are gray and diffuse. In this case (Fig. 1):

The emissivity effectively involved in a radiometric measurement is actually a value averaged over the spectral sensitivity range of the radiometer. Let 5(A) be its spectral responsivity; 5(A) is different from zero only over spectral interval AA, where the detector sensitivity maintains a significant value. We then call the effective emissivity of the material over the spectral range of the apparatus quantity

which can be computed provided that e'x, L°x, and 5(A) are known. Obviously, if the material can be considered as gray over AA, we again get

P' £

AX

£ — p'

— x-

4.2. Radiative Balance on a Material Once the emitting behavior of the material has been characterized, we must consider the response of the material when external radiation impinges on its surface. Let d$¿ be the incident flux on a surface element of area dA, and d$ a be the absorbed flux. The total absorptivity of the material is defined as For a blackbody, which is perfectly absorbing, a is equal to unity; for a real medium, at least a part of the incident radiation is reflected and the absorptivity is strictly inferior to unity, a generally depends on the angular and spectral distributions of the incident radiation. We must then define, as has been done for the emissivities, the spectral and directional absorptivities. This introduces four parameters — a, a', a\, and a!x — thefirstthree being computablefroma'A (directional spectral absorptivity). To describe reflection of the incident flux by the material, we first define its total reflectivity: As in the case of absorption, reflectivity is generally dependent on the angular and spectral distribution of the incident radiation. Moreover, here, the angular distribution of the reflected radiation must be taken into

22

J. L. Beaudoin and C. Bissieux

FIGURE 2. Reflected and incident radiance over surface patch áS. account. This leads us to define more parameters: total or spectral, hemispherical, directional-hemispherical, hemispherical-directional, and bidirectional reflectivities. It can be shown that the fundamental quantity, specific to the sample and from which every parameter can be computed, is bidirectional reflectance distribution function (BRDF) fr:

where dLr is the reflected radiance in direction íí r (0 r ,

10 mm the involved model converts into a ID one, so that the functions mentioned above have a saturating character (these estimates can vary slightly when taking account of the anisotropy of the carbon specimen). Evaluation of the possibilities of TANDT and optimization of parameters implies an estimate of recording time and signal-to-noise level. For our particular case, the r m values range from 0.2 to 4 s, making unrealistic use of a manually controlled IR imager. In fact, successful investigations of carbon composites have been done with computerized equipment, and it was seen that all defects involved generate signals larger than the temperature resolution of the equipment (0.1-0.2° C). The optical properties of carbon composites are close to those of a "black body," so that the level of noise caused by absorbtivity and emissivity fluctuations is pretty low. Unfortunately, carbon fiber anisotropy creates structural noise. Its level for a Russian-made carbon epoxy composite was reported at 10-12% [33] (black painting was found to reduce the noise of carbon epoxy plastic by up to 5- 6%). Applying the threshold level of 10% to the calculated data,

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FIGURE 11. TANDT parameters for carbon epoxy composite (L = 2 mm; Q = 200 kW/m2): a — time evolution of temperature signal and contrast for heated surface (r¿ = 5 mm, d = 0.1 mm); b — time evolution of temperature signal and contrast for rear surface (r¿ = 5 mm, d = 0.1 mm); c — maximum values of temperature signal and contrast vs. defect depth (Td = 5 mm, d = 0.1 mm, Am corresponds to rSi (AT™); d — r m vs. 1 (Xd = 5 mm, d = 0.1 mm); e — Am vs. d (r¿ = 5 mm, Am corresponds to r ^ ( A T ^ ) ; / — Am vs. rd(d = 0.1 mm); g — r m vs. rd (d = 5 mm, «responds to AT^); h — r m vs. r¿ (d Tm corresponds to Am, and rR corresponds = 0.1 mm); 1 — / = 0.2 mm, 2 • 1 = 1 mm, 2 — / = 0.95 mm, 3 — / = 1.7 mm.

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FIGURE 11. cont'd it we can see seen that in a one-sided procedure defects located deeper than 1.5 mm are not reliably detected (see Fig. lie), while the two-sided procedure provides testing through the whole thickness of the specimen.

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FIGURE 11. cont'd Note that this conclusion relates to a thickness of 0.1 mm and that other defects can be reevaluated with the same method. Finally, the considerable decrease in the input energy can seriously deteriorate the testing results because of small temperature amplitudes. 9.4. Characterization of Defects in 2D Data Inversion Analysis Characterization of subsurface defects requires solving the inverse heat transfer problem (see §7.4). Many approaches described in the current literature (see the brief review in [43]) attempt to solve TANDT inverse problems. Most of them can be classified as: 1) methods which involve iterative calculation of direct problems, closing at each step theoretical and experimental results; 2) methods which require a set of predetermined connections between first-order parameters; and 3) methods based on a priori known or directly measured empirical information about some defect parameters. So far none of these methods has been successful in their pure form, being either too time-consuming or limited to specific cases.

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A combined approach was described recently for ribbon-like and disk-shaped 2D defects (models in Fig. 36,c) in an opaque and possibly anisotropic solid [43]. This finite-difference model combined with an implicit procedure was used to solve the direct problem, resulting in relationships between all the involved parameters which actually formed the multidimensional space of informative features. The input data to the inversion procedure were: Am/expi Fo+0.5/exp, and Fo_ 0 .5/ex P (corresponding to those described in §8.7) and apparent defect size i/ a p /ex P determined by steepest gradient analysis in the first iteration (exp relates to the experimental value). The ouput variables were: Z, H, R, and ft for delaminations, and Z, H, and ft for a bottom-open defect. As in the ID case [42], data inversion was based on minimization of the least-squares function. Because of the nonimportance of heat exchange coefficient ft, interpolations were only 3D with the ft value as a parameter. The interpolation method used 3D B-splines of orders 4 and 3 for three variables. The errors obtained in the retrieved values of Z and H by using the above procedure were smaller than 1%, while the errors in R and ft ranged from 1 to 100%. 9.5. Dynamic Thermal Tomography The principle of ordinary (X-ray, ultrasonic, nuclear magnetic resonance) tomography including reconstruction of the internal structure of specimens by using different spatial view angles cannot be applied to the heat transfer process, which occurs not in straight directions but according to differential (1), experiencing strong space relaxation and time delay. Nevertheless, the idea of "slicing" specimens to make visible the distribution of thermal properties inside the separated layer seems to be attractive. The term "thermal tomography" was initially proposed by Vavilov and Shiryaev in 1986. A simple algorithm was described by Vavilov in 1990 [47], one very close to image processing in the time-domain developed by Balageas, Thomas, and Favro et al. [6,16-19]. Probably the first experimental tomograms were obtained by Vavilov, Thomas, and Favro et al. in 1990 [48], and development of this algorithm was discussed later [49]. A simple real-time tomography algorithm recently became available [50,51]. Instead of spatial view angles, dynamic thermal tomography uses multiple IR images ("time angles") of the transient temperature field in a specimen. In fact, this method does not need any new installation or procedure, as it is essentially a special way of processing and presenting data. Suppose the surface response of a defect with thickness d located at depth U is described by function AT(Z¿,d, r 7 ) , which looks like that

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shown in Fig. 11a. In thermal tomography, depth resolution is reduced to resolved delay time Ar res , which is obviously connected to equivalent noise level ATnoiSe by the following expression: (14) where 7 corresponds to the accepted level of AT measurement. The noise value has to be found empirically. In the ideal case, AT no i se = sAT res . In temperature contrast terms, ATno¡Se = sAnth, where An is the standard deviation of the noise contrast. From (14): (15) The depth resolution of thermal tomography can be treated as the minimum thickness of a defect located at depth U. This minimum defect thickness can be determined by the following obvious expression:

where Ar res , as follows from (15), is limited by the data sampling rate (in thermography procedures this limit is given by IR imager field time T/). On the other hand, the minimum thickness value must provide a temperature signal not less than the ATnoi8e value, i.e.,

The maximum value of d found from the two last expressions yields the thickness of the resolvable layer. Parameters r m , T0.5, and ro.72 can be taken as the r 7 values. Experimental examples of thermal tomography are shown in Fig. 12. The unsmoothed image in Fig. 12a shows the temperature field upon a bottomhole defect in plexiglas taken at optimum time r m = 11.7 s (defect diameter 10 mm, depth 4 mm). Doublefilteringproduced the image in Fig. 12b. The distrubution of AT m values above the threshold of 6.5% of contrast is presented in Fig. 12c. Figure 12d shows the synthesized time-domain image depicting the distribution of r m values (notice that edge effects are still visible). This image in fact resembles very much the defect depth image in Fig. 4b. The particular tomograms for different internal layers are presented in Fig. 12e-h, illustrating good separation of noise and defect

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FIGURE 12. Thermal tomography: a — nonsmoothed IR image of defect (diameter 10 mm, depth 4 mm) in Plexiglas; b — same as (a) but smoothed with 3 x 3 and 7 x 7 filters; c - -distribution of maximum temperature signals ATm (ATm-image), relatively fixed nondefect point (threshold 6.5% of temperature contrast); d — time-domain image (rm-image); e — tomogram of 1.4-2.1 mm layer; / — tomogram of 2.8-4.2 mm layer; g — tomogram of 4.8-5.6 mm layer; h — tomogram of 7.5-8.2 mm layer (results of Figs, \2a-h were obtained at Laval University, Canada, 1991); i — IR image of four bottom-hole defects in plastics 50 s after heating (defect depths from right bottom to left top: 0.9, 1.8, 2.8, and 3.5 mm); j — time-domain image showing distribution of r m values; k — tomogram of I = 0.5-1.4 mm layer; / — tomogram of layer / 3.1-3.9 mm layer (results of Fig. 12;-/ obtained at Wayne State University, USA, 1990 [48]).

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FIGURE 12. cont'd signals. The distribution of the temperature upon four bottom-hole defects in plastic is shown in Fig. 12/. The time-domain image synthesized from 60 consecutive amplitude images and treated to smooth the noise is again presented in Fig. 12/. Applying the isotherm technique to the image in Fig.

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FIGURE 12. cont'd 12/, it is possible to get particular tomograms representing the specimen structure at a particular depth (Fig. 12£,/).

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FIGURE 12. cont'd. (See color plate.)

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FIGURE 12. cont'd. (See color plate.)

Application of the above expressions to tomography of the carbon epoxy specimen of thickness 2 mm described in §9.3 showed that there is a critical depth value (lCT) dependent on the data treatment method. For region I = 0 — lCT the resolved time is constant and equal to the IR imager field time r/, though the TANDT procedure itself can provide a better rres value. In this region the thickness of the resolved layer is nearly constant. For region lCT — L the specimen and heater determine the resolvable time

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value. The thickness of the resolvable layer changes sharply throughout the specimen. It is important to note that the best spatial resolution occurs naturally near the heated surface. The method described above allowed us to estimate the number of layers resolved with thermal tomography techniques in the range from 5 to 30 depending on the level of structural or detector noise. It was also shown that small variations (up to 20%) of the thermal parameters in the thin subsurface layers could hardly be detected with tomography techniques because of strong heat dissipation [49]. This means that thermal tomography is more suitable for air-containing defects. In spite of its novelty, this technique has proved its validity in investigations of impact-damaged carbon plastics [50]. 10. SIGNAL-TO-NOISE CONSIDERATIONS 10.1. Spatial Spectra of Noise and Signal Spatial filtration algorithms used to enhance the signal-to-noise ratio require a knowledge of the spatial spectra of useful signals and noise. A general approach suitable for IR imaging systems was described by Hudson [1]. In TANDT this field is hardly investigated. Vavilov proposed the following approximate expression for spectrum U{v) of the output electrical signal in the case when a rectangular spot travels with speed V across the defect area with a bell-shaped temperature signal [38]: U(v) =

Urnsa(7rum)exp(-2ir2i'H)i

where v = f/V is the spatial frequency; / is the electrical frequency; m is the size of the scanning spot; sa(x) = (sin#)/a;. Structural noise in many practical cases can be viewed as a stationary ergodic process with Gaussian statistical properties. It was stated that the noise and signal spectra cross each other, making spatial filtration difficult [38]. To determine the noise amplitude by a general statistical procedure would yield a rather large value of the standard deviation (a = 6Tn)> which is necessary to estimate TANDT possibilities (see §7.7). The corresponding noise contrast (An = sa/th) is given in Table 9 for s = 2 (corresponding to a false alarm probability of 2.3%). Another approach to estimating the threshold value of noise contrast is to omit the low trend in temperature profiles because of edge influence, nonuniform heating, reflections, etc. In this case, only small apparentdefect positive or negative signals can be viewed, and the noise can be

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Table 9. Parameters of Optical Noise for Active TANDT Procedure (Indium Antimonide IR Detector, Scanning Spot 0.8 mm, Heater with Open Filament) Material and surface conditions Stainless steel Steel with corrosion spots Steel with corrosion spots (scanning spot increased up to 2.5 mm) Copper oxidized Copper covered with black lacquer Copper covered with red point Copper covered with black soot Copper covered with black soot and scratched Copper covered with black soot and scratched (scanning spot increased up to 2.5 mm) Aluminium Brass covered with aquadag Brass covered with boron nitride Glass-cloth-base laminate Teflon (fluoroplastic) Cloth-based laminate Carbon epoxy plastic Carbon epoxy plastic* raw image smoothed with filter 3 x 3 high-frequency filtering 3 x 3

Noise temperature contrast, At = 2o/th, %

Max. relative amplitude of local signal, %

14.3 34.2 22.2

4.7 60.0 28.6

4.9 10.2 8.8 5.6 28.0

5.8 8.2 5.0 7.5 30.0

27.0

15.0

14.3 -

-

13.0 4.0 15.0 3.9 2.0 0.6 12.0

6.4 5.2 13.6

-

1.5 1.1

*Results are extracted from IR images obtained with Inframetrics Inc. equipment.

characterized by value An = ATm/th, where AT m is the maximum temperature signal found by an operator in the nondefect profile [13]. These values are also given in Table 9. The data of this table illustrate the influence of a bigger scanning spot which integrates small irregularities, the

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effect of "black painting," and data processing. This approach resembles low-frequency filtration and requires an experienced operator. 10.2. Emissivity Problem Suppression of emissivity noise is one of the central problems of IR pyrometry. It has two aspects related to TANDT problems: 1) an unknown emissivity value makes real temperature measurements impossible, which is not so important for defect detection, though inverse algorithms need exact temperature values; 2) fluctuation of emissivity is a source of false signals, thus perturbing the test procedure. There are many "cute" methods developed in IR pyrometry to take emissivity into account, but their validity for TANDT is questionable due to the following factors: • Thermographic procedures require correction for emissivity variations not in single points but over a large area. • Pyrometry methods are usually too slow. • Multicolor methods suitable for high temperatures are of small interest for temperatures close to the ambient because of the small difference in thermal radiation between neighboring spectral bands. Short descriptions of methods for correcting emissivity effects are given in Table 10. This table describes methods requiring some preliminary information about the object to be tested and the methods for processing the radiation flux. The most popular method from the first group is the well known "black painting," using coatings which could be easily applied and then removed from the surface: soot, paint, acquadag, etc. Some technical problems can arise in this case, such as air bubbles under the coating or visibility of the host specimen through the coating. Comparison with a reference specimen (in the visual or IR regions) is the other most popular method. In active TANDT, the tested specimen itself can play the role of reference when the defect is not yet seen. The modern version of this method pioneered by Green [8] can involve pixel-by-pixel division with prerecorded IR images. Figure 13a shows a thermogram of a carbon plastic composite with delamination and surface irregularity (green area) (the same specimen as in Fig. 8g). After dividing this image by the image recorded at the very end of the cooling process, the final thermogram without the presence of a large area of noise is obtained (Fig. 136).

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Table 10. Methods for Emissivity Correction in IR Pyrometry Short description

Method Methods requiring preliminary processing of an object tested "Black painting"

Primer, soot enamel, paint acquadag, etc. are used as coatings. Low productivity. Not suitable for objects with complex shape. Emissivity depends on the type, thickness and adhesion quality of coating.

"Forcing" the radiation

Radiation from inspected surface is made to resemble black body radiation using holes and placing some additional devices near the surface (reflecting sphere, adiabatic plate(s), etc.). Not suitable for quick scanning of objects.

Change of the temperature of IR detector

Based on third law of thermodynamics/ heat exchange is absent between bodies with the same temperature. Complex shape of the detector makes it barely suitable for quick TANDT.

Comparison with reference specimen

Emissivity value is not determined. Detection of defects occurs if the signal is outside of statistical variation level. Popular in radioelectronics.

Contact with compressible high emissivity body

Tested object is put into contact after heating with compressible high emissivity body and observation of this body is performed.

Recording of transient temperature at the different times

Proposed for active TANDT and based on the fact that the emissivity signal occurs all the time but the defect signal varies over time.

External irradiation

Emissivity value is determined by reflection. Spectral composition of irradiation has to fit the thermal radiation of a specimen.

Heating of an object in thermal camera

Used in radioelectronics. First the emissivity is determined, then measured values are corrected. Based on the weak dependence of emissivity on temperature.

Processing of thermal flux Use of short wavelength spectrum

Based on relative increase of temperature sensitivity by using shorter wavelength. Limited by reduction of absolute temperature resolution and increase of background noise.

Multicolor method

Many modifications are often used in high-temperature pyrometry. Barely suitable for TANDT because of weak dependence on wavelength at temperatures close to ambient.

Polarization method

Uses polarization effects. Labor-consuming. Applicability in TANDT is not clear.

Mathematical processing of spectrum

Based on solution of equations with many unknown values. Labor-consuming. Applicability in TANDT is not clear.

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FIGURE 13. Suppression of emissivity noise through division of thermograms taken at different times: a — IR image of carbon epoxy composite with delamination (red area) and emissivity noise (green area); b — resulting image. (See color plate.)

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10.3. Statistical Decision Making TANDT devices can be viewed as pattern recognition systems which, in the simplest case, classify tested objects as "good" or "bad," depending on the set of used features. Recognition of an object involves its comparison with reference features and classification into two or more classes. When classifying objects based on amplitude features, threshold value C/th depends on the required values of probability of false alarm (P{