Advances in Acoustic Microscopy Volume 2

Advances in Acoustic Microscopy Volume 2

Edited by

Andrew Briggs University of Oxford Oxford, United Kingdom

and

Waiter Arnold Fraunhofer Institute for Nondestructive Testing Saarbriicken, Germany

Springer Science+Business Media, LLC

The Library of Congress cataloged the first volume of this title as follows:

Advances in acoustic microscopy / edited by Andrew Briggs. p. cm.

Includes bibliographical references and index. I. Materials--Microscopy. 2. Acoustic microscopy. I. Briggs, Andrew.

TA417.23.A38 1994 620.1' I 274-dc20

ISBN 978-1-46l3-7682-8 ISBN 978-1-4615-5851-4 (eBook) DOl 10.1007/978-1-4615-5851-4

© 1996 Springer Science+Business Media New York Originally published by Plenum Press in 1996 Softcover reprint of the hardcover 1 st edition 1996

10 9 8 7 6 54 32 1

All rights reserved

95-3646 CIP

No part of this book may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording, or otherwise, without written permission from the Publisher

For Diana, Felicity, Lizzie, and Inge

You listen with your eyes and see with your ears.

-Tim Winton

Contributors

Marceau Berson, INSERM, Universite de Tours, 37032 Tours-cedex, France

Guy Feuillard, JE 409, GIP ULTRASONS, Universite de Tours, 37032 Tours-cedex, France

Mathias Fink, Laboratoire Ondes et Acoustique, ESPCI, Universite Paris VII, URA CNRS 1503, 75005 Paris, France

Wolfgang Grill, Physikalisches Institut der Johann Wolfgang Goethe-Univer­sitat Frankfurt am Main, 0-60325 Frankfurt am Main, Germany; present ad­dress: Institut flir Experimentalphysik II der Universitat Leipzig, 0-04103 Leipzig, Germany

Kristian Hillman, Physikalisches Institut der Johann Wolfgang Goethe-Uni­versitat Frankfurt am Main, 0-60325 Frankfurt am Main, Germany

Marc Lethiecq, JE 409, GIP ULTRASONS, Universite de Tours, 37032 Tours-cedex, France

Noritaka Nakaso, Toppan Technical Research Institute, Saitama 345, Japan

Katsumi Ohira, Toppan Technical Research Institute, Saitama 345, Japan

'Frederic Patat, JE 409, GIP ULTRASONS, Universite de Tours, 37032 Tours-cedex, France

Gabriele Pfannschmidt, Siemens AG, 0-81541 Munich, Germany vii

viii CONTRIBUTORS

Claire Prada, Laboratoire Ondes et Acoustique, ESPCI, Universite Paris VII, URA CNRS 1503, 75005 Paris, France

Yusuke Tsukahara, Toppan Technical Research Institute, Saitama 345, Japan

Joachim Wesner, Physikalisches Institut der Johann Wolfgang Goethe-Uni­versitat Frankfurt am Main, 0-60325 Frankfurt am Main, Germany; present address: Leica Mikroskopie und Systeme GmbH, 0-35530 Wetzlar, Germany

Karl Ulrich Wiirz, Physikalisches Institut der Johann Wolfgang Goethe-Uni­versitat Frankfurt am Main, 0-60325 Frankfurt am Main, Germany

Masa-aki Yanaka, Toppan Technical Research Institute, Saitama 345, Japan

Preface

This is the second volume of Advances in Acoustic Microscopy. It continues the aim of presenting applications and developments of techniques that are related to high-resolution acoustic imaging. We are very grateful to the authors who have devoted considerable time to preparing these chapters, each of which describes a field of growing importance. Laboratories that have high-performance acoustic microscopes are frequently asked to examine samples for which the highest available resolution is not necessary, and the ability to penetrate opaque layers is more significant. Such applications can be thought of as bridging the gap be­tween acoustic microscopy at low gigahertz frequencies, and on the one hand nondestructive testing of materials at low megahertz frequencies and on the other hand medical ultrasonic imaging at low megahertz frequencies. Commercial acoustic microscopes are becoming increasingly available and popular for such applications. We are therefore delighted to be able to begin the volume with chapters from each of those two fields.

The first chapter, by Gabriele Pfannschmidt, describes uses of acoustic microscopy in the semiconductor industry. It provides a splendid balance to the opening chapter of Volume 1, which came from a national research center, being written from within a major European electronics industry itself. Dr Pfann­schmidt describes the use of two quite different types of acoustic microscopes, and points out the advantages of each for specific purposes. She carefully com­pares the results with more conventional radiography, and makes it clear in what cases acoustic microscopy is able to reveal defects that cannot be characterized by radiography. She also makes a clear distinction between what can be seen nondestructively and what must be reserved for the failure analysis laboratory. The chapter is extensively illustrated with a large range of examples from practi­cal experience, and it concludes with a summary of the requirements for acoustic microscopy in several international quality standards.

ix

x PREFACE

Clinical medical ultrasonic imaging is generally carried out at a frequency of about 5 MHz. This is because for imaging internal organs or a fetus it is necessary to penetrate several centimeters of tissue, and at higher frequencies the attenuation would be too great. But there are a number of important medical applications of ultrasonic imaging for which high penetration is not necessary because it is possible to place the transducer close to the tissue to be charac­terized. Examples include the skin, the interior of the eye, and the walls of blood vessels where an ultrasound catheter can be inserted. For all of these it is possible to use frequencies of up to 50 MHz or even higher, with a consequent im­provement of a factor of ten in the resolution over conventional medical ultra­sound. The techniques and applications described in Chapter 2, combined with laboratory studies using acoustic microscopy at these higher frequencies at Aarhus and elsewhere, may be expected to lead to significant advances in clinical diagnosis.

In applications of acoustic microscopy to materials characterization, the reflection of acoustic waves from the fluid-solid interface plays a crucial role. This is true both for imaging and for quantitative characterization of the elastic properties of surfaces by V(z) measurements and related techniques (cf. Chapters 5 and 6 of Volume 1). There are various surprises in store for the unwary: For example, measurements of the longitudinal wave velocity by line-focus-beam acoustic microscopy give a result that is about 50 ms- I slower than the bulk wave velocity. There are also a number of phenomena that can be exploited to advantage: An example is the excitation of Sezawa waves when a slow material such as a polymer coating is on a stiffer material. Dr. Tsukahara and his col­leagues from Toppan present a definitive study of the behavior of acoustic waves incident from a fluid on a solid surface. It is notable that such a rigorous funda­mental analysis should have been developed in an industrial laboratory. The analysis is applied to a variety of measurements of materials in an ultrasonic microspectrometer-a technique that measures surface wave excitation by an­alyzing the frequency response at a constant geometry [the V(f) technique de­scribed in Chapter 4 of Volume 1 has much in common with this). Some com­pletely new measurements of wedge waves are presented.

It has long been recognized that phase information is present in the detected acoustic signal in acoustic microscopy, but that this is discarded in most detec­tion systems. In Chapter 4, Professor Wolfgang Grill and his colleagues present a phase-sensitive acoustic microscope that has a demonstrated performance up to 1.2 GHz. The development of the instrument was originally stimulated by Pro­fessor Bereiter-Hahn for measuring the elastic properties of living cells by acous­tic microscopy (Volume 1, Chapter 3). The principles of the apparatus are described, and a number of applications in reflection are shown, including sensi­tive measurements of topography and combination with atomic force microscopy (combination with ultrasonic force microscopy remains to be achieved). Some

PREFACE xi

very elegant images are obtained in transmission, using separate lenses to trans­mit and receive. By this means it is possible to image the effects of anisotropy in single crystals, whereby the direction of energy propagation is no longer perpen­dicular to the wave fronts as it is in isotropic materials. These effects have long been known for phonons, especially in low-temperature physics, and there is now growing activity worldwide (in places as far apart as Illinois and Johan­nesburg) to study the effects with coherent acoustic waves. The beautiful patterns that are seen from samples such as wafers of semiconductor materials can be inverted to yield the anisotropic elastic constants.

Volume 1 ended with two chapters describing techniques that were related to acoustic microscopy, but went beyond conventional acoustic microscopy in new ways. We have continued this tradition in Volume 2. The final chapter describes how to use acoustic time reversal mirrors to make sharp diffraction­limited images of objects through media that introduce random distortions. Time reversal has long been used with light using phase-conjugate four-wave mixing to reverse the wave vectors, and that technique has also been used with phonons in solids. It requires a nonlinear interaction between the incident wave and two high-amplitude pump waves, in order to produce a fourth time-reversed wave that will exactly cancel out the distortions in the path back to the detector. Such a scheme has been proposed (but never implemented) for nondestructive inspection through highly inhomogeneous materials, such as austenitic stainless steel cladding on pressure vessels for power generation. Digital waveform cap­ture techniques are fast enough to enable ultrasonic waves to be recorded and time-reversed digitally, and Mathias Fink and Claire Prada present a variety of uses of digital time reversal mirrors. Applications to a number of problems are shown, including the characterization of cylindrical objects by creeping waves. They have developed sophisticated algorithms for optimizing the signals through distorting media, including an automatic method for focusing on the most strong­ly scattering feature within an object.

As with Volume 1 (Plenum Press, 1995), a knowledge of the basic princi­ples of acoustics and techniques described in the monograph Acoustic Microsco­py (Oxford, Clarendon Press, 1992) is assumed, and is not repeated here. We hope that this new volume will prove of great interest, and will help many readers to learn about the marvelous advances that are being made in the field.

Oxford and Saarbrucken

Andrew Briggs Walter Arnold

Contents

List of Symbols and Abbreviations. . . . . . . . . . . . . . . . . . . . . . . . . . XIX

1. Characterization of Electronic Components by Acoustic Microscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

Gabriele Pfannschmidt

I . I. Introduction......................................... I 1.2. Commonly Used Ultrasonic Microscope Equipment. . . . . . . . 2 1.3. Failure Mechanisms Induced by Assembly-Related Problems 3 1.4. Advantages and Limitations of Acoustic Microscopy in the

Semiconductor Industry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.5. Ultrasonic Microscope Applications in the Production,

Qualification, and Failure Analysis of Semiconductor Devices. .... .. ..... .... ..... .... ........... ...... .. 8 1.5.1 Acoustic Microscopy Investigations of Ceramic

Packages. . . . . . . . . . . . . .. . . . .. . .. . . . . . . . . . . . . . . . 8 1.5.2 Investigation of Die Attach by SAM, SLAM, and X

Rays. . . . . . . .. . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . 10 1.5.3 Die Attach Investigations Using Acoustic Microscopy

in Correlation with Other Techniques. . . . . . . . . . . . . . . 16 1.5.4 Detection of Delaminations: A Comparison between

the Dye Penetration Test and Acoustic Microscopy . . . 19 1.5.5 Detection of Die Cracks Using SLAM and SAM. . . . . 21 1.5.6 Investigation of Cracks in the Plastic Encapsulant of

ICs. . . . . . . . . .. . . . . . . . . . . . . .. . .. . .. . . . . . . . . . . . . 23 1. 5.7 Investigation of Molding Compounds by Different

Ultrasonic Scanning Techniques Using SAM. . . . . . . . 25 xiii

xiv CONTENTS

1.5.8 Investigation of Solder Joints on Printed Circuit Boards........................................ 30

1.5.9 Special Effects Imaged by Acoustic Microscopy. . . . . . 33 1.6. Conclusions......................................... 35 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

2. Principles and Applications of High-Frequency Medical Imaging 39

Marc Lethiecq, Marceau Berson, Guy Feuillard, and Frederic Patat

2.1. Introduction......................................... 39 2.2. Historical Perspective of Echographic Concepts. . . . . . . . . . . 41 2.3. High-Frequency Medical Ultrasonic Systems. . . . . . . . . . . . . . 45

2.3.1 Interest and Constraints Linked to High-Frequency Operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

2.3.2 Basic Schematics of a High-Frequency Imaging System ..................... "................... 46

2.4. Scanning Modes and Scanning Electronics. . . . . . . . . . . . . . . . 49 2.4.1 Single-Element Transducer Probes. . . . . . . . . . . . . . . . . 49 2.4.2 Array-Transducer Probes... ... ... ... . . ... ... . ... . 51 2.4.3 Three-Dimensional and C Scans. . . . . . . . . . . . . . . . . . . 53 2.4.4 Image Display. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

2.5. Ultrasonic High-Frequency Imaging Transducers. . . . . . . . . . 55 2.5.1 Electroacoustic Aspects. . . . . . . . . . . . . . . . . . . . . . . . . . 55 2.5.2 Piezoelectric Materials for High-Frequency

Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 2.5.3 Passive Materials for High-Frequency Applications. . . 61 2.5.4 Characterization Methods. . . . . . . . . . . . . . . . . . . . . . . . 61 2.5.5 Transducer Technology. . . . . . . . . . . . . . . . . . . . . . . . . . 64

2.6. Dermatological Applications. . . . . . . . . . . . . . . . . . . . . . . . . . . 70 2.6.1 Skin Structure.................................. 71 2.6.2 Ultrasound Examination of the Skin... . . ... .... .. .. 71 2.6.3 Conclusion... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

2.7. Ophthalmological Applications . . . . . . . . . . . . . . . . . . . . . . . . . 77 2.7.1 Anatomy, Size, and Properties of Eye Structures. . . . . 78 2.7.2 Imaging of the Ocular Globe ..................... 79 2.7.3 Imaging of the Anterior Segment. . . . . . . . . . . . . . . . . . 80 2.7.4 Conclusion . . .. . .. . .. . .. . . . .. . . . . . . . .. . . . . . . . . . 89

2.8. Intravascular Ultrasound Imaging. . . . . . . . . . . . . . . . . . . . . . . 90 2.8.1 Anatomy and Exploration of the Arterial Walls. . . . . . 91 2.8.2 Imaging of Normal and Pathological Arteries. . . . . . . . 93

CONTENTS

2.9. Conclusion References ............................................. .

3. Interaction of Acoustic Waves with Solid Surfaces ..•..•••••.

Yusuke Tsukahara, Noritaka Nakaso, Katsumi Ohira, and Masa-aki Yanaka

xv

97 98

103

3.1. Introduction......................................... 103 3.2. Acoustic Reflection Coefficient at a Liquid/Solid Interface. . 104

3.2.1 Analytic Properties of Reflection Coefficient. . . . . . . . 104 3.2.2 Leaky Surface Acoustic Waves. . . . . . . . . . . . . . . . . . . . 105 3.2.3 LSSCW at a Longitudinal Critical Angle. . . . . . . . . . . . 108 3.2.4 What Happens When Acoustic Attenuation Is

Large?....................................... 113 3.3. Layered Materials and Guided Waves. . . . . . . . . . . . . . . . . . . 114

3.3.1 Calculation of Reflection Coefficients for Layered Materials. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114

3.3.2 Slow-on-Fast................................... 119 3.3.3 Fast-on-Slow.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122

3.4. Method and Apparatus of Measurement. . . . . . . . . . . . . . . . . . 125 3.4.1 Ultrasonic Microspectrometer with SPP Lenses. . . . . . 125 3.4.2 Theory. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 3.4.3 The Experimental System. . . . . . . . . . . . . . . . . . . . . . . . 133

3.5. Applications to Materials Characterization. . . . . . . . . . . . . . . . 138 3.5.1 Measurement of Reflection Coefficients. . . . . . . . . . . . . 138 3.5.2 Phase Velocity Measurement of Rayleigh Waves. . . . . 140 3.5.3 Acoustic Attenuation. . . . . . . . . . . . . . . . . . . . . . . . . . . . 144 3.5.4 Anisotropic Material ............................ 148 3.5.5 Leaky Wedge Acoustic Waves. ... ... .. ... . ... .. . . 150

3.6. Conclusion ......................................... 155 References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156 Appendixes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158

A.I. Analytic Continuation and Riemann Sheet. . . . . . . . . . . 158 A.2. Transformation Matrix for Abbreviated Stiffness

Constants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160 A.3. Mathematica Program for Reflection Coefficient. . . . . . 161

4. Scanning Ultrasonic Microscopy with Phase Contrast ....•... 167

Wolfgang Grill, Kristian Hillmann, Karl Ulrich Warz, and Joachim Wesner

4.1. The Phase-Sensitive Acoustic Microscope. . . . . . . . . . . . . . . . 167

xvi CONTENTS

4.1.1 Introduction 4.l.2 Detection Scheme .............................. . 4.l.3 Comparison with Optical Microscopy ............. . 4.1.4 Scanner ...................................... .

4.2. Topographical Measurements ......................... .

167 168 170 171 172 172 172 175 177 180 180 185 187 187 187 189 190 191 191 194 197 204

4.2.1 Introduction .................................. . 4.2.2 Resolution .................................... . 4.2.3 Applications .................................. . 4.2.4 Combined Applications with AFM ................ .

4.3. Lens Characterization ................................ . 4.3.1 Complex V(z) ................................. . 4.3.2 Holographic Characterization .................... .

4.4. Determination of the Elastic Properties of Small Samples .. . 4.4.1 Homogeneous Samples ......................... . 4.4.2 Indirectly Determined Surface Topography ......... . 4.4.3 Cells ........................................ . 4.4.4 Time-Resolved Characterization .................. .

4.5. Determination of Elastic Constants of Single Crystals ..... . 4.5.1 Introduction .................................. . 4.5.2 Review of Related Methods ..................... . 4.5.3 PSAM Experiments on Single Crystals ............ . 4.5.4 Comparison with Simulated Theoretical Images ..... . 4.5.5 Determination of Elastic Constants by Fitting

Procedure .................................... . 4.5.6 Results, Conclusions, and Outlook ................ .

References ............................................. .

5. Ultrasonic Focusing with Time Reversal Mirrors ..........•.

Mathias Fink and Claire Prada

212 216 216

219

5.l. Introduction......................................... 219 5.2. Principles of Time Reversal Acoustics. . . . . . . . . . . . . . . . . . . 221

5.2.1 Time Reversal of Ultrasonic Fields: Basic Principles. . 221 5.2.2 The Time Reversal Cavity. . . . . . . . . . . . . . . . . . . . . . . . 222 5.2.3 The Time Reversal Mirror. . . . . . . . . . . . . . . . . . . . . . . . 223 5.2.4 Comparison between Time Reversal and Phase-

Conjugated Mirrors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224 5.2.5 Ultrasonic Phase-Conjugated Mirrors. . . . . . . . . . . . . . . 226

5.3. Applications of Time Reversal Mirrors. . . . . . . . . . . . . . . . . . . 227 5.3.1 Echographic Focusing with a TRM . . . . . . . . . . . . . . . . 227 5.3.2 Autoadaptive Focusing in Solid Media: Applications

to NDT....................................... 230

CONTENTS XVII

5.3.3 Inverse Scattering Analysis with a TRM . . . . . . . . . . . . 234 5.3.4 The Iterative Time Reversal Process ............... 238

5.4. The DORT Method (Decomposition de l'Operateur de Retoumement Temporel) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241 5.4.1 Principle...................................... 241 5.4.2 Selective Focusing through an Inhomogeneous

Medium....................................... 244 5.4.3 Application to an Inverse Problem. . . . . . . . . . . . . . . . . 245

5.5. Conclusion ......................................... 249 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 250

Index. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253

Symbols and Abbreviations

Chapters where symbol or abbreviation is principally used are indicated.

AFM atomic force microscope 4 ai ith eigenvalue of matrix A 3 Ao first antisymmetrical Lamb wave 5 C capacitance 2 C scattering matrix 5 C speed of sound 2 C-AM C-mode acoustic microscope I C-SAM C-mode scanning acoustic mircoscope 1 Co sound velocity in water 5 q>3 open-circuit stiffness 2 Cej> phase velocity of Lamb wave 5 cij reduced stiffness matrix element 3 Cmn reduced elastic stiffness constant 4 D diameter of cylinder 5 D number of Rayleigh scatterers 5 d layer thickness 3 d lattice constant 4 d transducer diameter 2 dB decibel, unit of attenuation expressed as 10 3

X logarithm to base 10 of ratio of powers DIP dual in-line package DORT decomposition de l' operateur de

retoumement temporel 5 DRAM dual random access memory 1 DSO dual small outline

xix

XX SYMBOLS AND ABBREVIATIONS

e thickness of plate 2 e33 piezoelectric coefficient 2 e33 constant strain dielectric constant 2 E(w) complex-valued transmitted signal 5 em(t) transmitted signal from element m 5 F focal length of lens 3

f focal length 2 f frequency == wl2", 3 j{z) regular function in complex z-plane 3 Fe center frequency 2 Ff fast transverse 4 GHz gigahertz == 109 Hz 4 H propagation matrix 5 h1m(t) interelement impulse response 5 Hz hertz, cycles per second 1 IC integrated circuit 1 IVUS intravascular ultrasound 2 k wave vector 4 K(w) transfer matrix 5 ko leaky Rayleigh zero in complex plane 3 kjz wave-vector component perpendicular to 3

interface (j == w, 1, s) kp leaky Rayleigh pole in complex plane 3 kR real part of leaky Rayleigh wave number 3 KSI Kramer Scientific Instruments, Herbom, 4

Germany kl wave number of longitudinal waves in solid 3 ks wave number of shear waves in solid 3 k, piezoelectric coupling 2 kw wave number in liquid 3 kx wave-vector component parallel to interface 3 L longitudinal 4 LFBAM line-focus-beam acoustic microscope 3 LSAW leaky surface acoustic wave 3 LSSCW leaky surface skimming compressional wave 3 MHz megahertz == 106 Hz 4 MOSFET metal-ox ide-semiconductor field effect 2

transistor 2 MRayl unit of acoustic impedance, == 106 kg m-2 S-l NDT nondestructive testing 2,5 P(r,w) Fourier transform of p(r,w) 5

SYMBOLS AND ABBREVIATIONS xxi

p(r,t) pressure field 5 P-MQFP plastic metric quad flat pack P-QFP plastic quad flat pack P-TQFPxx plastic thin quad flat pack, xx = number of

pins PC polycarbonate 3 PCB printed circuit board I PCM phase-conjugated mirror 5 PLCC plastic leaded chip carrier I PS/PR point source/point receiver 4 PSAM phase-sensitive scanning acoustic microscope 4 PT modified lead titanate 2 PVOF poly(vinylidene fluoride) 2 P(VOF-TrFE) poly( vinylidene fluoride-trifluorethylene) 2 PZT lead zirconate titanate 2 Q quality factor, = 21T x ratio of energy 2

stored in an oscillation to energy lost per cycle

R amplitude of reflected wave 5 r correlation coefficient 4 r position vector 4 R(k) reflection coefficient as a function of kx 3 R(6) reflection coefficient as a function of 3

incident angle R(w) complex-valued received signal 5 r.h. relative humidity I Rd damping resistance 2 RF radio frequency 2,4 rj position vector 5 r,(t) received signal on element I 5 Rm impedance matching resistance 2 Ron resistance of transistor in "on" state 2 SIN signal-to-noise ratio 3 SAM scanning acoustic microscope 1,3,4 SAT scanning acoustic tomograph I SAW surface acoustic wave 3 SLAM scanning laser acoustic microscope 1,3 SMO surface-mounted device 1 So first symmetrical Lamb wave 5 SO] small outline ]-Ieaded I

xxii SYMBOLS AND ABBREVIATIONS

SPP spherical-planar-pair 3 ST slow transverse 4 T amplitude of transmitted wave 5 T time interval 5

time 5 td delay time 4 T-QFP thin quad flat pack 1 TAB tape automated bonded 1 TC thermal cycle 1 TGC time gain control 2 to backpropagation matrix 5 THz terahertz = 1012 Hz 4

Tmax maximum incident angle of lens (semiangle 3 of lens)

TO transistor outline I TRM time reversal mirror 5 TSOP thin small outline package I u(r,t) acoustic displacement field 5 UFI ultrasonic flux imaging 4 u/ displacement vector component 3 u/m strain tensor component 3 UMSM ultrasonic microspectrometer 3 V detected video output signal 3 V voltage 2 V(z) detected video signal V as a function of 3

defocus z Vg group velocity vector 4 VI longitudinal wave velocity in solid 2, 3 Vp phase velocity of LSA W 3 Vs shear wave velocity in solid 3 Vw sound velocity in liquid 3 x distance from source 2 Xm Cartesian coordinate vector 3 Xi ith eigenvector of matrix A 3 YAG yttrium aluminum garnet 3 Z acoustic impedance 2 z defocus (distance of sample surface beyond 3

focal plane) z distance from array 5 a attenuation coefficient 2 a imaginary part of leaky Rayleigh wave

number 3

SYMBOLS AND ABBREVIATIONS xxiii

ad attenuation factor due to dissipation of the 3 leaky Rayleigh wave

aL attenuation factor of leaky Rayleigh wave 3 0.1 longitudinal attenuation factor 3 at transverse attenuation factor 3

13 exponent in frequency dependence of 2 attenuation

13 x-component of wave vector 3 a anisotropy 4 8e dielectric loss 2 8m mechanical loss 2 TJijkl viscosity tensor 3 B angle of incidence 5 Be critical angle 3 Ole longitudinal critical angle of LSA W 3 OR Rayleigh critical angle 3 A wavelength 2, 4, 5 A Lame elastic stiffness constant 5 Ai(W) ith eigenvalue of time reversal operator 5 A ik1m stiffness tensor component 3 A1mjk stiffness tensor 3 IJ. Lame elastic stiffness constant (shear 5

modulus) v ultrasonic frequency 2 Va antiresonant frequency 2 P density 3 Ps density of solid 3, 5 Pw density of liquid 3 (J'ik stress tensor component 3 (J'lm stress tensor 3 '1'1 angular spectral distribution 3 W angular frequency = 2Tr1 3