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ACOUSTICAL IMAGING

TECHNIQUES AND APPLICATIONS FOR ENGINEERS

Woon Siong Gan

Acoustical Technologies Singapore Pte Ltd

A John Wiley & Sons, Ltd., Publication

This edition ﬁrst published 2012C 2012 John Wiley & Sons, Ltd

Registered ofﬁce

John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex, PO19 8SQ, United Kingdom

For details of our global editorial ofﬁces, for customer services and for information about how to apply for permission to reuse the copyright material in this book please see our website at www.wiley.com.

The right of the author to be identiﬁed as the author of this work has been asserted in accordance with the Copyright, Designs and Patents Act 1988.

All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, except as permitted by the UK Copyright, Designs and Patents Act 1988, without the prior permission of the publisher.

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Designations used by companies to distinguish their products are often claimed as trademarks. All brand names and product names used in this book are trade names, service marks, trademarks or registered trademarks of their respective owners. The publisher is not associated with any product or vendor mentioned in this book. This publication is designed to provide accurate and authoritative information in regard to the subject matter covered. It is sold on the understanding that the publisher is not engaged in rendering professional services. If professional advice or other expert assistance is required, the services of a competent professional should be sought.

Library of Congress Cataloging-in-Publication Data

Gan, Woon Siong.

Acoustical imaging : techniques and applications for engineers / Woon Siong Gan. p. cm.

Includes bibliographical references and index. ISBN 978-0-470-66160-4 (hardback)

1.Acoustic imaging. 2. Sound-waves–Scattering. I. Title.

TA1770.G36 2012 620.2 8–dc23

2011052023

A catalogue record for this book is available from the British Library.

ISBN: 978-0-470-66160-4

Typeset in 10/12pt Times by Aptara Inc., New Delhi, India

Contents

About the Author			xv
Foreword			xvii
1	Introduction		1
	References		4
2	Physics of Acoustics and Acoustical Imaging		5
2.1	Introduction		5
2.2	Sound Propagation in Solids		5
	2.2.1	Derivation of Linear Wave Equation of Motion and
		its Solutions	5

2.2.2Symmetries in Linear Acoustic Wave Equations and the

		New Stress Field Equation	6
2.3	Use of Gauge Potential Theory to Solve Acoustic Wave Equations		7
2.4	Propagation of Finite Wave Amplitude Sound Wave in Solids		8
	2.4.1	Higher-Order Elasticity Theory	9
	2.4.2	Nonlinear Effects	9
	2.4.3	Derivation of the Nonlinear Acoustic Equation of Motion	9
	2.4.4	Solutions of the Higher-Order Acoustics Equations of Motion	10
2.5	Nonlinear Effects Due to Energy Absorption		11
	2.5.1	Energy Absorption Due to Thermal Conductivity	11
	2.5.2	Energy Absorption Due to Dislocation	11
2.6	Gauge Theory Formulation of Sound Propagation in Solids		12

2.6.1Introduction of a Covariant Derivative in the Inﬁnitesimal

Amplitude Sound Wave Equation

2.6.2Introduction of Covariant Derivative to the Large Amplitude

		Sound Wave Equation	13
	References		14
3	Signal Processing		15
3.1	Mathematical Tools in Signal Processing and Image Processing		15
	3.1.1	Matrix Theory	15

3.1.2

Some Properties of Matrices

vi			Contents
	3.1.3	Fourier Transformation	17
	3.1.4	The Z-Transform	22
3.2	Image Enhancement		23
	3.2.1	Spatial Low-Pass, High-Pass and Band-Pass Filtering	23
	3.2.2	Magniﬁcation and Interpolation (Zooming)	24
	3.2.3	Replication	24
	3.2.4	Linear Interpolation	24
	3.2.5	Transform Operation	24
3.3	Image Sampling and Quantization		24
	3.3.1	Sampling versus Replication	26
	3.3.2	Reconstruction of the Image from its Samples	26
	3.3.3	Nyquist Rate	27
	3.3.4	Sampling Theorem	27

3.3.5Examples of Application of Two-Dimensional

		Sampling Theory	27
	3.3.6	Sampling Theorem for Radom Fields	28
	3.3.7	Practical Limitation in Sampling and Reconstruction	28
	3.3.8	Image Quantization	28
3.4	Stochastic Modelling of Images		28
	3.4.1	Autoregressive Models	29
	3.4.2	Properties of AR Models	30
	3.4.3	Moving Average Model	30
3.5	Beamforming		30
	3.5.1	Principles of Beamforming	30
	3.5.2	Sonar Beamforming Requirements	32
3.6	Finite-Element Method		32
	3.6.1	Introduction	32
	3.6.2	Applications	33
3.7	Boundary Element Method		34
	3.7.1	Comparison to Other Methods	35
	References		36
4	Common Methodologies of Acoustical Imaging		37
4.1	Introduction		37
4.2	Tomography		37
	4.2.1	The Born Approximation	42
	4.2.2	The Rytov Approximation	42
	4.2.3	The Fourier Diffraction Theorem	43
	4.2.4	Reconstruction and Backpropagation Algorithm	44
4.3	Holography		50
	4.3.1	Liquid Surface Method	50
4.4	Pulse–Echo and Transmission Modes		53
	4.4.1	C-Scan Method	53
	4.4.2	B-Scan Method	55
4.5	Acoustic Microscopy		59
	References		60

Contents			vii
5	Time-Reversal Acoustics and Superresolution		63
5.1	Introduction		63
5.2	Theory of Time-Reversal Acoustics		63
	5.2.1	Time-Reversal Acoustics and Superresolution	68
5.3	Application of TR to Medical Ultrasound Imaging		69

5.4Application of Time-Reversal Acoustics to Ultrasonic

Nondestructive Testing		70
5.4.1	Theory of Time-Reversal Acoustics for Liquid–Solid Interface	72

5.4.2Experimental Implementation of the TRM for Nondestructive

		Testing Works	73
	5.4.3	Incoherent Summation	75
	5.4.4	Time Record of Signals Coming from a Speckle Noise Zone	76
	5.4.5	The Iterative Technique	77
	5.4.6	Iterative Process for a Zone Containing a Hard-Alpha	77
	5.4.7	Iterative Process as a Pure Speckle Noise Zone	77
5.5	Application of TRA to Landmine or Buried Object Detection		80
	5.5.1	Introduction	80
	5.5.2	Theory	81
	5.5.3	Experimental Procedure	82
	5.5.4	Experimental Setup	83
	5.5.5	Wiener Filter	84
	5.5.6	Experimental Results	84
5.6	Application of Time-Reversal Acoustics to Underwater Acoustics		86
	References		86
6	Nonlinear Acoustical Imaging		89
6.1	Application of Chaos Theory to Acoustical Imaging		89
	6.1.1	Nonlinear Problem Encountered in Diffraction Tomography	89
	6.1.2	Deﬁnition and History of Chaos	89
	6.1.3	Deﬁnition of Fractal	90
	6.1.4	The Link between Chaos and Fractals	91
	6.1.5	The Fractal Nature of Breast Cancer	92
	6.1.6	Types of Fractals	93
	6.1.7	Fractal Approximation	96
	6.1.8	Diffusion Limited Aggregation	96
	6.1.9	Growth Site Probability Distribution	96
	6.1.10	Approximating the Scattered Field Using GSPD	98
	6.1.11	Discrete Helmholtz Wave Equation	99
	6.1.12	Kaczmarz Algorithm	100
	6.1.13	Hounsﬁeld Method	101
	6.1.14	Applying GSPD into Kaczmarz Algorithm	102
	6.1.15	Fractal Algorithm Using Frequency Domain Interpolation	103

6.1.16Derivation of Fractal Algorithm’s Final Equation Using

	Frequency Domain Interpolation	103
6.1.17	Simulation Results	104
6.1.18	Comparison between Born and Fractal Approximations	106

viii			Contents
6.2	Nonclassical Nonlinear Acoustical Imaging		107
	6.2.1	Introduction	107
	6.2.2	Mechanisms of Harmonic Generation via CAN	108
	6.2.3	Nonlinear Resonance Modes	111
	6.2.4	Experimental Studies on Nonclassical CAN Spectra	112

6.2.5CAN Application for Nonlinear Acoustical Imaging

		and NDE	113
	6.2.6	Conclusion	115
6.3	Modulation Method of Nonlinear Acoustical Imaging		116
	6.3.1	Introduction	116
	6.3.2	Principles of Modulation Acoustic Method	117
	6.3.3	The Modulation Mode Method of Crack Location	117
	6.3.4	Experimental Procedure of the Modulation Method for NDT	118
	6.3.5	Experimental Procedures for the Modulation Mode System	118
	6.3.6	Conclusions	121
6.4	Harmonic Imaging		121
	References		122
7	High-Frequencies Acoustical Imaging		125
7.1	Introduction		125
7.2	Transducers		125
7.3	Electronic Circuitry		126
7.4	Software		127

7.5Applications of High-Frequencies In Vivo Ultrasound

	Imaging System		127
7.6	System of 150 MHz Ultrasound Imaging of the Skin and the Eye		128
7.7	Signal Processing for the 150 MHz System		129
7.8	Electronic Circuits of Acoustical Microscope		135
	7.8.1	Gated Signal and Its Use in Acoustical Microscope	135
	7.8.2	Quasi-Monochromatic Systems	137
	7.8.3	Very Short Pulse Technique	138
	References		138
8	Statistical Treatment of Acoustical Imaging		141
8.1	Introduction		141
8.2	Scattering by Inhomogeneities		142
8.3	Study of the Statistical Properties of the Waveﬁeld		143
	8.3.1	Fresnal Approximation or Near-Field Approximation	146
	8.3.2	Farﬁeld Imaging Condition (Fraunhofer Approximation)	147
	8.3.3	Correlation of Fluctuations	152
	8.3.4	Quasi-static Condition	156
	8.3.5	The Time Autocorrelation of the Amplitude Fluctuations	157
	8.3.6	Experimental Veriﬁcation	160

8.3.7Application of Fluctuation Theory to the Diffraction Image

	of a Focusing System	162
8.3.8	Conclusion	163

Contents			ix
8.4	Continuum Medium Approach of Statistical Treatment		163
	8.4.1	Introduction	163
	8.4.2	Parabolic Equation Theory	163
	8.4.3	Assumption for the Refractive Index Fluctuation	164
	8.4.4	Equation for the Average Field and General Solution	165
	References		168
9	Nondestructive Testing		169
9.1	Defects Characterization		169
9.2	Automated Ultrasonic Testing		171
	9.2.1	Introduction	171
	9.2.2	Testing Procedure	172
	9.2.3	Example of an AUT System	173

9.2.4Signal Processing and Automatic Defects and Features

		Clariﬁcation in AUT	174
9.3	Guided Waves Used in Acoustical Imaging for NDT		176
9.4	Ultrasonic Technologies for Stress Measurement and Material Studies		178
	9.4.1	Introduction	178
	9.4.2	Internal Stress Measurements	180
	9.4.3	V(z) Curve Technique in the Characterization of Kissing Bond	183
9.5	Dry Contact or Noncontact Transducers		185
	9.5.1	Defect Depth, Sizing and Characterization	185
	9.5.2	Pitch/Catch Swept Method	185
	9.5.3	Pitch/Catch Impulse Method	185
	9.5.4	MIA Test Method	185
9.6	Phased Array Transducers		186
	9.6.1	Introduction	186
	9.6.2	Meaning of Phased Array	187
	9.6.3	Principle of Phased Array Ultrasonic Technology	188
	9.6.4	Focal Laws	191
	9.6.5	Basic Scanning and Imaging	191

9.6.6Advantages of Phased Array Testing as Compared with

		Conventional UT	192
	References		193
10	Medical Ultrasound Imaging		195
10.1	Introduction		195
10.2	Physical Principles of Sound Propagation		196
	10.2.1	Propagation of Sound Wave in Solids	196
	10.2.2	Contrast	197
10.3	Imaging Modes		198
	10.3.1	B-Scan	198
	10.3.2	C-Scan	205
10.4	B-scan Instrumentation		207
	10.4.1	Manual Systems	207
	10.4.2	Real-Time System	210

x			Contents
	10.4.3	Mechanical Scan	210
	10.4.4	Electronic Scan	211
10.5	C-scan Instrumentation		217
	10.5.1	Sokolov Tube	217
	10.5.2	Ultrasonic Holography	218
10.6	Tissue Harmonic Imaging		220
	10.6.1	Introduction	220
	10.6.2	Principles of Tissue Harmonic Imaging	221
	10.6.3	Image Formation in Tissue Harmonics	224
	10.6.4	Tissue Harmonic Image Characteristics	226
	10.6.5	Some Examples of Commercial Systems	228
10.7	Elasticity Imaging		228
	10.7.1	Introduction	228
	10.7.2	Comparison of Human Palpation and Elasticity Imaging	229
	10.7.3	Choice of Force Stimulus and Imaging Modality	231
	10.7.4	Physics of Elasticity Imaging	233
	10.7.5	Image Formation Algorithm	236
	10.7.6	Some Examples of Commercial Systems	238
10.8	Colour Doppler Imaging		244
	10.8.1	Doppler Ultrasound	244
	10.8.2	Pulsed (Gated) and Spectral Doppler	245
	10.8.3	Quantitative Doppler Techniques	246
	10.8.4	Velocity Measurements	247
	10.8.5	Spectral Doppler Waveform Measurements	247
	10.8.6	Volume Blood Flow Measurements	248
	10.8.7	Colour Doppler	248
	10.8.8	Newer Techniques	250
10.9	Contrast-Enhanced Ultrasound		250
	10.9.1	Introduction	250
	10.9.2	Bubble Echocardiogram	251
	10.9.3	Microbubble Contrast Agents	251
	10.9.4	How it Works	253
	10.9.5	Applications	253
10.10 3D Ultrasound Medical Imaging			254
	10.10.1	Introduction	254
	10.10.2	Elective 3D Ultrasound	255
	10.10.3	Risk Reduction of 3D Ultrasounds	257
	10.10.4	Future Developments	257
	10.10.5	Regional Anaesthesia	258
10.11	Development Trends		258
	References		259
11	Underwater Acoustical Imaging		263
11.1	Introduction		263
11.2 Principles of Underwater Acoustical Imaging Systems			264
	11.2.1	Spreading Loss	264

11.2.2

Attenuation Loss

264

Contents			xi
	11.2.3	Propagation Theory	265
	11.2.4	Reﬂection and Scattering from the Sea Surface	266
	11.2.5	Reﬂection and Scattering from the Sea Bottom	267
	11.2.6	Sea Bottom – Reﬂection Loss	267
	11.2.7	Sound Channel	269
11.3	Principles of Some Underwater Acoustical Imaging Systems		270
11.4	Characteristics of Underwater Acoustical Imaging Systems		273
11.5	Imaging Modalities		275
	11.5.1	Sonar Acoustical Imaging	275
	11.5.2	Orthoscopic Acoustical Imaging	277
11.6	A Few Representative Underwater Acoustical Imaging System		278
	11.6.1	Focused Acoustical Imaging System	278

11.6.2Electronic Beam-Focused Underwater Acoustical

		Imaging System	279
	11.6.3	Holographic Acoustical Imaging	283
11.7	Application of Robotics to Underwater Acoustical Imaging		287
	References		287
12	Geophysical Exploration		289
12.1	Introduction		289
12.2	Applications of Acoustical Holography to Seismic Imaging		290
12.3	Examples of Field Experiments		291
	12.3.1	One-Dimensional Holographic Arrays	291
	12.3.2	Two-Dimensional Holographic Arrays	292
12.4	Laboratory Modelling		297
12.5	Techniques of Image Processing and Enhancement		297
	12.5.1	Weak Signal Enhancement	298
	12.5.2	Phase Contrast Enhancement Technique	298
12.6	Computer Reconstruction		298
	12.6.1	Removal of Conjugate Images	299
	12.6.2	Fourier Transform Hologram	299
	12.6.3	Examples of Computer Reconstruction	300
	12.6.4	Backward Wave Propagation or Frequency Domain Migration	302
	12.6.5	Correlation Holography	302
12.7	Other Applications of Seismic Holography		303
	12.7.1	Monitoring Burning Fronts in Oil-Shale Retorts	303
12.8	Signal Processing in Seismic Holography		303
	12.8.1	Velocity Filtering	303
	12.8.2	Two-Dimensional Fourier Transform Techniques	304
	12.8.3	Tau-p Transform (Slant Stack)	305
	12.8.4	The Inverse Tau-p Transform	306
	12.8.5	Examples of k-ω and Tau-p Transforms	308
12.9	Application of Diffraction Tomography to Seismic Imaging		310
	12.9.1	Reconstruction Algorithms	317
	12.9.2	Computer Simulations for the VSP Case	321
12.10	Conclusions		322
	References		323

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