ACOUSTICAL HOLOGRAPHY Volume 1

ACOUSTICAL HOLOGRAPHY Volume 1

Proceedings of the First International Symposium on Acoustical Holography held at the Douglas Advanced Research Laboratories, Huntington Beach, California December 14-15,1967

Edited by

A. F. Metherell Douglas Advanced Research Laboratories McDonnell Douglas Corporation Huntington Beach, California

H. M. A. EI-Sum EI-Sum Consultants Atherton, California

Lewis Larmore Douglas Advanced Research Laboratories McDonnell Douglas Corporation Huntington Beach, California

~ PLENUM PRESS • NEW YORK • 1969

First Printing-February 1969 Second Printing-May 1971

ISBN-13 :978-1-4615-8206-9 e-ISBN-13 :978-1-4615-8204-5

DOl: 10.1007/978-1-4615-8204-5

Library of Congress Catalog Card Number 69-12533

©1969 Plenum Press Softcover reprint of the hardcover 1st edition 1969

A Division of Plenum Publishing Corporation 227 West 17 Street, New York, N. Y. 10011

All rights reserved

No part of this publication may be reproduced in any form without permission from the publisher

ACOUSTICAL HOLOGRAPHY Volume 1

Speakers at the First International Symposium on Acoustical Holography . Reading from the left, Top Row: A. F. Metherell, Douglas Advanced Research Laboratories; A. A. DeSousa, UC Santa Barbara; H. Berger, Argonne National Laboratory; F . L. Thurstone, Duke University; J. W. Goodman, Stanford University; G. Wade, UC Santa Barbara. MIDDLE Row: B. B. Brenden, Ba/lel/e Memorial Research Institute; J. de Klerk, Westinghouse ; O. K. Mawardi, Case-Western Reserve University; A. Korpel, Zenith Radio Corporation; J. L. Kreuzer, Perkin-Elmer Corpora­tion; J. M. Smith, University of Toronto; C. J. Landry, UC Santa Barbara. FRONT Row : B. A. Auld, Stanford University; D. Gabor, Imperial Col/ege, University of London; J . J. Dreher, Douglas Advanced Research Laboratories; L. Larmore, Douglas Advanced Research Laboratories; H. M. A. EI-Sum, EI-Sum Consultants. Not shown: D. Fritzler and R. K. Mueller. Bendix Research Laboratories, Y. Aoki, Hokkaido University, and P. Greguss, RSRI Ultrasonics Laboratory.

PREFACE

Only a space limitation of 115 seats prevented this First International Symposium on Acoustical Holography from having an attendance of over 250. Unfortunately, the size of the auditorium of the Douglas Advanced Research Laboratories required that attendance be by invitation only, and many deserving and interested scientists could not be present. This volume presents the proceedings of the symposium, and hopefully will help compen­sate those individuals who were unable to attend.

The symposium itself consisted of sixteen formal papers. The seven­teenth, by Dr. P. Greguss, was not received in time to be read but is included in these proceedings. The presence of Professor Dennis Gabor considerably enhanced the informal sessions, which frequently became as spirited as one might expect in a new field.

Dr. H. M. A. El-Sum, a consultant to the Douglas Advanced Research Laboratories and a pioneer in the field of holography, set the stage with the first paper. He provided a general introduction to the physical principles and practical methods involved in optical and acoustical holography. His paper also included a summary of various specific techniques currently used in sound holography, with the advantages, disadvantages, and limitations involved for each approach.

Mr. Harold Berger, of the Argonne National Laboratory, concentrated on the various methods for detecting ultrasonic images. He categorized the methods into (1) photographic and chemical, (2) thermal, (3) optical and mechanical, and (4) electronic. Each of the four methods requires a threshold ultrasonic radiation intensity which varies from 1 W /cm2 for the photo­graphic and chemical to values at least eleven orders of magnitude lower for the electronic techniques.

Bendix Research Laboratories' work on using a liquid-gas interface as a recording medium was reported by Dr. R. K. Mueller. Sound waves impinging on a liquid-gas interface generate a surface deformation consisting of components proportional to linear and quadratic terms in the acoustic amplitUde. The quadratic term seems to be the more important for acoustical hologram formation, but the paper discussed the implication of both terms.

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Dr. Byron B. Brenden, of Battelle Memorial Research Institute, com­pared the two principal methods of imaging ultrasound by holography with reconstruction in light. One case employs a scanned acoustical receiver and a modulated 11ght source. The other uses a liquid surface to record the holo­gram by means of a reflected light beam. He showed several examples of holograms and their reconstructed images produced by both methods.

Mr. Justin L. Kreuzer, of Perkin-Elmer Corporation, discussed the feasibility of applying acoustical holographic techniques to obtain three­dimensional images of opaque objects encountered in nondestructive testing. He found that acoustic wavelengths of 0.3 mm in water provided image detail smaller than 1 mm. Several typical holograms and their re­constructions showed the feasibility of this method, which promises to be an extremely useful tool in the future.

The application of Fourier transforms in assessing the performance of ultrasonic holography systems was reported by Mr. 1. M. Smith, of the Institute of Biomedical Electronics, University of Toronto, Canada. He considered the events in the frequency domain, which allows a graphical representation of the effects of system parameters. By using the association between frequency components and resolution he determined the corres­ponding effects in the spatial domain. This kind of analysis provides an aid to assessing the maximum useful frequency and justifies the use of the spatial frequency of an extreme ray as the maximum frequency of interest.

Dr. F. L. Thurstone, of Duke University, presented some interesting ideas concerning applications of ultrasound holography to biomedical problems. The possibility of using acoustical techniques to replace X rays for certain diagnostic information shows much promise and was also mentioned by other speakers. However, the nature of the propagation of ultrasound in biologic tissue and the resulting image information present in an ultrasound field emanating from such a subject have yet to be fully understood or analyzed.

One of the interesting problems in the field of animal communication concerns the ability of porpoises and dolphins to use echo-location for discrimination between real and false targets. Dr. John Dreher, ofthe Douglas Advanced Research Laboratories, gave new insight to a possible explanation of this phenomenon. An anatomical description of these animals reveals a possible array of acoustical sensors in the "fatty melon" portion of the animal's head. This array compares with the scanning systems or the liquid­gas interface array used in acoustical holography. Dr. Dreher postulated that these animals possess a neural network which allows them to reconstruct images by means of a holographic process.

Dr. John de Klerk, of Westinghouse Research Laboratories, reviewed the most promising techniques for sound generation as applied to acoustical

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holography. His presentation covered methods and problems in the fre­quency range from audio to microwave regions. Special emphasis was placed on the high-frequency spectrum, where sound and optical wavelengths are more nearly comparable.

Although not strictly a holographic technique, acoustical imaging by Bragg diffraction offers promise as an alternate method for producing visual images of a sound source. Mr. A. Korpel, of Zenith Radio Corporation, presented the theory behind this technique and showed some experimental results. In particular, he discussed the property of imaging in depth which is inherent in this process and compared it with optical holographic methods.

Dr. Glen Wade, of the University of California at Santa Barbara, presented the results of the UCSB research utilizing acoustic transparencies for optical imaging and ultrasonic diffraction. This research team illuminates coherent sound in water with either converging or diverging laser light which, in turn, images the cross section of the sound beam. Elastic plates inserted in the sound beam can be rendered acoustically transparent under certain conditions. By treating the back surface of such plates with metal deposits the reconstruction of these deposits appears in the laser beam. Dr. Wade showed examples of line drawings and other figures reconstructed in this manner.

Many workers in acoustical holography have suggested that the re­construction process be accomplished with a computer instead of the usual optical technique. A study by Dr. 1. W. Goodman, of Stanford University, revealed the feasibility of this method. He described in detail the image degradations introduced by scanning errors, insufficient sampling, and digital quantization, as well as reporting on current experimental work in digital reconstruction.

Professor o. K. Mawardi, of Case-Western Reserve University, presented a theoretical analysis of phase distortion due to nonlinear effects in an acoustic field. In particular, he pointed out that the linear superposition concept for weak signals does not apply to strong signals due to harmonic distortion, wave-wave, interaction and induced secondary flow. Besides discussing these nonlinear effects, he gave methods of estimating quantitatively the magnitude of the phase distortions introduced by the second-order effects.

Dr. A. F. Metherell, of the Douglas Advanced Research Laboratories, discussed the relative importance of phase and amplitude in acoustical holography. The technique essentially uses a "variable gamma" recording system to enhance the diffraction fringes at large distances from the axis. His results, illustrated by comparative examples, showed the main effect to be a modification of the overall image intensity but with no effect on the relative intensities of points in the object plane that are visible at all points in

x Preface

the hologram plane. The apparent resolution of the reconstruction appears to improve with this method.

Significant acoustical holography work in Japan was described in a paper by Dr. Yoshinao Aoki, of Hokkaido University, and which was read by Dr. EI-Sum. Both theoretical and experimental research were discussed, covering the effects of scanning lines, the hologram-limited aperture, con­version efficiency of the light intensity in the reconstruction, the role of the acoustic frequency on the reconstructed images, and the three-dimensional information storage in acoustical holograms.

Miss D. Fritzler, of Bendix Research Laboratories, described an ultra­sonic camera adapted to making holograms. The camera, manufactured by James Electronics, Inc., uses a quartz crystal located at the front window of a cathode ray tube. The crystal is irradiated by the sound beam, and the interference pattern is picked up by the scanning electron beam, which is amplified and displayed on a TV monitor. A photograph of the TV display allows reconstruction by the usual laser technique. Miss Fritzler showed experimental results of this method and discussed some of the limita­tions.

At the end of the formal presentation, Professor Dennis Gabor sum­marized the new techniques presented at the symposium. One of the topics which evoked a lively discussion concerned methods of coping with distor­tion in the reconstructed image due to differences in axial and lateral magnifi­cation. Although Dr. Thurstone mentioned a possible solution in his talk by means of a frequency doubling technique, no consensus evolved from the group's comments. However, the participants all agreed that the principal barrier to the acoustical holographic techniques was the lack of a suitable recording array corresponding to the fine-grain film used in optical holo­graphy. We would expect to find considerable research and development effort concentrated toward the solution of this problem during the next few years.

Rather than causing unnecessary delay in publication, the editors have allowed the authors to express themselves in their own way. Consequently, different symbols for the same quantity may appear throughout the book. However, this lack of continuity should not cause any confusion, since all symbols are well defined.

A supplementary bibliography at the end of the formal papers contains a compilation of abstracts of nearly all publications on acoustical holography up through 1967. The editors hope new workers in the field will find this collection a useful adjunct to the book as well as a source for references.

The editing of these proceedings has been accomplished with the help and cooperation of all of the authors and many of the staff members of the Douglas Advanced Research Laboratories. The editors are sincerely grateful

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to all of these individuals and to the McDonnell Douglas Corporation for sponsoring the symposium.

A. F. Metherell H. M. A. El-Sum Lewis Larmore

CONTENTS

CHAPTER 1 by H. M. A. El-Sum The Scope of the Symposium

Introduction ........................................... 1 Definitions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Generalized Principles of Holography. . . . . . . . . . . . . . . . . . . . . . 3 Sound Recording . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Liquid Surface Deformation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Scanning or Sampling Technique. . . . . . . . . . . . . . . . . . . . . . . . . . 14

Mechanical Scanning. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 Electronic Scanning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 Laser Beam Scanning. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

Effect of Scanning on Hologram Reconstruction. . . . . . . . . . . . . 19 Direct Visualization of Sound Field by Bragg Diffraction of Light. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 General Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

CHAPTER 2 by H. Berger A Survey of Ultrasonic Image Detection Methods

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 Photographic and Chemical Methods . . . . . . . . . . . . . . . . . . . . . . 30 Thermal Techniques. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 Optical and Mechanical Methods ......................... 36 Electronic Methods .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 Conclusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

CHAPTER 3 by R. K. Mueller and P. N. Keating The Liquid-Gas Interface as a Recording Medium for Acoustical Holography

Introduction ........................................... 49 The Wave Equation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

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The Boundary Conditions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 The Surface Deformation ................................ 52 The Surface Under Plane Wave Excitation. . . . . . . . . . . . . . . . . . 53 General Surface Excitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 Conclusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

CHAPTER 4 by B. B. Brenden A Comparison of Acoustical Holography Methods

Introduction .. . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . 57 Acoustical Holography Employing a Liquid Surface ......... 58

Experimental Arrangement. . . . . . . . . . . . . . . . . . . . . . . . . . . 58 Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 Two-step Holography Using a Liquid Surface. . . . . . . . . . . 62 Real-time Holography With a Liquid Surface. . . . . . . . . . . 63

Ultrasonic Holography Using a Scanned Hologram Method. . 65 Construction of the Hologram. . . . . . . . . . . . . . . . . . . . . . . . 65 Reconstruction of the Image. . . . . . . . . . . . . . . . . . . . . . . . . . 67 Holograms and Reconstructions ...................... 68

Conclusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 Acknowledgments ...................................... 71 References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

CHAPTER 5 by J. L. Kreuzer and P. E. Vogel Acoustic Holographic Techniques for Nondestructive Testing

Introduction....... ........................... ......... 73 Experiments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

The Acoustical Hologram. . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 Acoustical Hologram Recorder. . . . . . . . . . . . . . . . . . . . . . . 74 Visible Image Formation from the Acoustical Hologram. . 77 Some Acoustical Holograms and Images .. . . . . . . . . . . . . . 78

Theoretical Analysis and Discussion of Some Properties of Acoustical Holograms ....................... 83

General Theory. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 Effects of Sampling the Acoustical Hologram . . . . . . . . . . . 87 Properties of the Image Formed by an Acoustical Hologram. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

Potential Uses of Acoustical Holographic Techniques in Nondestructive Testing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

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CHAPTER 6 by J. M. Smith and N. F. Moody Application of Fourier Transforms in Assessing the Performance of an Ultrasonic Holography System

Introduction ........................................... 97 A Criterion for the Maximum Frequency in a Hologram. . . . . . 98 Analysis of the Effect of Scanning System on Recorded Information. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 Analysis in the Fourier Transform Domain. . . . . . . . . . . . . . . . . 107 Practical Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 Summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112

CHAPTER 7 by F. L. Thurstone Biomedical Prospects for Ultrasound Holography

Introduction ........................................... 113 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 Appendix. Ultrasound Holography and Visual Reconstruction 120

Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 Conclusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 Acknowledgments .................... '. . . . . . . . . . . . . . 125 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125

CHAPTER 8 by J. J. Dreher Acoustical Holographic Model of Cetacean Echo-Location

Introduction ........................................... 127 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136

CHAPTER 9 by J. de Klerk The Generation of Sound

Introduction ........................................... 139 Sound Generation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141

Sound Generation in a Gas. . . . . . . . . . . . . . . . . . . . . . . . . . . 141 Sound Generation in a Liquid ........................ 142 Sound Generation in a Solid. . . . . . . . . . . . . . . . . . . . . . . . . . 143

Detection of Sound ..................................... 147 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148

CHAPTER 10 by A. Korpel Acoustical Imaging by Diffracted Light-Two-Dimensional Interaction

Introduction ........................................... 149 Plane Wave Interaction Formalism. . . . . . . . . . . . . . . . . . . . . . . . 151 Acoustical Imaging. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158

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CHAPTER 11 by G. Wade, C. J. Landry, and A. A. de Souza Acoustical Transparencies for Optical Imaging and Ultrasonic Diffraction

Introduction ........................................... 159 Acoustical Transparencies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163 Transparencies as Diffracting Screens . . . . . . . . . . . . . . . . . . . . . . 166 Transparent Plates as Band-Pass Spatial Filters. . . . . . . . . . . . . . 169 Transparent Plates for Velocity Measurement . . . . . . . . . . . . . . . 171 Conclusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172 References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172

CHAPTER 12 by J. W. Goodman Digital Image Formation from Detected Holographic Data

Introduction ........................................... 173 Optical Image Reconstruction From Nonoptical Data. . . . . . . . 174

Production of a Photographic Transparency . . . . . . . . . . . . 174 Sources of Image Degradation. . . . . . . . . . . . . . . . . . . . . . . . 174 Advantages of Optical Image Reconstruction ........... 175

Digital Image Reconstruction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175 General Procedure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175 The Required Digital Operations. . . . . . . . . . . . . . . . . . . . . . 176 The Fast Fourier Transform. . . . . . . . . . . . . . . . . . . . . . . . . . 177

Effects of Quantization, Sampling, and Scan Nonuniformities. 179 Qua.ntization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179 Sampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180 Scan Nonuniformities ............................... 181

Experimental Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184 References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184

CHAPTER 13 by O. K. Mawardi Phase Distortions Due to Nonlinear Effects in an Acoustic Field

Introduction ........................................... 187 Formulation of the Problem. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188 The Interaction Terms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191 Description of Interference Pattern . . . . . . . . . . . . . . . . . . . . . . . . 192 The Second-Order Induced Field. . . . . . . . . . . . . . . . . . . . . . . . . . 194 Phase Distortion in Wavefront. . . . . . . . . . . . . . . . . . . . . . . . . . . . 197 Conclusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200 Appendix. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200 References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201

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CHAPTER 14 by A. F. Metherell The Relative Importance of Phase and Amplitude in Acoustical Holography

Introduction ........................................... 203 Experiments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204

General Instrumentation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204 Reconstruction Technique. . . . . . . . . . . . . . . . . . . . . . . . . . . . 206 First Experiments with the Letter "R" ... . . . . . . . . . . . . . . 207 The Three Point-source Experiments. . . . . . . . . . . . . . . . . . . 207 Elimination of the Conjugate Images .................. 211

The Phase and Amplitude of an Object Wave. . . . . . . . . . . . . . . 211 Qualitative Mathematical Explanation. . . . . . . . . . . . . . . . . 212

A Point Object ................................. 212 An Extended Object. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213

Qualitative Physical Explanation. . . . . . . . . . . . . . . . . . . . . . 214 Conventional and "Phase-only" Hologram Fringe Patterns 216 The Hologram as a Spatial Frequency Carrier. . . . . . . . . . . 219 Effect on Image Resolution. . . . . . . . . . . . . . . . . . . . . . . . . . . 219

Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220 Acknowledgments ...................................... 220 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220

CHAPTER 15 by Y. Aoki Acoustical Holograms and Optical Reconstruction

Introduction ........................................... 223 Matrix Representation of Holographic Systems. . . . . . . . . . . . . . 224

Scalar Sound Waves. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224 Matrix of a Lens. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224 Matrix of a Diffraction Grating. . . . . . . . . . . . . . . . . . . . . . . 226 Matrix of a Zone-Plate .............................. 227 Matrix of Gabor's Hologram. . . . . . . . . . . . . . . . . . . . . . . . . 228

Construction of Acoustical Holograms. . . . . . . . . . . . . . . . . . . . . 230 Experimental Arrangement. . . . . . . . . . . . . . . . . . . . . . . . . . . 230 Acoustical Hologram. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232

Optical Reconstruction of Images ....... . . . . . . . . . . . . . . . . . . 232 Reconstruction Condition. . . . . . . . . . . . . . . . . . . . . . . . . . . . 232 Reconstruction of Virtual and Conjugate Images . . . . . . . . 234 Experimental Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235

Effect of Scanning Lines on the Reconstructed Images. . . . . . . . 236 Scanning Lines as a Diffraction Grating. . . . . . . . . . . . . . . . 236 Effect of Scanning Lines on the Reconstructed Images. . . . 237 Improvement of Reconstructed Images. . . . . . . . . . . . . . . . . 238

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Effects of Hologram Construction Condition on the Reconstructed Images ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240

Effect of Light Intensity Level on the Reconstructed Images ............................... 240 Effect of Limited Scanning Plane on Reconstructed Images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241 Effect of Frequency of Sound Wave on Reconstructed Images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243

Some Properties of Acoustical Holograms. . . . . . . . . . . . . . . . . . 244 Detection of Objects in a Turbid and Turbulent Medium. . 244 Three-Dimensional Information Storage in Acoustical Holograms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245

Acknowledgment ....................................... 247 References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247

CHAPTER 16 by D. Fritzler, E. Marom, and R. K. Mueller Ultrasonic Holography via the Ultrasonic Camera

Introduction ........................................... 249 Acknowledgments ...................................... 255 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255

CHAPTER 17 by P. Greguss, Jr. Acoustical Filtering with Holographically Matched Spatial Filters

Introduction ........................................... 257 Extending Spatial Filtering to Acoustic Waves ........... . . . 258 Preliminary Experiments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 260 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262 General Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263 References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264

CHAPTER 18 by D. Gabor Summary and Directions for Future Progress 267

CHAPTER 19 Compiled by A. F. Metherell Supplementary Bibliography 277

Index .......................................... , . .. . . .. . . . . 287