Table Of ContentSpringer Series in Optical Sciences Volume 46
Edited by Theodor Tamir
Springer Series in Optical Sciences
Editorial Board: I.M. Enoch D.L. MacAdam AL. Schawlow K. Shimoda T. Tamir
Volume 42 Principles of Phase Conjugation
By B. Ya. Zel'dovich, N. F. Pilipetsky, and V. V. Shkunov
Volume 43 X-Ray Microscopy
Editors: G. Schmahl and D. Rudolph
Volume 44 Introduction to Laser Physics
ByK Shimoda
Volume 45 Scanning Electron Microscopy
Physics of Image Formation and Microanalysis
By L. Reimer
Volume 46 Holography and Deformation Analysis
By W Schumann, 1.-P. Ziircher, and D. Cuche
Volume 47 Tunable Solid State Lasers
Editors: P. Hammerling, A. B. Budgor, and A. Pinto
Volume 48 Integrated Optics
Editors: H.-P. Nolting and R Ulrich
Volume 49 Laser Spectroscopy VII
Editors: T. W. Hansch and Y. R. Shen
Volume 50 Laser-Induced Dynamic Gratings
By H. 1. Eichler, P. GOOter, and D. W Pohl
Volume 51 Tunable Solid· State Lasers for Remote Sensing.
Editor: R. L. Byer
Volumes 1-41 are listed on the back inside cover
W. Schumann I-P' Zurcher
D. Cuche
Holography
and
Defonnation Analysis
With 78 Figures
Springer-Verlag
Berlin Heidelberg GmbH
Prof. Dr. WALTER SCHUMANN
Dr. JEAN-PIERRE ZURCHER
Dr. DENIS CUCHE
Laboratorium fiir Photoelastizitiit, ETH Ziirich, Riimistr. 101
CH-8092 Ziirich, Switzerland
Editorial Board ARTHUR L. SCHAWLOW, Ph. D.
Department of Physics, Stanford University
Stanford, CA 94305, USA
JAY M. ENOCH, Ph. D. Professor KOICHI SHIMODA
School of Optometry, Faculty of Science and Technology,
University of California Keio University, 3-14-1 Hiyoshi, Kohoku-ku
Berkeley, CA 94720, USA Yokohama 223, Japan
L.
DAVID MACADAM, Ph. D. THEODOR TAMIR, Ph. D.
68 Hammond Street, 981 East Lawn Drive,
Rochester, NY 14615, USA Teaneck, NJ 07666, USA
ISBN 978-3-662-13559-4 ISBN 978-3-540-38981-1 (eBook)
DOI 10.1007/978-3-540-38981-1
Library of Congress Cataloging-in-Publication Data. Schumann, Walter, 1927-Holography and deformation
analysis. (Springer series in optical sciences; v. 46) Bibliography: p. Includes index. 1. Holography. 2.
Holographicinterferometry. 3. Deformations (Mechanics) I. Ziircher, J .-P. (Jean-Pierre), 1953-. II. Cuche, D.
(Denis), 1954-. III. Title. TA1542.S38 1985 621.36'75 85-12563
This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned,
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are made for other than private use, a fee is payable to "Verwertungsgesellschaft Wort", Munich.
© Springer-Verlag Berlin Heidelberg 1985
Originally published by Springer-Verlag Berlin Heidelberg New York Tokyo in 1985
Softcover reprint of the hardcover I st edition 1985
The use of registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific
statement, that such names are exempt from the relevant protective laws and regulations and therefore free for
general use.
Typesetting: Schwetzinger Verlagsdruckerei GmbH
2153/3130-5 432 1 0
To Brigitte Schumann
Monique Zurcher
Erika Cuche
Preface
In this book series on Optical Sciences, holography has been the subject of three
previous volumes. In particular, Vol. 16, written by one of us (W.S.) and Dr. M.
Dubas, treated holographic interferometry of opaque bodies from the standpoint
of deformation analysis. However, the fundamental principles of holography are
developed there only briefly in preparation for a discussion of interference fringe
modifications.
This new volume in the series is intended to consider in detail many topics
which were previously omitted, such as the deformation or distortion of holo
graphic images, the theory of volume holograms, composite or multiplex holo
graphy, holographic interferometry of transparent media, time dependent
effects, holographic contouring, and applications of fringe modifications to the
deformation of opaque bodies. In addition, these and other subjects will be
treated with the same unifying concept developed in Vol. 16, but with an addi
tional emphasis on those features that have their origins in classical optics, espe
cially the small-wavelength approach, the coupled-wave theory, and the Seidel
aberrations. Since the field of holography and its various applications is growing
rapidly, it is impossible to be comprehensive in a single book. Every effort has
beep. made to avoid unnecessary duplication of Vol. 16. For example, displace
ment and fringe localization problems are only briefly discussed, while some
modification techniques (e.g., sandwich holography) are not included. When
needed, however, the reader is directly referred to complementary publications.
Apart from the literature itself, stimulation for this work originates from
personal communications, particularly with Prof. R. Diindliker and Dr. K. A.
Stetson, as well as from some reviews of previous work. The authors are most
grateful to those who have made this publication possible: Dr. H. Lotsch for his
constructive help and support; Prof. T. Tamir for accepting it in this series;
collaborators at Springer-Verlag, in particular Mrs. A. Rapp, for the editing and
printing; Drs. P. Colberg and G. Hanselmann for conscientiously revising the
English text; Mr. L. Pellegrinelli for carefully drawing the many detailed figures;
and Mrs. V. Schaer for her careful typing of the manuscript which Mr. Ph.
Tatasciore and Mr. J.-P. Koob read over again.
Zurich, June 1985 W. Schumann
J. P. Zurcher
D. Cuche
Contents
1. Introduction ...................... . 1
2. Elements of Analysis, Geometrical Optics, and Kinematics 4
2.1 Review of Some Basic Concepts of Tensor Analysis 4
2.1.1 Dyadics, Derivatives, and Projectors . . . . . 4
2.1.2 Calculus on Surfaces. . . . . . . . . . . . . . 11
2.2 Introduction to Some Elements of Geometrical Optics 19
2.2.1 Wave Equation, Eikonal, and Ray Equation 20
2.2.2 Refraction at Interfaces . . . . . . . . . . . . . 28
2.3 Kinematics of Deformation .............. 37
2.3.1 General Equations for the Deformation of a Body 37
2.3.2 Deformation of a Surface and a Thin Body 40
3. Elements of Holography and Image Modification . . . . . . . . . . .. 48
3.1 Formation and Aberration of the Image at the Reconstruction.
Coupled-Wave Theory. . . . . . . . . . . . . . . . . . . . . .. 48
3.1.1 Image Formation in Standard Holography ......... 48
3.1.2 Image Formation of a Point Source for a Modification at the
Reconstruction ....................... 52
3.1.3 Bragg Condition and Coupled-Wave Theory for Volume
Holograms ......................... 63
3.2 Deformation and Distortion of the Image of an Object at the
Reconstruction. . . . . . . . . . . . . . . . . . . . . . . . . .. 75
3.2.1 Primary Seidel Aberrations for a Rotational Symmetric
Modification . . . . . . . . . . . . . . . . . . . . . 75
3.2.2 Apparent Deformation of an Image and Duality in
Holography . . . . . . . . . . . . . . . 84
3.2.3 Deformation of an Image in Space ......... 91
3.3 Particular Modifications at the Reconstruction ...... 101
3.3.1 Basic Concepts of Cylindrical Composite Holograms 101
3.3.2 Small Modifications . . . . . . . . . . . . . . . . . 104
4. Holographic Interferometry or Fringe Interpretation . . . . . . .. 110
4.1 Basic Relations for Deformed Opaque Bodies and Isotropic
Nonhomogeneous Transparent Media . . . . . . . . . . . . . .. 111
X Contents
4.1.1 Optical Path Difference and Its Derivative for a Deformed
Opaque Object . . . . . . . . . . . . . . . . . . . . . .. 111
4.1.2 Optical Path Difference and Its Derivative for a Transparent
Isotropic Medium with a Varying Index of Refraction. The
Analogy . . . . . . . . . . 118
4.1.3 Problem ofInversion .... 127
4.2 Fringe Visibility and Localization . 131
4.2.1 Theory of Homologous Rays 131
4.2.2 Visibility and Shift of Fringes for a Finite Aperture 136
4.2.3 Time Dependent Effects ............. 144
5. Modification at the Reconstruction in Holographic Interferometry 151
5.1 Modifications with a Single Reference Source and a Single
Hologram . . . . . . . . . . . . . . . . . . . . . . . . . . 151
5.1.1 Large Modification in the Double-Exposure Method . 151
5.1.2 Two Close Wavelengths at the Recording. Holographic
Contouring ................... 156
5.1.3 Small Modifications in the Real-Time Technique . . 160
5.2 Modifications with Two Reference Sources . . . . . . . . 164
5.2.1 General Equations. Wavelength Changes with Two
Reference Sources . . . . . . . . . . . . . . . . . . 165
5.2.2 Moderate Shifts of Moderately Close Reference Sources 171
5.2.3 Derivatives of the Path Difference for Two Moderately
Close Reference Sources: Applications 175
References 185
Author Index . 221
Subject Index. 231
1. Introduction
As the history of holography is admittedly well known, we will confine the first
part of this introduction to a brief summary of the most significant events. The
foundations of holography were laid in 1948 by Gabor [1.1, 2] who demonstrated
that it was possible, in principle, to reconstruct the image of an object from a
diffraction pattern created at the recording, when the object and reference waves
interfered with one another on a thin, photographic plate termed the hologram.
However, this technique became a reality only 14 years later with the advent of
the laser, which provided the needed source of intense, coherent, monochroma
tic light. In 1962, Leith and Upatnieks [1.3] used laser beams and simultaneously
varied the directions of both the object and reference waves in order to avoid
their overlapping. In 1963, Denisyuk [1.4] and van Heerden [1.5] independently
proposed recording in a three-dimensional medium, resulting in production of
thick holograms, which have subsequently gained importance in information
storage, in white light reconstruction, and other applications. About 1965, it was
technically possible to cause holographically produced wavefields to interfere
with other wavefields, holographically or non-holographically produced, which
resulted in fringe patterns. The first contributions in the so-called fields of holo
graphic interferometry were made by Powell and Stetson [1.6], Burch [1.7],
Brooks et al. [1.8]. Most oftheir investigations were concerned with the deforma
tion and vibration analysis of opaque bodies, on the one hand, and the determi
nation of changes of indices of refraction in fluids (phase objects), on the other
hand. These studies later found applications also in photoelasticity. Since discus
sion of this latter area will be omitted, interested readers may, for instance,
consult Vol. 11 in this series. Shortly after the introduction of the laser, the basic
principles of holography were rapidly elucidated. However, the more refined
analysis of image formation and fringe patterns in general configurations, such as
needed for industrial applications, required a much longer time to develop.
In holography, the case in which the reconstructed image is identical to the
configuration of the recorded object represents the exception rather than the
rule. Intentionally or unintentionally produced optical modifications are almost
always perceived at the reconstruction as aberrations of the image points; these
points become blurred and distortions of the whole apparent object image appear
as a virtual deformation. Investigation of these effects is not trivial and some
times they cannot even be avoided as, for instance, in conjugate images.
Moreover, these studies are relevant because of both their relationship to classi
callens imaging and their role in holographic interferometry, where the modified
