Holographic Interferometry: Principles and Methods

343 Pages·1994·11.18 MB·English

by  P. K. Rastogi (auth.)

Springer Series in Optical Sciences Volume 68
Springer Series in Optical Sciences
Editorial Board: A. L. Schawlow K. Shimoda A. E. Siegman T. Tamir
Managing Editor: H. K. V. Lotsch
42 Principles of Phase Conjugation 58 Photoacoustic and Photothermal Phenomena
By B. Ya. Zel'dovich, N. F. Pilipetsky, Editors: P. Hess and 1. Pelzl
and V. V. Shkunov
59 Photorefractive Crystals
43 X-Ray Microscopy in Coherent Optical Systems
Editors: G. Schmahl and D. Rudolph By M. P. Petrov, S. I. Stepanov,
44 Introduction to Laser Physics and A. V. Khomenko
By K. Shimoda 2nd Edition
60 Holographic Interferometry
45 Scanning Electron Microscopy in Experimental Mechanics
Physics of Image Formation and Microanalysis By Yu. I. Ostrovsky, V. P. Shchepinov,
By L. Reimer and V. V. Yakovlev
46 Holography aod Deformation Analysis
61 Millimetre and Submillimetre Wavelength Lasers
By W. Schumann, J.-P. Ziircher, and D. Cuche
By N. G. Douglas
47 Tunable Solid State Lasers
Editors: P. Hammeriing, A. B. Budgor, 62 Photoacoustic and Photothermal Phenomena II
and A. Pinto Editors: 1. C. Murphy,
1. W. Maclachlan Spicer,
48 Integrated Optics L.c. Aamodt, and B. S. H. Royce
Editors: H. P. Nolting and R. Ulrich
63 Electron Energy Loss Spectrometers
49 Laser Spectroscopy VII
The Technology of High Performance
Editors: T. W. Hansch and Y. R. Shen
By H. Ibach
50 Laser-Induced Dynamic Gratings
By H. 1. Eichler, P. Giinter, and D. W. Pohl 64 Handbook of Noolinear Optical Crystal!;
By V. G. Dmitriev, G. G. Gurzadyan,
51 Tunable Solid State Lasers for Remote Sensing and D. N. Nikogosyan
Editors: R. L. Byer, E. K. Gustafson,
and R. Trebino 65 High-Power Dye Lasers
52 Tunable Solid-State Lasers II Editor: F. J. Duarte
Editors: A. B. Budgor, L. Esterowitz,
66 Silver Halide Recording Materials for
and L. G. DeShazer
Holography and Their Processing
53 The CO2 Laser By W.J. Witteman By H. I. Bjelkhagen
54 Lasers, Spectroscopy and New Ideas 67 X-Ray Microscopy III
A Tribute to Arthur L. Schawlow Editors: A. G. Michette,
Editors: W. M. Yen and M. D. Levenson G. R. Morrison, and C. J. Buckley
55 Laser Spectroscopy VTII
68 Holographic Interferometry
Editors: W. Persson and S. Svanberg
Editor: P. K. Rastogi
56 X-Ray Microscopy II
Editors: D. Sayre, M. Howells, J. Kirz, and 69 Photoacoustic and Photothermal Phenomena III
H. Rarback Editor: D. Bicanic
57 Single-Mode Fibers Fundamentals 70 Electron Holography
By E.-G. Neumann By A. Tonomura
Volumes 1-41 are listed on the back inside cover
P.K. Rastogi
(Ed.)
Holographic
In terferometry
Principles and Methods
With 178 Figures, Some in Colour
Springer-Verlag Berlin Heidelberg GmbH
PRAMOD K. RASTOGI, Sr. Res. Engineer
Laboratory of Stress Analysis, Swiss Federal Institute of Technology
CH-1015 Lausanne, Switzerland
Editorial Board
ARTHUR L. SCHAWLOW, Ph. D. Professor ANTHONY E. SIEGMAN, Ph. D.
Department of Physics, Stanford University Electrical Engineering
Stanford, CA 94305, USA E.L. Ginzton Laboratory, Stanford University
Stanford, CA 94305, USA
Professor KOICHI SHIMODA, Ph.D.
Faculty of Science and Technology THEODOR T AMIR, Ph. D.
Keio University, 3-14-1 Hiyoshi, Polytechnic University
Kohoku-ku
333 Jay Street, Brooklyn, NY 11201, USA
Yokohama 223, Japan
Managing Editor: Dr. HELMUT K.V. LOTSCH
Springer-Verlag, Tiergartenstrasse 17, D-69121 Heidelberg, Germany
ISBN 978-3-662-13990-5
Library of Congress Cataloging-in-Publication Data. Rastogi, Pramod. Holographic interferometry jPramod
Rastogi. p. cm.--(Springer series in optical sciences; v. 68) Includes bibliographical references and index.
ISBN 978-3-662-13990-5 ISBN 978-3-540-48078-5 (eBook)
DOI 10.1007/978-3-540-48078-5
I. Holographic inter-ferometry. I. Title. II. Series. TA 1555.R37 1994 621.36'75--dc20 93-39992
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Preface
Holographic interferometry is an important and widely used technique in the
measurement of variations in certain important physical quantities such as
displacements, strains, densities, etc. in solid mechanics and flow problems. The
fundamentals of the technique stand on a firm theoretical foundation. The
applications of the method have developed at a rapid pace and a stage has
reached where it would seem hazardous, if not impossible, to single out outright
a field of research not yet penetrated by the technique. A survey of literature
shows that a significant amount of research and development work is being
carried out in holographic interferometry. The shortcomings of the technique
are being addressed and the interest in the field is growing substantially.
The aim ofthe present volume is to provide a valuable and up-to-date source
of information in this fast expanding field. It is organized in eight chapters, with
each chapter dealing with a particular aspect of holographic interferometry. The
book has been written within a framework covering the principles and methods
currently in use in holographic interferometry. The scope of the book has been
limited to the study of opaque objects. Ample space has been devoted to
a comprehensive treatment of the phenomena of fringe formation, with a par
ticular emphasis on the quantitative evaluation of the holographic interference
fringe patterns. The emergence of computer-aided fringe analysis and phase
shifting techniques have simplified considerably the quantitative real-time
measurement of object shapes and deformations. The last two chapters provide
a reasonably detailed overview of full field holographic methods for the
measurement of shapes, displacements, derivatives, difference displacements and
vibrations. Apart from reviewing the current state-of-the-art, the book also aims
at stimulating research activities which are likely to expand further the horizons
of holographic interferometry.
The book addresses to both researchers and practising engineers alike. To
the researcher it should provide invaluable insights, an objective appraisal of the
holographic methods and above all, directions to the present and emerging lines
of research. To those contemplating the use of holographic interferometry in
their respective disciplines, it presents a useful and pertinent information on
available techniques and systems needed to solve their specific measurement
problems. The outlook projected by the present volume when compared with
those published earlier in the field is distinctly different in style and in content,
with particular emphasis on evolving user requirements.
VI Preface
The state-of-the-art reports are meant to provide fairly detailed summaries
of different facets to anyone who needs to apply holographic interferometry in
nondestructive testing and metrological investigations in a wide range of scient
ific and engineering disciplines. Furthermore, the set of contributions contained
in the book should be of value as a source of reference to engineers and research
workers interested or active in the field.
I wish to express my sincere gratitude to Professor L. Pflug for his encour
agement and support. I want to thank Dr. A. Lahee for her many helpful and
friendly discussions. My special thanks go to Dr. H. Lotsch who in spite of his ill
health worked tirelessly to get the project through in a timely manner. Finally,
I wish to thank E. Crombie for her cheerful assistance.
Lausanne PRAMOD K. RASTOGI
January 1994
Contents
1 Introduction
P.K. Rastogi. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2 Basic Principles
P. Hariharan. With 18 Figures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.1 The Development of Holography. . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2 The Off-Axis Hologram. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2.1 Reflection Holograms ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.2.2 Image Holograms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.3 The Reconstructed Image. ...... ........................... 12
2.4 Image Speckle. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.4.1 Signal-to-Noise Ratio. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.5 Types of Holograms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.5.1 Thin Amplitude and Phase Gratings. .. .. .. .. .. ....... 14
2.5.2 Volume Gratings.. .. .. .. .... .. .. .. .. .. ...... .. .. .... 15
2.5.3 Holograms of Diffusely Reflecting Objects. . . . . . . . . . . . . 18
2.5.4 Multiply Exposed Holograms. . . . . . . . . . . . . . . . . . . . . . . . 18
2.6 Light Sources and Optical Systems. . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.6.1 Coherence Requirements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.6.2 Laser Beam Expansion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.6.3 Beam Polarization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.6.4 Optical Systems for Holography. . . . . . . . . . . . . . . . . . . . . . 21
2.6.5 Holography with Pulsed Lasers .. . . . . . . . . . . . . . . . . . . . . 22
2.6.6 Laser Safety . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.7 The Recording Medium.................................... 22
2.7.1 Effects of Nonlinearity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.8 Recording Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.8.1 Photographic Emulsions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.8.2 Photothermoplastics................................. 25
2.8.3 Photorefractive Crystals. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.9 Holographic Interferometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.9.1 Real-Time Holographic Interferometry......... .. .. .. . 27
2:9.2 Double-Exposure Holographic Interferometry... .. .. .. 28
2.9.3 Phase Difference in the Interference Pattern. . . . . . . . . . . 29
VIII Contents
2.9.4 The Holodiagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.9.5 Localization of the Interference Fringes. . . . . . . . . . . . . . . 31
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3 Quantitative Determination of Displacements and Strains
from Holograms
R.J. Pryputniewicz. With 19 Figures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.1 Projection matrices: Definition and properties. . . . . . . . . . . . . . . . 33
3.1.1 Normal Projection. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.1.2 Oblique Projection. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.2 Illumination, Observation, and Sensitivity Vectors. . . . . . . . . . . . 38
3.3 Determination of Displacements. . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.3.1 Determination of Displacements when Fringe
Order is Known . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.3.2 Determination of Displacements when Fringe
Order is Unknown. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
3.3.3 Determination of Displacements from Multiple
Holograms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
3.4 Determination of Strains and Rotations . . . . . . . . . . . . . . . . . . . . . 53
3.4.1 Spatial Dependence of the Fringe-Locus
Function. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
3.4.2 Rigid-Body Rotations and Homogeneous Strains ...... 57
3.5 Electro-Optic Holography. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
3.5.1 Fundamentals of EOH .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
3.5.2 Elect!onic Processing of Holograms .................. 60
3.5.2.1 Static Measurements........................ 60
3.5.2.2 Dynamic Measurements . . . . . . . . . . . . . . . . . . . . . 64
3.5.3 Representative Applications of EOH. . . . . . . . . . . . . . . . . . 68
3.6 Conclusions............................................... 70
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
4 Two-Reference-Beam Holographic lnterferometry
R. Dandliker. With 22 -Figures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
4.1 _E lectronic Interference Phase Measurement.................. 75
4.1.1 Phase-Shifting and Heterodyne Detection............. 76
4.1.2 Double-Exposure with Two_Reference Beams.......... 78
4.2 Interferometry with Speckle Fields (Diffusely
Scattering Objects) ........................................ 82
4.2.1 Speckle Statistics for Coherent Imaging. . . . . . . . . . . . . . . 83
4.2.2 Measuring Intensity with a Detector of Finite
Size................................................ 84
4.2.3 Interference Fringe Formation ........... ; .. -.. ~ . . . . . . 86
Contents IX
4.3 Sources of Errors in Interference Phase Measurement. . . . . . . . . 88
4.3.1 Systematic Errors from Holographic
Interferometry with Two Reference Sources ........... 88
4.3.1.1 Misalignment of Hologram and
Reconstructing Reference Waves.......... .... 88
4.3.1.2 Cross-Talk from Holographic Recording... .. . 89
4.3.1.3 Spurious Fringes Due to Overlapping
Reconstructions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
4.3.2 Statistical Errors Due to Speckle Noise. . . . . . . . . . . . . . . 90
4.3.2.1 Non-Overlapping Reconstructions. .. ...... ... 91
4.3.2.2 Overlapping Reconstructions. . . . . . . . . . . . . . . . . 94
4.4 Applications.............................................. 95
4.4.1 Double-Exposure Holography with Phase-Shift
Fringe Evaluation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
4.4.2 Multiple-Exposure Holographic Interferometry..... ... 98
4.4.3 Double-Pulse Holography for 3-D Displacement
Measurement. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
4.4.4 Strain Measurement by Heterodyne Holographic
Interferometry. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
4.5 Conclusions............................................... 106
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
5 Phase-Shifting Holographic Interferometry
K. Creath. With 23 Figures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
5.1 Background. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
5.1.1 Real-Time Holographic Secondary Interference
Fringes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
5.1.2 From Wavefront to Object Displacement............. 110
5.2 Phase-Measurement Basics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
5.2.1 General Phase Measurement Theory.................. 112
5.2.2 Phase-Modulation Techniques....................... 114
5.2.3 Phase Unwrapping............ .. .... ................ 116
5.2.4 Sampling Requirements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
5.2.5 Intensity-Modulation Requirements. . . . . . . . . . . . . . . . . . . 119
5.2.6 Measurement Examples. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
5.3 Temporal Phase-Measurement (Phase-Shifting) Algorithms. . . . 122
5.3.1 Three Frames (90°, 120°, and General Phase
Shifts). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
5.3.2 Four Frames (90° Phase Shifts). . . . . . . . . . . . . . . . . . . . . . . 123
5.3.3 Five Frames (90° Phase Shifts) . . . . . . . . . . . . . . . . . . . . . . . 124
5.3.4 Carre (Four Frames with General Phase Shifts)........ 125
5.3.5 Synchronous Detection (2n/N Phase Shifts). . . . . . . . . . . . 125
5.3.6 (N + 1) Frames (2n/N Phase Shifts). . . . . . . . . . . . . . . . . . . 126