Table Of ContentIntroduction to Holography
This fully updated second edition of Introduction to Holography provides a theoretical background in optics and
holography with a comprehensive survey of practical applications. It is intended for the non-s pecialist with an
interest in using holographic methods in research and engineering.
The text assumes some knowledge of electromagnetism, although this is not essential for an understanding
of optics, which is covered in the first two chapters. A descriptive approach to the history and principles of
holography is followed by a chapter on volume holography. Essential practical requirements for successful
holographic recording are explained in detail. Recording materials are considered with detailed discussions
of those in common use. Properties peculiar to holographically reconstructed images are emphasised as well
as applications for which holography is particularly suitable. Mathematical tools are introduced as and when
required throughout the text with important results derived in detail. In this new edition, topics such as pho-
topolymers, dynamic holographic displays, holographic optical elements, sensors, and digital holography are
covered in greater depth. New topics have been added, including UV and infrared holography, holographic
authentication and encryption, as well as particle beam, X-r ay, and acoustic holography. Numerical problems
are provided at the end of each chapter.
This book is suitable for undergraduate courses and will be an important resource for those teaching optics and
holography. It provides scientists and engineers with knowledge of a wide range of holographic applications in
research and industry, as well as an understanding of holography’s potential for future use.
Vincent Toal was formerly Director of the Centre for Industrial and Engineering Optics and Head of the School
of Physics at Dublin Institute of Technology, now the Technological University Dublin. He obtained his BSc
degree in Physics and Mathematics from the National University of Ireland, an MSc degree in Optoelectronics
at Queen’s University, Belfast, and a PhD in Electronic Engineering at the University of Surrey. He is a member
of Optica with research interests in optics and holographic applications.
Series in Optics and Optoelectronics
Detection of Optical Signals
Antoni Rogalski, Zbigniew Bielecki
Handbook of Optoelectronics, Second Edition
Applied Optical Electronics (Volume Three)
John P. Dakin, Robert G. W. Brown
Handbook of Optoelectronic Device Modeling and Simulation
Lasers, Modulators, Photodetectors, Solar Cells, and Numerical Methods, Vol. 2
Joachim Piprek
Handbook of Optoelectronics, Second Edition
Concepts, Devices, and Techniques (Volume One)
John P. Dakin, Robert Brown
Handbook of GaN Semiconductor Materials and Devices
Wengang (Wayne) Bi, Haochung (Henry) Kuo, Peicheng Ku, Bo Shen
Handbook of Optoelectronic Device Modeling and Simulation (Two-Volume Set)
Joachim Piprek
Handbook of Optoelectronics, Second Edition (Three-Volume Set)
John P. Dakin, Robert G. W. Brown
Optical MEMS, Nanophotonics, and Their Applications
Guangya Zhou, Chengkuo Lee
Thin-Film Optical Filters, Fifth Edition
H. Angus Macleod
Laser Spectroscopy and Laser Imaging
An Introduction
Helmut H. Telle, Ángel González Ureña
Fourier Optics in Image Processing
Neil Collings
Holography
Principles and Applications
Raymond K. Kostuk
An Introduction to Quantum Optics, Second Edition
Photon and Biphoton Physics
Yanhua Shih
Polarized Light and the Mueller Matrix Approach, Second Edition
José J. Gil, Razvigor Ossikovski
Introduction to Holography, Second Edition
Vincent Toal
For more information about this series, please visit: https://www.crcpress.com/Series-in-Optics-and-Optoelectronics/
book-series/TFOPTICSOPT
Introduction to Holography
Second Edition
Vincent Toal
Front cover image: The Author
Second edition published 2023
by CRC Press
6000 Broken Sound Parkway NW, Suite 300, Boca Raton, FL 33487-2742
and by CRC Press
4 Park Square, Milton Park, Abingdon, Oxon, OX14 4RN
CRC Press is an imprint of Taylor & Francis Group, LLC
© 2023 Vincent Toal
First edition published by CRC Press in 2011.
Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for
the validity of all materials or the consequences of their use. The authors and publishers have attempted to trace the copyright holders of
all material reproduced in this publication and apologise to copyright holders if permission to publish in this form has not been obtained.
If any copyright material has not been acknowledged, please write and let us know so we may rectify in any future reprint.
Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced, transmitted, or utilised in any form by
any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in
any information storage or retrieval system, without written permission from the publishers.
For permission to photocopy or use material electronically from this work, access www.copyright.com or contact the Copyright Clearance
Center, Inc. (CCC), 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400. For works that are not available on CCC, please contact
[email protected]
Trademark notice: Product or corporate names may be trademarks or registered trademarks and are used only for identification and
explanation without intent to infringe.
Library of Congress Cataloging-in-Publication Data
Names: Toal, Vincent, author.
Title: Introduction to holography / Vincent Toal.
Description: Second edition. | Boca Raton : CRC Press, 2023. | Series:
Series in optics and optoelectronics | Includes bibliographical
references and index.
Identifiers: LCCN 2022023437 (print) | LCCN 2022023438 (ebook) | ISBN
9780367712341 (hardback) | ISBN 9780367725815 (paperback) | ISBN
9781003155416 (ebook)
Subjects: LCSH: Holography.
Classification: LCC QC449 .T63 2023 (print) | LCC QC449 (ebook) | DDC
621.36/75--dc23/eng20221006
LC record available at https://lccn.loc.gov/2022023437
LC ebook record available at https://lccn.loc.gov/2022023438
ISBN: 978-0-367-71234-1 (hbk)
ISBN: 978-0-367-72581-5 (pbk)
ISBN: 978-1-003-15541-6 (ebk)
DOI: 10.1201/9781003155416
Typeset in Palatino
by SPi Technologies India Pvt Ltd (Straive)
Contents
Preface .................................................................................................................................................................................xv
Acknowledgements .......................................................................................................................................................xvii
Section I Optics
1. Light Waves and Rays ................................................................................................................................................3
1.1 Introduction .......................................................................................................................................................3
1.2 Description of Light Waves .............................................................................................................................3
1.3 Spatial Frequency ..............................................................................................................................................4
1.4 The Equation of a Plane Wave .........................................................................................................................5
1.5 Non-planar Wavefronts ....................................................................................................................................6
1.6 Geometrical Optics ...........................................................................................................................................7
1.6.1 The Thin Lens .......................................................................................................................................7
1.6.2 Spherical Mirror ...................................................................................................................................9
1.6.3 Refraction and Reflection ....................................................................................................................9
1.7 Reflection, Refraction, and the Fresnel Equations ......................................................................................10
1.7.1 Reflection and Refraction ..................................................................................................................10
1.7.2 The Fresnel Equations .......................................................................................................................11
1.7.2.1 Electric Field Perpendicular to the Plane of Incidence .................................................12
1.7.2.2 Electric Field Parallel to the Plane of Incidence .............................................................13
1.7.2.3 Anti-reflection Coatings ....................................................................................................13
1.7.2.4 Total Internal Reflection and Evanescent Waves ...........................................................15
1.7.2.5 Intensity Reflection and Transmission Ratios ................................................................15
1.8 Introduction to Spatial Filtering ....................................................................................................................16
1.8.1 Phase Contrast Imaging ....................................................................................................................17
Problems ......................................................................................................................................................................19
2. Physical Optics ..........................................................................................................................................................21
2.1 Introduction .....................................................................................................................................................21
2.2 Diffraction ........................................................................................................................................................21
2.2.1 The Diffraction Grating .....................................................................................................................21
2.2.1.1 Single Slit .............................................................................................................................23
2.2.1.2 Double Slit ...........................................................................................................................24
2.2.1.3 The Diffraction Grating (Multiple Slits) ..........................................................................24
2.2.1.4 Resolution and Resolving Power .....................................................................................26
2.2.2 Circular Aperture ...............................................................................................................................28
2.3 Diffraction and Spatial Fourier Transformation .........................................................................................31
2.4 Phase Effect of a Thin Lens ............................................................................................................................33
2.5 Fourier Transformation by a Lens ................................................................................................................34
2.6 Fourier Transform Property of a Lens—A Physical Argument ................................................................35
2.7 Interference by Division of Amplitude ........................................................................................................35
2.8 Coherence .........................................................................................................................................................37
2.8.1 Production of Light ............................................................................................................................37
2.8.2 The Bandwidth of Light Sources .....................................................................................................38
2.8.3 Spatial Coherence ..............................................................................................................................39
2.9 Polarized Light ................................................................................................................................................41
2.9.1 Plane Polarized Light ........................................................................................................................41
2.9.2 Other Polarization States ..................................................................................................................41
v
vi Contents
2.9.3 Production of Linearly Polarized Light by Reflection and Transmission ..................................42
2.9.4 Anisotropy and Birefringence ..........................................................................................................44
2.9.5 Birefringent Polarizers and Polarizing Beamsplitters ..................................................................46
References ...................................................................................................................................................................46
Problems ......................................................................................................................................................................46
Section II Principles of Holography
3. Introducing Holography ..........................................................................................................................................51
3.1 Introduction: Difference between Two Spatial Frequencies .....................................................................51
3.2 Recording and Reconstruction of a Simple Diffraction Grating ..............................................................51
3.2.1 Amplitude Gratings ...........................................................................................................................51
3.2.2 Phase Gratings ....................................................................................................................................53
3.3 Generalised Recording and Reconstruction ................................................................................................54
3.4 A Short History of Holography.....................................................................................................................54
3.4.1 X-ray Diffraction ................................................................................................................................54
3.4.2 Diffraction and Fourier Transformation .........................................................................................54
3.4.3 Electron Microscopy and the First Holograms ..............................................................................56
3.4.4 Photographic Emulsions and Gabor Holography ........................................................................57
3.5 Simple Theory of Holography ......................................................................................................................59
3.5.1 Holographic Recording .....................................................................................................................59
3.5.2 Amplitude Holograms ......................................................................................................................60
3.5.2.1 Gabor (In-Line) Holography .............................................................................................61
3.5.2.2 Off-Axis Holography .........................................................................................................61
3.6 Phase Conjugacy .............................................................................................................................................61
3.7 Phase Holograms ............................................................................................................................................63
References ...................................................................................................................................................................64
Problems ......................................................................................................................................................................64
4. Volume Holography .................................................................................................................................................67
4.1 Introduction .....................................................................................................................................................67
4.2 Volume Holography and Coupled Wave Theory .......................................................................................67
4.2.1 Thick Holographic Diffraction Gratings.........................................................................................67
4.2.2 Light Waves in a Dielectric Medium ...............................................................................................67
4.2.3 Light Waves in a Dielectric Medium with a Grating ....................................................................68
4.3 Characteristics of Thick Holographic Gratings ..........................................................................................72
4.3.1 Transmission Gratings.......................................................................................................................72
4.3.1.1 Phase Transmission Gratings ............................................................................................72
4.3.1.2 Q and ρ Parameters ............................................................................................................73
4.3.1.3 Unslanted Amplitude Gratings ........................................................................................74
4.3.2 Unslanted Reflection Gratings .........................................................................................................76
4.3.2.1 Unslanted Reflection Phase Gratings ..............................................................................77
4.3.2.2 Reflection Amplitude Gratings ........................................................................................79
4.4 Rigorous Coupled-Wave Theory ..................................................................................................................80
4.5 A Simpler Approach .......................................................................................................................................81
4.5.1 Bandwidth ...........................................................................................................................................81
4.5.2 Diffraction Efficiency .........................................................................................................................82
References ...................................................................................................................................................................84
Problems ......................................................................................................................................................................84
Contents vii
Section III Holography in Practice
5. Requirements for Holography ...............................................................................................................................89
5.1 Introduction .....................................................................................................................................................89
5.2 Coherence .........................................................................................................................................................89
5.3 The Michelson Interferometer .......................................................................................................................89
5.4 Lasers ................................................................................................................................................................91
5.5 The Fabry-Perot Interferometer, Etalon, and Cavity ..................................................................................91
5.6 Stimulated Emission and the Optical Amplifier .........................................................................................93
5.7 Laser Systems ..................................................................................................................................................94
5.7.1 Gas Lasers ...........................................................................................................................................94
5.7.1.1 The Helium-Neon Laser ....................................................................................................94
5.7.1.2 Argon Ion Lasers ................................................................................................................96
5.7.1.3 Krypton Ion Lasers .............................................................................................................97
5.7.1.4 Helium-Cadmium Lasers ..................................................................................................97
5.7.1.5 Exciplex Lasers ...................................................................................................................97
5.7.2 Solid State Lasers ...............................................................................................................................98
5.7.2.1 Semiconductor Diode Lasers ............................................................................................98
5.7.2.2 Quantum Cascade Lasers ..................................................................................................98
5.7.2.3 Doped Crystal Lasers .........................................................................................................99
5.7.3 Dye Lasers ...........................................................................................................................................99
5.8 Q-switched Lasers .........................................................................................................................................100
5.9 Frequency Doubled Lasers ..........................................................................................................................101
5.10 Free Electron Lasers ......................................................................................................................................101
5.11 Mode Locking of Lasers ...............................................................................................................................102
5.12 Spatial Coherence of Lasers .........................................................................................................................103
5.13 Laser Safety ....................................................................................................................................................104
5.14 Mechanical Stability ......................................................................................................................................104
5.15 Thermal Stability ...........................................................................................................................................104
5.16 Checking for Stability ...................................................................................................................................105
5.17 Resolution of the Recording Material ........................................................................................................106
5.18 Good Practice in Hologram Recording ......................................................................................................106
Problems ....................................................................................................................................................................107
6. Practical Recording Materials ...............................................................................................................................109
6.1 Introduction ...................................................................................................................................................109
6.2 Silver Halide ..................................................................................................................................................109
6.2.1 Available Silver Halide Materials ..................................................................................................110
6.2.2 Processing of Silver Halide to Obtain an Amplitude Hologram ..............................................111
6.2.3 Processing to Obtain a Phase Hologram – Rehalogenation.......................................................112
6.2.4 Processing to Obtain a Phase Hologram – Reversal Bleaching .................................................112
6.2.5 Silver Halide Processing in Practice ..............................................................................................112
6.3 Dichromated Gelatin ....................................................................................................................................114
6.4 Thermoplastics ..............................................................................................................................................115
6.5 Photoresists ....................................................................................................................................................116
6.6 Self-Processing Recording Materials ..........................................................................................................117
6.6.1 Photochromic and Photodichroic Materials.................................................................................117
6.6.2 Photorefractives ...............................................................................................................................117
6.6.3 Nonlinear Optical Materials ...........................................................................................................119
6.6.4 Photopolymers .................................................................................................................................120
6.6.4.1 Photopolymerisation Using Acrylamide Monomer ....................................................120
6.6.4.2 Mechanism of Hologram Formation in Photopolymer ..............................................120
6.6.4.3 Mathematical Models of Holographic Grating Formation in Acrylamide
Photopolymer ...................................................................................................................121
viii Contents
6.6.4.4 Single-beam Recording in Photopolymer .....................................................................124
6.6.4.5 Advances in Photopolymers for Holographic Recording ..........................................125
6.6.5 Other Recording Materials .............................................................................................................128
References .................................................................................................................................................................128
Problems ....................................................................................................................................................................130
7. Recording and Reconstruction in Practice .........................................................................................................131
7.1 Introduction ...................................................................................................................................................131
7.2 Holographic Sensitivity ................................................................................................................................131
7.3 Non-linear Effects .........................................................................................................................................131
7.3.1 Non-linearity in an Amplitude Hologram ...................................................................................132
7.3.2 Non-linearity in Phase Holograms ................................................................................................135
7.4 Grain Noise ....................................................................................................................................................136
7.4.1 Reduction in Fringe Contrast .........................................................................................................136
7.4.2 Noise Gratings ..................................................................................................................................137
7.4.3 Measurement of Noise Spectrum ..................................................................................................140
7.5 The Speckle Effect .........................................................................................................................................140
7.5.1 The Origin of Speckle ......................................................................................................................140
7.5.2 Speckle Size .......................................................................................................................................141
7.5.3 Speckle Contrast ...............................................................................................................................142
7.6 Signal-to-noise Ratio in Holography ..........................................................................................................144
7.7 Experimental Evaluation of Holographic Characteristics ......................................................................145
7.7.1 Diffraction Efficiency .......................................................................................................................145
7.7.2 Shrinkage ..........................................................................................................................................147
7.8 Effects Arising from Dissimilarities between Reference Beams in Recording and Reconstruction ....147
7.8.1 Phase Conjugation Effects ..............................................................................................................149
7.8.2 Reconstruction Using Non-Laser Light ........................................................................................149
References .................................................................................................................................................................150
Problems ....................................................................................................................................................................150
Section IV Applications
8. Holographic Displays ............................................................................................................................................155
8.1 Introduction ...................................................................................................................................................155
8.2 Single-beam Holographic Display ..............................................................................................................155
8.2.1 Spatial Filtering ................................................................................................................................156
8.3 Split-beam Holographic Displays ...............................................................................................................157
8.3.1 Control of Beam Ratio in Split-beam Holography ......................................................................158
8.3.1.1 Use of Beamsplitters ........................................................................................................158
8.3.1.2 Polarizing Beamsplitters and Halfwave Plates ............................................................158
8.4 Benton Holograms ........................................................................................................................................159
8.4.1 Image Plane Holography ................................................................................................................161
8.4.2 Single-step Image Plane Rainbow Holography ..........................................................................161
8.4.3 Blur in Reconstructed Images from Rainbow Holograms .........................................................162
8.5 White Light Denisyuk Holograms .............................................................................................................163
8.6 Wide Field Holography ................................................................................................................................164
8.7 Colour Holograms ........................................................................................................................................166
8.8 Edge-lit Holograms .......................................................................................................................................168
8.9 Large-format Holographic Displays ..........................................................................................................171
8.10 Quantum Entanglement Holography ........................................................................................................172
8.11 Dynamic Three-dimensional Displays .......................................................................................................173
8.11.1 Light Field Displays.........................................................................................................................174
8.11.2 Holographic Displays ......................................................................................................................174
Contents ix
8.11.2.1 Photorefractive Polymer Systems ..................................................................................174
8.11.2.2 Spatial Light Modulator-based Dynamic Holographic Displays ..............................175
8.11.2.3 Metasurfaces .....................................................................................................................180
8.11.3 Tiled Holographic Displays Using LCSLMs ................................................................................180
8.12 Further Developments in SLM-based Holographic Systems .................................................................181
8.12.1 Reduced Pixel Size ...........................................................................................................................181
8.12.2 Scanning Systems .............................................................................................................................182
8.13 Dynamic Displays Using Speckle Fields ...................................................................................................183
8.14 Cascading SLMs for Complex Amplitude .................................................................................................184
References .................................................................................................................................................................186
Problems ....................................................................................................................................................................188
9. Other Imaging Applications .................................................................................................................................189
9.1 Introduction ...................................................................................................................................................189
9.2 Holographic Imaging of Three-Dimensional Spaces ...............................................................................189
9.3 Further Applications of Phase Conjugation ..............................................................................................191
9.3.1 Lensless Image Formation ..............................................................................................................191
9.3.2 Dispersion Compensation ..............................................................................................................193
9.3.3 Distortion and Aberration Correction ...........................................................................................193
9.4 Multiple Imaging ..........................................................................................................................................196
9.5 Total Internal Reflection and Evanescent Wave Holography .................................................................197
9.6 Evanescent Waves in Diffracted Light .......................................................................................................200
9.6.1 Diffracted Evanescent Wave Holography ....................................................................................201
References .................................................................................................................................................................203
Problems ....................................................................................................................................................................204
10. Holographic Interferometry ..................................................................................................................................205
10.1 Introduction ..................................................................................................................................................205
10.2 Basic Principle ..............................................................................................................................................205
10.3 Phase Change Due to Object Displacement ............................................................................................206
10.4 Fringe Localisation ......................................................................................................................................206
10.4.1 Pure Translation ............................................................................................................................206
10.4.2 In-plane Rotation ..........................................................................................................................207
10.4.3 Out-of-plane Rotation ..................................................................................................................207
10.5 Live Fringe Holographic Interferometry .................................................................................................208
10.6 Frozen Fringe Holographic Interferometry .............................................................................................208
10.7 Compensation for Rigid Body Motion Accompanying Loading .........................................................209
10.8 Double Pulse Holographic Interferometry ..............................................................................................211
10.9 Holographic Interferometry of Vibrating Objects ..................................................................................211
10.9.1 Time-averaged Holographic Interferometry ............................................................................212
10.9.2 Live Holographic Interferometry of a Vibrating Object ..........................................................212
10.9.3 Double Exposure with Phase Shift .............................................................................................213
10.9.4 Frequency Modulation of the Reference Wave ........................................................................213
10.10 Stroboscopic Methods .................................................................................................................................214
10.11 Surface Profilometry ...................................................................................................................................215
10.11.1 Surface Profiling by Change in Wavelength .............................................................................215
10.11.2 Refractive Index Method .............................................................................................................216
10.11.3 Change in Direction of Illumination ..........................................................................................217
10.12 Phase Conjugate Holographic Interferometry ........................................................................................218
10.13 Fringe Analysis ............................................................................................................................................218
10.14 Speckle Pattern Interferometry ..................................................................................................................219
10.14.1 Speckle Pattern Correlation Interferometry ..............................................................................220
10.14.2 Electronic Speckle Pattern Interferometry ................................................................................221
10.14.2.1 Fringe Analysis in Electronic Speckle Pattern Interferometry ............................222
10.14.2.2 Vibration Studies Using Electronic Speckle Pattern Interferometry ..................223
