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Introduction 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

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Introduction 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

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