Table Of ContentHolography
Series in Optics and Optoelectronics
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
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Holography
Principles and Applications
Raymond K. Kostuk
CRC Press
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Library of Congress Cataloging‑in‑Publication Data
Names: Kostuk, Raymond K., 1950- author.
Title: Holography : principles and applications / Raymond K. Kostuk.
Other titles: Series in optics and optoelectronics.
Description: Boca Raton, FL : CRC Press, Taylor & Francis Group, [2019] |
Series: Series in optics and optoelectronics
Identifiers: LCCN 2019007593 | ISBN 9781439855836 (hardback ; alk. paper) |
ISBN 1439855838 (hardback ; alk. paper) | ISBN 9780429185830 (ebook) |
ISBN 0429185839 (ebook)
Subjects: LCSH: Holography.
Classification: LCC QC449 .K65 2019 | DDC 621.36/75--dc23
LC record available at https://lccn.loc.gov/2019007593
Visit the Taylor & Francis Web site at
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For
My Wonderful Wife Diane and Daughters Michelle and Marla
and
In Memory of Parents Walter and Eleanor
Contents
Preface ....................................................................................................................................................xiii
Author ......................................................................................................................................................xv
1. Introduction and Brief History of Holography .............................................................................1
1.1 Introduction ...............................................................................................................................1
1.2 Historical Background ..............................................................................................................1
1.3 Philosophy and Content of the Book.........................................................................................4
References ..........................................................................................................................................5
2. Background of Physical and Geometrical Optics for Holography ..............................................9
2.1 Introduction ...............................................................................................................................9
2.2 Light as an Electromagnetic Wave ............................................................................................9
2.3 Polarization of an Optical Field ..............................................................................................12
2.3.1 Linear Polarization ......................................................................................................13
2.3.2 Circular Polarization ...................................................................................................13
2.3.3 Elliptical Polarization...................................................................................................14
2.4 Coherence ................................................................................................................................15
2.4.1 Temporal Coherence ...................................................................................................15
2.4.2 Spatial Coherence .........................................................................................................18
2.5 Geometrical Optics .................................................................................................................20
2.5.1 Ray Propagation ..........................................................................................................20
2.5.2 Reflection at Dielectric Interfaces ...............................................................................21
2.5.2.1 Fresnel Formulae ..........................................................................................21
2.5.2.2 Brewster Angle .............................................................................................24
2.5.2.3 Total Internal Reflection ..............................................................................25
2.5.3 Optical Lenses .............................................................................................................25
2.5.4 Focusing Mirrors .........................................................................................................28
2.5.5 Paraxial Rays and Basic Image Analysis Methods .....................................................28
2.5.5.1 Paraxial Approximation and Ray Trace Relations .......................................28
2.5.5.2 Basic Image Analysis Methods ....................................................................29
2.6 Diffraction Analysis ................................................................................................................30
2.6.1 Huygens-Fresnel Diffraction Relation .........................................................................31
2.6.2 Fresnel or Near-Field Diffraction Region ...................................................................32
2.6.3 Fraunhofer or Far-Field Diffraction Region ................................................................32
2.6.4 Fourier Transform Properties of a Lens ......................................................................33
2.6.5 Diffraction by Apertures .............................................................................................35
2.6.5.1 Rectangular Aperture ...................................................................................35
2.6.5.2 Circular Aperture .........................................................................................36
Problems ...........................................................................................................................................37
References ........................................................................................................................................40
vii
viii Contents
3. Introduction to the Basic Concepts of Holography ......................................................................41
3.1 Introduction ..............................................................................................................................41
3.2 Holographic Recording Process ...............................................................................................41
3.2.1 Step 1: Superimposing the Object and Reference Beams ............................................41
3.2.2 Step 2: Expose the Recording Material and Convert to a Physical Holographic
Grating.........................................................................................................................43
3.2.3 Step 3: Reconstructing the Holographic Image ..........................................................43
3.3 Scattering from a Periodic Array of Scattering Points and the Grating Equation .................44
3.4 Hologram Terminology ...........................................................................................................46
3.4.1 Diffraction Efficiency .................................................................................................46
3.4.2 Linear, Computer Generated, and Digital Holography Recording .............................46
3.4.3 Thin and Thick (Volume) Holographic Gratings ........................................................47
3.4.4 Transmission and Reflection Type Holograms ...........................................................48
3.5 Hologram Geometries .............................................................................................................49
3.5.1 “In-Line” (Gabor Type) Holograms ............................................................................49
3.5.2 “Off-Axis” Hologram ..................................................................................................50
3.5.3 Fourier Transform Hologram ......................................................................................50
3.5.4 Fraunhofer Hologram ..................................................................................................52
3.5.5 Hologram Geometry Diagram ....................................................................................53
3.6 Plane Wave Analysis of Holograms ........................................................................................54
3.6.1 Grating Vector .............................................................................................................55
3.6.2 K-Vector Closure or Bragg Condition .........................................................................56
3.6.3 Reflection Hologram Example ....................................................................................56
3.6.4 Bragg Circle Diagram .................................................................................................57
3.7 Dispersion of Thin Gratings....................................................................................................59
3.7.1 Example of a Spectrometer with a Holographic Grating ............................................60
Problems ...........................................................................................................................................61
References ........................................................................................................................................63
4. Holographic Image Formation ......................................................................................................65
4.1 Introduction .............................................................................................................................65
4.2 Exact Ray Tracing ...................................................................................................................65
4.2.1 Exact Ray Tracing Algorithm .....................................................................................65
4.2.2 Primary and Secondary Image Formation ..................................................................69
4.2.3 Forming a Real Image with a Conjugate Reconstruction Beam.................................69
4.3 Hologram Paraxial Imaging Relations ....................................................................................70
4.3.1 Analysis of the Phase Distribution from a Point Source to a Hologram Plane ..........71
4.3.2 Image Magnification Effects .......................................................................................75
4.3.3 Effect of Spectral Bandwidth on Hologram Image Resolution ..................................76
4.4 Aberrations in Holographic Imaging ......................................................................................77
4.4.1 Spherical Aberration Coefficient ................................................................................79
4.4.2 Coma Aberration Coefficient ......................................................................................79
4.4.3 Astigmatism and Field Curvature Aberration Coefficients ........................................79
4.4.4 Distortion Aberration Coefficient ...............................................................................80
4.4.5 Example of a Holographic Lens Formed with Spherical Waves and Methods
to Reduce Image Aberration .......................................................................................80
4.5 Dispersion Compensation .......................................................................................................83
4.6 Analyzing Holographic Lenses with Optical Design Tools ....................................................85
4.7 Hologram Formation with Aspheric Wavefronts ....................................................................87
4.8 Holographic Lenses Recorded and Reconstructed at Different Wavelengths ........................89
4.9 Combining Image Analysis with Localized Diffraction Efficiency .......................................90
Problems ...........................................................................................................................................90
References ........................................................................................................................................92
Contents ix
5. Hologram Diffraction Efficiency ..................................................................................................93
5.1 Introduction .............................................................................................................................93
5.2 Fourier Analysis of Thin Absorption and Sinusoidal Phase Gratings ....................................93
5.2.1 Diffraction by a Thin Sinusoidal Absorption Grating ................................................94
5.2.2 Diffraction by a Thin Sinusoidal Phase Grating .........................................................96
5.3 Coupled Wave Analysis...........................................................................................................99
5.3.1 Approximate Coupled Wave Analysis (“Kogelnik” Model) .......................................99
5.3.1.1 Assumptions and Background Conditions .................................................99
5.3.1.2 The Bragg Condition .................................................................................101
5.3.1.3 Dispersion Properties of a Volume Grating .............................................104
5.3.1.4 Solving the Coupled Wave Equations ......................................................104
5.3.1.5 General Solution .......................................................................................106
5.3.1.6 Transmission Grating Field Amplitude ....................................................106
5.3.1.7 Reflection Grating Field Amplitude .........................................................108
5.3.1.8 Diffraction Efficiency ..............................................................................109
5.3.1.9 Properties of Specific Grating Types .......................................................109
5.3.1.10 Polarization Aspects of Volume Holograms Using ACWA ......................119
5.3.2 Criteria for Using “Thin” and “Thick” Grating Models ............................................121
5.3.3 Rigorous Coupled Wave Analysis .............................................................................122
5.3.3.1 Properties of the Electric Field within the Grating ..................................123
5.3.3.2 Fields Outside the Grating Region ...........................................................125
5.3.3.3 Solving for the Amplitudes of the Diffraction Orders .............................125
5.3.4 Comparison of RCWA with ACWA and Special Grating Cases ..............................129
Problems .........................................................................................................................................130
References .......................................................................................................................................132
6. Computer-Generated Holograms ................................................................................................133
6.1 Introduction ............................................................................................................................133
6.2 Preliminary Considerations for the CGH Process .................................................................133
6.2.1 Basic Concept .............................................................................................................133
6.2.2 Sampling Continuous Functions ...............................................................................134
6.2.3 Continuous and Discrete Fourier Transform Operations ...........................................135
6.2.4 Sampling Requirements at the Object and Hologram Planes ...................................136
6.3 CGH Encoding Methods .......................................................................................................137
6.3.1 Binary Detour Phase Encoding .................................................................................138
6.3.2 Binary Interferogram Computer-Generated Holograms............................................141
6.3.3 Example of a Binary Fourier Transform Hologram...................................................143
6.4 Dammann Gratings ...............................................................................................................146
6.5 Dynamic CGHs Formed with a Spatial Light Modulator ......................................................148
6.6 CGH Design Algorithm Optimization Methods ...................................................................150
Problems .........................................................................................................................................150
References .......................................................................................................................................151
7. Digital Holography ........................................................................................................................153
7.1 Introduction ............................................................................................................................153
7.2 Digital Hologram Process ......................................................................................................153
7.3 DH Recording Considerations ...............................................................................................155
7.4 Construction Geometries ......................................................................................................156
7.5 Reconstruction Methods .......................................................................................................159
7.5.1 Fresnel Approximation Method ................................................................................159
7.5.2 Convolution Method ...................................................................................................161
