Holography : principles and applications

349 Pages·2019·20.315 MB·English

by  Kostuk, Raymond K

Holography
Series in Optics and Optoelectronics
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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
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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