Introduction to Computer Holography: Creating Computer-Generated Holograms As the Ultimate 3D Image

Preface
Contents
1 Introduction
	1.1 Computer Holography
	1.2 Difficulty in Creating Holographic Display
	1.3 Full-Parallax High-Definition CGH
2 Overview of Computer Holography
	2.1 Optical Holography
	2.2 Computer Holography and Computer-Generated Hologram
	2.3 Steps for Producing CGHs and 3D Images
	2.4 Numerical Synthesis of Object Fields
		2.4.1 Object Field
		2.4.2 Field Rendering
		2.4.3 Brief Overview of Rendering Techniques
	2.5 Coding and Reconstruction
3 Introduction to Wave Optics
	3.1 Light as Wave
		3.1.1 Wave Form and Wave Equation
		3.1.2 Electromagnetic Wave
		3.1.3 Complex Representation of Monochromatic Waves
		3.1.4 Wavefield
	3.2 Plane Wave
		3.2.1 One-Dimensional Monochromatic Wave
		3.2.2 Sampling Problem
		3.2.3 Plane Wave in Three Dimensional Space
		3.2.4 Sampled Plane Wave
		3.2.5 Maximum Diffraction Angle
		3.2.6 More Rigorous Discussion on Maximum Diffraction Angle
	3.3 Spherical Wave
		3.3.1 Wave Equation and Solution
		3.3.2 Spherical Wavefield and Approximation
		3.3.3 Sampled Spherical Wavefield and Sampling Problem
	3.4 Optical Intensity of Electromagnetic Wave
4 The Fourier Transform and Mathematical Preliminaries
	4.1 Introduction
	4.2 The Fourier Transform of Continuous Function
		4.2.1 Definition
		4.2.2 Theorems
		4.2.3 Several Useful Functions and Their Fourier Transform
	4.3 Symmetry Relation of Function
		4.3.1 Even Function and Odd Function
		4.3.2 Symmetry Relations in the Fourier Transform
	4.4 Convolution and Correlation
	4.5 Spectrum of Sampled Function and Sampling Theorem
	4.6 Discrete Fourier Transform (DFT)
	4.7 Fast Fourier Transform (FFT)
		4.7.1 Actual FFT with Positive Indexes
		4.7.2 Use of Raw FFT with Symmetrical Sampling
		4.7.3 Discrete Convolution Using FFT
5 Diffraction and Field Propagation
	5.1 Introduction
		5.1.1 Field Propagation
		5.1.2 Classification of Field Propagation
	5.2 Scalar Diffraction Theory
		5.2.1 Angular Spectrum Method
		5.2.2 Fresnel Diffraction
		5.2.3 Fraunhofer Diffraction
	5.3 Optical Fourier Transform by Thin Lens
		5.3.1 Wave-Optical Property of Thin Lens
		5.3.2 Wavefield Refracted by Thin Lens
	5.4 Propagation Operator
		5.4.1 Propagation Operator as System
		5.4.2 Backward Propagation
6 Numerical Field Propagation Between Parallel Planes
	6.1 Far-Field Propagation
		6.1.1 Discrete Formula
		6.1.2 Destination Sampling Window
		6.1.3 Numerical Example
		6.1.4 Sampling Problem
	6.2 The Fourier Transform by Lens
	6.3 Single-Step Fresnel Propagation
		6.3.1 Formulation
		6.3.2 Numerical Example
		6.3.3 Sampling Problem
	6.4 Convolution-Based Technique: Band-Limited Angular Spectrum Method
		6.4.1 Discrete Formula
		6.4.2 Sampling Problem of Transfer Function
		6.4.3 Problem of Field Invasion
		6.4.4 Discussion on Band Limiting
		6.4.5 More Accurate Technique
7 Holography
	7.1 Optical Interference
	7.2 Thin Hologram and Volume Hologram
	7.3 Types of Holography
	7.4 Mathematical Explanation of Principle
	7.5 Spatial Spectrum of Amplitude Hologram
	7.6 Conjugate Image
	7.7 Theory and Examples of Thin Hologram
		7.7.1 Hologram with Plane Wave
		7.7.2 Hologram with Spherical Wave
		7.7.3 Fourier Transform Hologram
8 Computer Holography
	8.1 Introduction
	8.2 Viewing Angle
	8.3 Space-Bandwidth Product Problem
	8.4 Full-Parallax and Horizontal-Parallax-Only CGH
	8.5 Coding and Optimization of Fringe Pattern
	8.6 Amplitude CGH
		8.6.1 Amplitude Encoding
		8.6.2 Brightness and Noise
		8.6.3 Binary-Amplitude CGH
	8.7 Phase CGH
		8.7.1 Phase Encoding
		8.7.2 Example of Phase CGH
		8.7.3 Binary-Phase CGH
	8.8 Spatial Frequency of Fringe Pattern
		8.8.1 Formulation
		8.8.2 Example of Fringe Frequency
		8.8.3 Fringe Oversampling
	8.9 Fourier-Transform CGH
		8.9.1 Higher-Order Diffraction Images
		8.9.2 Generation of Fringe Pattern
		8.9.3 Amplitude Fringe Pattern Based on Hermitian Function
	8.10 Single-Sideband Method in Amplitude CGH
		8.10.1 Principle
		8.10.2 Generation of Fringe Pattern
9 The Rotational Transform of Wavefield
	9.1 Introduction
	9.2 Coordinate Systems and Rotation Matrices
	9.3 Principle
	9.4 Formulation
		9.4.1 General Formulation
		9.4.2 Paraxial Approximation
	9.5 Numerical Procedure
		9.5.1 Sampling Distortion
		9.5.2 Shifted Fourier Coordinates
		9.5.3 Actual Procedure to Perform the Rotational Transform
		9.5.4 Resample of Uniformly Sampled Spectrum
	9.6 Numerical Examples and Errors
		9.6.1 Edge Effect and Sampling Overlap
		9.6.2 The Rotational Transform with Carrier Offset
		9.6.3 Examples of the Rotational Transform in Practical Wavefield
10 The Polygon-Based Method
	10.1 Surface Source of Light
		10.1.1 Generation of Scattered Light
		10.1.2 Theoretical Model of Polygonal Surface Source of Light
	10.2 Basic Theory for Rendering Diffused Surface
		10.2.1 Surface Function
		10.2.2 Spectrum Remapping by Incident Plane Wave
		10.2.3 Rotation Matrix
		10.2.4 Rotational Transform of Remapped Spectrum
		10.2.5 Short Propagation to Object Plane
		10.2.6 Superposition of Polygon Fields and Propagation to Hologram Plane
	10.3 Practical Algorithm for Rendering Diffused Surface
		10.3.1 Input Data and Controllable Parameters
		10.3.2 Tilted and Parallel Frame Buffers
		10.3.3 The Fourier Transform of Surface Function
		10.3.4 Basic Procedure for the Rotational Transform and Short Propagation
		10.3.5 Maximum Diffraction Area of Polygon
		10.3.6 Determination of Sampling Interval of Surface Function by Probing Sample Points
		10.3.7 How to Determine Sizes of PFB and TFB
		10.3.8 Back-Face Culling
		10.3.9 Overall Algorithm for Rendering Diffused Surface
		10.3.10 Variation of Probing Sample Points
	10.4 Band Limiting of Polygon Field
		10.4.1 Principle
		10.4.2 Limit of Bandwidth
		10.4.3 Modification of Algorithm
	10.5 Computation Time of Object Field
	10.6 Shading and Texture-Mapping of Diffused Surface
		10.6.1 Brightness of Reconstructed Surface
		10.6.2 Amplitude of Surface Function
		10.6.3 Shading of Diffused Surfaces
		10.6.4 Texture-Mapping
	10.7 Rendering Specular Surfaces
		10.7.1 Spectrum of Diffuse and Specular Reflection
		10.7.2 Phong Reflection Model
		10.7.3 Spectral Envelope of Specular Component
		10.7.4 Generation of Specular Diffuser for Surface Function
		10.7.5 Fast Generation of Specular Diffuser by Shifting Spectrum
		10.7.6 Flat Specular Shading
		10.7.7 Smooth Specular Shading
		10.7.8 Examples of High-Definition CGHs with Specular Shading
11 The Silhouette Method
	11.1 Occlusion
	11.2 Processing of Mutual Occlusion
		11.2.1 Silhouette Method
		11.2.2 Formulation of Object-by-Object Light-Shielding for Multiple Objects
		11.2.3 Actual Example of Object-by-Object Light-Shielding
		11.2.4 Translucent Object
	11.3 Switch-Back Technique for Processing Self-Occlusion by the Silhouette Method
		11.3.1 Principle of Polygon-by-Polygon Light-Shielding and Associated Problem
		11.3.2 The Babinet\'s Principle
		11.3.3 Light-Shielding by Use of Aperture Instead of Mask
		11.3.4 Formulation for Multiple Polygons
		11.3.5 Practical Procedure for Computation of Object Field with P-P Shielding
		11.3.6 Inductive Explanation of the Switch-Back Technique
		11.3.7 Numerical Technique and Sampling Window for Switch-Back Propagation
		11.3.8 Emulation of Alpha Blend of CG
		11.3.9 Acceleration by Dividing Object
		11.3.10 Integration with the Polygon-Based Method
		11.3.11 Actual Examples of P-P Light-Shielding and Computation Time
	11.4 Limitation of the Silhouette Method
12 Shifted Field Propagation
	12.1 Introduction
		12.1.1 What is Shifted Field Propagation
		12.1.2 Rectangular Tiling
	12.2 Mathematical Preliminary
		12.2.1 Fractional DFT
		12.2.2 Scaled FFT for Symmetric Sampling
	12.3 Shifted Far-Field Propagation
		12.3.1 Formulation
		12.3.2 Numerical Example
		12.3.3 Sampling Problem
	12.4 Shifted Fresnel Propagation
		12.4.1 Formulation
		12.4.2 Numerical Example
		12.4.3 Sampling Problem
	12.5 Shifted Angular Spectrum Method
		12.5.1 Coordinate System
		12.5.2 Formulation
		12.5.3 Band Limiting
		12.5.4 Actual Procedure for Numerical Calculation
		12.5.5 Numerical Example
		12.5.6 Discussion on the Limit Frequency
13 Simulated Reconstruction Based on Virtual Imaging
	13.1 Need for Simulated Reconstruction
	13.2 Simulated Reconstruction by Back Propagation
		13.2.1 Examples of Reconstruction by Back-Propagation
		13.2.2 Control of DOF Using Aperture
		13.2.3 Control of View-Direction Using Aperture
	13.3 Image Formation by Virtual Lens
		13.3.1 Sampling Problem of Virtual Lens
		13.3.2 Equal Magnification Imaging by Virtual Lens
		13.3.3 Reduced Imaging by Virtual Lens
		13.3.4 Change of Viewpoint
	13.4 Simulated Reconstruction from Fringe Pattern
		13.4.1 Formulation
		13.4.2 Comparison Between Simulated and Optical Reconstructions
	13.5 Simulated Reconstruction in Color
		13.5.1 Production of Full-Color Reconstructed Image
		13.5.2 Examples of Simulated Reconstruction in Color
14 Digitized Holography
	14.1 Concept of Digitized Holography
	14.2 Digital Holography
		14.2.1 Phase-Shifting
		14.2.2 Lensless-Fourier Digital Holography for Converting Sampling Interval
		14.2.3 Synthetic Aperture Digital Holography for Capturing Large-Scale Wavefield
	14.3 Capture of Object-Field
		14.3.1 Monochromatic Object Field
		14.3.2 Object Fields in Full-Color
	14.4 Occlusion Processing Using the Silhouette Method
		14.4.1 The Silhouette Method Including Captured Object Fields
		14.4.2 Making Silhouette Masks
	14.5 Examples of Optical Reconstruction
		14.5.1 Monochrome CGH
		14.5.2 Full-Color CGH
	14.6 Resizing Object Image
		14.6.1 Resizing by Change of Sampling Intervals
		14.6.2 Resizing by Virtual Imaging
		14.6.3 Resizing by Shifted Fresnel Propagation
15 Fabrication of High-Definition CGH
	15.1 Introduction
	15.2 Fringe Printers
		15.2.1 Spot-Scanning Fringe Printer
		15.2.2 Image-Tilling Fringe Printer
	15.3 Laser Lithography
		15.3.1 Photomasks as a Binary-Amplitude CGH
		15.3.2 Structure of Photomasks
		15.3.3 Process to Fabricate Photomasks
		15.3.4 Pattern Drawing by Laser Writer
		15.3.5 Actual Processes of Development and Etching
		15.3.6 Creation of Phase CGHs
	15.4 Wavefront Printer
		15.4.1 Principle and Difference from Holographic Printer
		15.4.2 Optical Systems for Generating Object Fields
		15.4.3 Calculation of Object Fields and Encoding of Fringes
		15.4.4 Denysyuk-Type Wavefront Printer
	15.5 Full-Color Reconstruction of HD-CGHs Using Optical Combiner
	15.6 Full-Color CGH Using RGB Color Filters
		15.6.1 Principle and Structure
		15.6.2 Fringe Pattern
		15.6.3 Design Parameters of RGB Color Filters
		15.6.4 Examples of Optical Reconstruction
	15.7 Full-Color Stacked CGVH
		15.7.1 Principle
		15.7.2 Compensation for Thickness and Refractive Index of Substrates
		15.7.3 Fabrication of Stacked CGVH
		15.7.4 Optical Reconstruction of Stacked CGVH
Appendix Data of Major HD-CGHs
A.1 Parameters of Major HD-CGHs
References
		
Index