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

Description

This book covers basic- to expert-level applications in computer holography, a strong candidate for the ultimate 3D display technology. The computer holography developed in the course of the past decade represents the basis of wave optics. Accordingly, the book presents the basic theory of wave optics and practical techniques for handling wave fields by means of the fast Fourier transform. Numerical techniques based on polygons, as well as mask-based techniques, are also presented for calculating the optical fields of virtual 3D models with occlusion processing. The book subsequently describes simulation techniques for very large-scale optical fields, and addresses the basics and concrete applications of simulation, offering a valuable resource for readers who need to employ it in the context of developing optical devices. To aid in comprehension, the main content is complemented by numerous examples of optical fields and photographs of reconstructed 3D images. 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