Diffraction-Specific Fringe Computation for Electro-Holography

by Mark Lucente

Doctoral Thesis Dissertation, MIT Dept. of Electrical Engineering and Computer Science, Sept. 1994.

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Abstract

Diffraction-specific fringe computation is a novel system for the generation of holographic fringe patterns for real-time display. This thesis describes the development, implementation, and analysis of diffraction-specific computation, an approach that considers the reconstruction process rather than the interference process in optical holography. The primary goal is to increase the speed of holographic computation for real-time three-dimensional electro-holographic (holovideo) displays. Diffraction-specific fringe computation is based on the discretization of space and spatial frequency in the fringe pattern. Two holographic fringe encoding techniques are developed from diffraction-specific fringe computation and applied to make most efficient use of hologram channel capacity. A "hogel-vector encoding" technique is based on undersampling the fringe spectra. A "fringelet encoding" technique is designed to increase the speed and simplicity of decoding. The analysis of diffraction-specific computation focuses on the trade-offs between compression ratio, image fidelity, and image depth. The decreased image resolution (increased point spread) that is introduced into holographic images due to encoding is imperceptible to the human visual system under certain conditions. A compression ratio of 16 is achieved (using either encoding method) with an acceptably small loss in image resolution. Total computation time is reduced by a factor of over 100 to less than 7.0 seconds per 36-MB holographic fringe using the fringelet encoding method. Diffraction-specific computation more efficiently matches the information content of holographic fringes to the human visual system. Diffraction-specific holographic encoding allows for "visual-bandwidth holography," i.e., holographic imaging that requires a bandwidth commensurate with the usable visual information contained in an image. Diffraction-specific holographic encoding enables the integration of holographic information with other digital media, and is therefore vital to applications of holovideo in the areas of visualization, entertainment, and information, including education, telepresence, medical imaging, interactive design, and scientific visualization.


1  Introduction   	13
   1.1	Overview of Thesis 	16

2  Background   	19
   2.1	Human Visual System 	19
	2.1.1	Acuity 	19
	2.1.2	Pupil Size 	20
	2.1.3	Depth Cues 	20
   2.2	Three-Dimensional Displays 	21
   2.3	Holography 	22
   2.4	Computational Holography 	27
   2.5	Holographic Displays 	28
   2.6	Bandwidth Compression in Holography 	31
   2.7	Iterative Hologram Computation Methods 	34

3  Motivation For Diffraction-Specific Computing   	37
   3.1	Problems with Interference-Based Fringe Computation 	37
	3.1.1	Noise 	38
	3.1.2	Lack of Speed 	38
	3.1.3	Analytical Image Model Constraint 	39
	3.1.4	Need for Encoding 	40
   3.2	Bipolar Intensity 	41
   3.3	Precomputed Elemental Fringes 	42
   3.4	Conclusion 	44

4  Diffraction-Specific Computation   	45
   4.1	Recipe for Diffraction-Specific Computation 	47
   4.2	Discretization of Space and Spatial Frequency: "Hogels" 	49
	4.2.1	Sampling: Concepts 	50
	4.2.2	Spatial Sampling 	52
	4.2.3	Spectral Sampling 	53
	4.2.4	Introduction of the Hogel 	55
   4.3	Generation of Hogel Vectors 	56
	4.3.1	Diffraction Tables 	57
	4.3.2	Use of 3-D Computer Graphics Rendering 	59
	4.3.3	Additional Techniques 	59
   4.4	Converting Hogel Vectors to Hogels 	60
   4.5	Implementation of Diffraction-Specific Computing 	62
	4.5.1	Cheops Overview 	63
	4.5.2	Normalization 	64
   4.6	Image Generation 	65
	4.6.1	Photographing of Images 	66
	4.6.2	Point Images 	67
	4.6.3	Incoherent Illumination Considerations 	69
   4.7	Speed 	71
   4.8	Conclusion 	73

5  Hogel-Vector Encoding   	77
   5.1	The Electro-Holographic Communication System 	78
	5.1.1	Information Symbols 	80
	5.1.2	Information Entropy 	80
   5.2	Description of Hogel-Vector Encoding 	82
   5.3	Image Generation 	85
   5.4	Discussion of Point Spread 	91
	5.4.1	Comparison of Theory and Experiment 	92
	5.4.2	Empirical Selection of System Parameters 	96
	5.4.3	Analytical Selection of System Parameters 	98
   5.5	Speed 	100
   5.6	Conclusion 	101

6  Fringelet Encoding   	103
   6.1	Fringelet Generation 	104
   6.2	Fringelet Decoding 	105
   6.3	Implementation 	111
   6.4	Image Generation 	112
   6.5	Discussion of Point Spread 	119
   6.6	Speed 	119

7  Holographic Encoding: Discussion   	123
   7.1	The Looks and Trends of Encoded Formats 	123
   7.2	Features of Encoding Schemes 	126
	7.2.1	Interoperability 	127
	7.2.2	Extensibility 	128
	7.2.3	Scalability 	129
	7.2.4	Manipulability 	130
	7.2.5	Second-Order Encodability 	131
	7.2.6	2-D Compatibility 	133
	7.2.7	Summary of Features 	133
   7.3	Engineering Trade-Off: Bandwidth, Depth, Resolution 	134
	7.3.1	Encoding Efficiency: Visual-Bandwidth Holography 	136

8  Future Directions   	139
   8.1	Specialized Fringelet Decoding 	139
	8.1.1	Digital Fringelet Decoding 	139
	8.1.2	Analog Electronic Fringelet Decoding 	140
	8.1.3	Optical Fringelet Decoding 	141
   8.2	Extension to Full Parallax Holovideo 	143

9  Conclusion   	145

Appendices:

A  Glossary of Terms and Abbreviations   	151

B  Spectral Decomposition of Diffracted Light   	153

C  Computation of Synthetic Basis Fringes   	159
   C.1	Method of Iterative Constraints 	160
   C.2	Simulated Annealing 	163

References   	169

Acknowledgments   	174

Preface Text

Thesis Supervisor: Professor Stephen A. Benton
Title: Allen Professor of Media Technology, Program in Media Arts and Sciences

Perche vede piu certa la cosa l'ochio ne'sogni che colla imaginatione, stando desto? - Leonardo da Vinci

Doctoral Thesis / Mark Lucente