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Toward Accurate Computation of Optically Reconstructed Holograms by John Stephen Underkoffler S.B

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Toward Accurate Computation of Optically Reconstructed Holograms by John Stephen Underkoffler S.B Toward Accurate Computation of Optically Reconstructed Holograms by John Stephen Underkoffler S.B. Massachusetts Institute of Technology Cambridge, Massachusetts 1988 Submitted to the Media Arts and Sciences Section, School of Architecture and Planning in partial fulfillment of the requirements for the degree of Master of Science at the Massachusetts Institute of Technology June 1991 @ 1991 Massachusetts Institute of Technology All Rights Reserved. Signature of Author \ U JNlledia Arts and Sciences Section 10 May 1991 Certified by -v Stephen A. Benton Professor of Media Technology Thesis Advisor Accepted by Stephen A. Benton Chairman Departmental Committee on Graduate Students MASSACHUSETTS INSTITUIE OF TECN' "Py JUL 23 1991 LIBRARIES gotch Room 14-0551 77 Massachusetts Avenue Cambridge, MA 02139 Ph: 617.253.2800 M ntLibraries Email: [email protected] Document Services http://Ilibraries.mit.edu/docs DISCLAIMER OF QUALITY Due to the condition of the original material, there are unavoidable flaws in this reproduction. We have made every effort possible to provide you with the best copy available. If you are dissatisfied with this product and find it unusable, please contact Document Services as soon as possible. Thank you. Both the Library and Archives versions of this thesis contain B&W photocopy images only. This is the best scanned version available. Toward Accurate Computation of Optically Reconstructed Holograms by John Stephen Underkoffler Submitted to the Media Arts and Sciences Section, School of Architecture and Planning, on 10 May 1991 in partial fulfillment of the requirements of the degree of Master of Science at the Massachusetts Institute of Technology Abstract Several algorithms for the production of interference patterns intended for reconstruction on an electronic holographic display are presented. The notion of realism of imagery is introduced, and a categorization of components defining and necessary to the evaluation of image realism is proposed. Particular realism components to be developed in the new context of electronic holography are identi- fied. Historical approaches to attaining realism in other imaging media are investigated, with particular attention paid to computer graphics techniques. Past computational models for synthetic generation of holographic interference patterns for non-electronic holographic media are summarized. Calculation of holographic images for display by the MIT device is introduced. The successful construction of a computational system for producing holographic images of polyhedrally-defined objects in wireframe representation but exhibiting proper occlusion is described, and resulting images are presented. An ex- tension of this system for conversion of polyhedral models to images with solid-appearing, continuous surfaces is discussed, and satisfactory application of this extended system to the production of such images is recounted. Finally, a new method for modeling rough surfaces with realistic optical properties is introduced, computational techniques for realizing holographic recordings of these simulated surfaces are enumerated, and preliminary results of exercising these calculations are disclosed. Thesis Supervisor: Stephen A. Benton Title: Professor of Media Technology To THOSE WHO HAVE MADE IT POSSIBLE. The author acknowledges the generous support of the past and present sponsors of the MIT Holographic Video project: USWest Advanced Technology, Inc.; Rome Air Development Center (RADC) of the Air Force System Command; and the Defense Advanced Research Project Agency (DARPA). The views and conclusions in this document are those of the author, of course, and should not be interpreted as necessarily representing the official policy, expressed or implicit, of the Rome Air Development Center (RADC) of the Air Force System Command, the Defense Advanced Research Projects Agency (DARPA), or the United States Government. 4 Contents 1 Introduction 9 1.1 Constituents of 'Realism' ................. 10 1.2 Overview of Contents ....... ............. ......... 14 2 The Lineage of Realism 17 2.1 Early Efforts at Realism ............. 18 2.1.1 Painting ........ ........ ........ ........ 18 2.1.2 Photography . ...... ...... ...... ...... ..... 19 2.2 Representationalversus Physical Issues .. ..... ..... ..... ... 20 2.3 Computer Graphics ..... ...... ....... ...... ...... 20 2.3.1 Computer Graphics Occlusion ........ ............ 24 2.3.2 Computer Graphics Optical Properties .... ............ 28 2.4 Holography .... ..... ..... ...... ..... ..... .... 31 2.4.1 Real Holography ... ... .... ... .... ... ... .... 32 2.4.2 Synthetic Holography (Stereography) .. .... .... .... ... 33 3 Computer-Generated Holograms 37 3.1 Historical Efforts ... ..... .... .... ..... .... .... ... 38 3.2 Fourier Transform Approach .......................... 39 3.2.1 Detour-Phase ............................. 39 3.3 Lesebergian Departures ............. ............... 44 3.3.1 Fourier Extensions .. ............ ............ 44 3.3.2 Analytic Field Computations ...... ...... ...... ... 45 3.3.3 Conclusion ...... ....... ...... ...... ...... 46 3.4 The MIT Holographic Video System ... ..... ..... ..... .... 46 3.4.1 Computational Philosophy . ..... ..... ..... .... ... 48 3.5 Point-Based Fringe Rendering ... ...... ....... ...... ... 49 3.5.1 Generalized Holographic Interference .. ...... ...... ... 49 3.5.2 Point Source Field Contributions ... .... .... .... .... 53 3.5.3 Aliasing Considerations . .... .... ..... ... .... ... 55 3.5.4 The Role of Point Sources .... .... ... ... .... ... .. 58 4 Occlusion Processing 59 4.1 The Nature of the Occlusion Phenomenon ....... ......... ... 59 4.1.1 Real Occlusion ... ... .. ... ... ... .. ... ... .. 59 4.1.2 The Model ... .. ... ... ... .. ... ... .. ... ... 61 4.1.3 The Expected Conclusion . ... .. ... .. .. ... .. ... .. 63 4.2 Occlusion Processing . ... .. .. ... .. ... .. .. ... .. .. .. 64 4.2.1 The Problem .. .. ... .. ... .. ... .. .. ... .. ... 64 4.2.2 Environment and Interface ... .. .. .. .. .. .. .. .. .. .. 65 4.2.3 Details Concerning OccFilt .. .. ... .. .. .. .. ... .. .. 67 4.3 Results ... .. ... .. ... ... .. ... ... .. ... .. ... .. 68 6 5 Dense-Point Surface Approximation 5.1 Approximating Continuity with Multiplicity ........ ..... 76 5.1.1 Density Tests . ...... ...... ..... 7 7 5.2 Implementation ......... ... ............ 80 5.2.1 Populating Polygons ... 80 5.2.2 Shading ......... ........ .......... 8 1 5.2.3 Occlusion .. ...... .. .... .... .... .... 8 3 5.2.4 Psychovisual Adjustments . .... .... .... .... .. 8 8 5.2.5 Experimental Results . .. ... ... ... ... ... 89 5.2.6 Failures of the Model . ... .... .... .... ... 9 1 5.3 Anisotropic Radiators .. .... ... ... ... ... ... ... 9 3 5.3.1 The Approach . ..... .... .... ... .... .. 9 3 5.3.2 Preliminary Tests . .... .... ... .... .. 9 5 5.3.3 Implementation..... .... .... .... .... 9 6 5.3.4 Results ... ... 6 Microfacet Surface Generation 101 6.1 Beckmann's Legacy .. ................ 102 6.2 Mathematical Development of Facet Contribution . .. 105 6.2.1 Isolated Facets: Derivation of Field Expression 105 6.2.2 A Concession and a Success .......... 108 6.2.3 Approximation Limits ............. 110 6.3 Surface Modeling ................... 111 6.3.1 Tiling Technique ........... ..... 111 6.3.2 Distribution Functions, with Examples .. 113 7 Caesura 127 7.1 Summary .. ..... ..... ...... ..... ..... ..... ... 127 7.2 The Utility of Point Sources .. ...... ..... ..... ..... ... 129 7.3 Further Directions . ... .... .... .... ... .... .... ... 131 A Occlusion Processing Details 135 B Getting at Erf 147 C Further Surface-Generating Distribution Functions 153 C.1 Uniform t, Gaussian 9 . .. ... ... .. ... ... .. ... .. ... .. 153 C.2 Linear f, Uniform 9 .. .. ... .. .. ... .. ... .. .. .. ... .. 157 C.3 Duplicating Beckmann's Surfaces . ... .. ... ... .. ... .. ... 160 Chapter 1 Introduction The title of this work, Toward Accurate Computation of Optically Reconstructed Holograms, despite accurately describing the contents that follow, belies their very specific nature. A careful explanation of the particular way in which the title does reflect the ensuing text will serve also as an introduction to the scope and thrust of the effort reported here. HOLOGRAMS refers to the medium whose advancement was the principal line of inquiry documented in the following pages. In particular, the work has involved a new kind of electronic holography, the MIT Holographic Video System; the purpose of that device is to accept an electronic representation of a complex interference pattern and diffract light, using this pattern, into a three-dimensional image immediately and continuously visible to a viewer. The process by which an image is formed by the system is equivalent to the way in which a traditional, static hologram manipulates incident light: the electronic information sent to the system is, in fact, OPTICALLY RECONSTRUCTED. The interference pattern electronically represented by this signal is, in turn, analogous to the interference pattern that would have been present on a microscopic scale in a real hologram of the same image, except that while these structures would have been formed automatically as a result of the optical recording of the real hologram, the electronic patterns are generated by calculations simulating the physics of that optical recording. Thus the patterns used by the MIT system are dependent on and a result of explicit COMPUTATION. ACCURATE is the actual topic of the efforts reported here. It
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