A Computational Light Field Display for Correcting Visual Aberrations
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A Computational Light Field Display for Correcting Visual Aberrations Fu-Chung Huang Electrical Engineering and Computer Sciences University of California at Berkeley Technical Report No. UCB/EECS-2013-206 http://www.eecs.berkeley.edu/Pubs/TechRpts/2013/EECS-2013-206.html December 15, 2013 Copyright © 2013, by the author(s). All rights reserved. Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission. A Computational Light Field Display for Correcting Visual Aberrations by Fu-Chung Huang A dissertation submitted in partial satisfaction of the requirements for the degree of Doctor of Philosophy in Computer Science in the Graduate Division of the University of California, Berkeley Committee in charge: Professor Brian Barsky, Chair Professor Carlo Sequin Professor Ravi Ramamoorthi Professor Austin Roorda Fall 2013 A Computational Light Field Display for Correcting Visual Aberrations Copyright 2013 by Fu-Chung Huang 1 Abstract A Computational Light Field Display for Correcting Visual Aberrations by Fu-Chung Huang Doctor of Philosophy in Computer Science University of California, Berkeley Professor Brian Barsky, Chair Vision problems such as near-sightedness, far-sightedness, as well as others, are due to optical aber- rations in the human eye. These conditions are prevalent, and the population is growing rapidly. Correcting optical aberrations is traditionally done optically using eyeglasses, contact lenses, or refractive surgeries; these are sometime not convenient or not always available to everyone. Fur- thermore, higher order aberrations are not correctable with eyeglasses. In this work, we introduce a new computation based aberration-correcting light field display: by incorporating the persons own optical aberration into the computation, we alter the content shown on the display, such that he or she will be able to see it in sharp focus without wearing eyewear. We analyze the image formation models; through the retinal light field projection, we find it is possible to compensate for the optical blurring on the target image by prefiltering with the inverse blur. Using off-the-shelf components, we built a light field display prototype that supports our de- sired inverse light field prefiltering. The results show a significant contrast improvement and res- olution enhancement over prior approaches. Finally, we also demonstrate the capability to correct for higher order aberrations. i To my wife Ia-Ju Chiang and our parents. ii Contents Contents ii List of Figures iv List of Tables vi 1 Introduction 1 1.1 Background ...................................... 2 1.2 The Goal ........................................ 5 1.3 Overview of Thesis Organization ........................... 7 2 Related Work 8 2.1 Image Restoration and Computational Photography ................. 8 2.2 Displays ........................................ 9 2.3 Computational Ophthalmology ............................ 11 3 Mathematical Models of Optical Blurring 13 3.1 Image Blurring as Convolution ............................ 13 3.2 Integrating Retinal Light Field ............................ 19 3.3 Summary ....................................... 22 4 Preliminary Ideas with Deconvolution 23 4.1 Frequency Domain Solvers .............................. 23 4.2 Spatial Domain Solvers ................................ 27 4.3 Theoretical Analysis ................................. 31 4.4 Summary ....................................... 33 5 Multilayer Displays 34 5.1 Frequency Preservation via Multilayer Prefiltering .................. 34 5.2 Partition Function and Contrast Optimization .................... 37 5.3 Requirement and Construction ............................ 41 5.4 Results ......................................... 45 5.5 Evaluations ...................................... 50 iii 5.6 Discussion ....................................... 53 6 Light Field Analysis 54 6.1 Light Field Displays .................................. 54 6.2 Image Formation in the Frequency Domain Light Field ............... 60 6.3 Summary ....................................... 63 7 Light Field Based Inverse Prefiltering 64 7.1 Analysis of Projection Matrix ............................. 65 7.2 Prototype, Experiments and Results ......................... 69 7.3 Evaluation ....................................... 74 7.4 Summary ....................................... 79 8 Light Field Wavefront Aberrometry 80 8.1 Frequency Decomposition of Wavefront Geometry ................. 80 8.2 Ray-tracing Wavefront Geometry. .......................... 83 8.3 Correcting Zernike Polynomials Aberrations ..................... 86 9 Future Work 93 9.1 Practicality. ...................................... 93 9.2 Applications ...................................... 95 9.3 Computational Optical Correction. .......................... 96 10 Conclusion 97 Bibliography 99 iv List of Figures 1.1 The Nimrud lens and early man-made reading stones. .................. 3 1.2 The early eyeglasses (left) and bifocals (right). ...................... 3 1.3 Contact lenses. ...................................... 4 1.4 Vision-correcting display. ................................. 5 3.1 Geometry of the optical setup for the eye. ........................ 13 3.2 Focal range of emmetropic, myopic, and hyperopic eye. ................. 15 3.3 Example wavefront surfaces. ............................... 16 3.4 Hartmann-Shack wavefront aberrometer. ......................... 17 3.5 Examples of non-planar wavefront generated point spread functions .......... 18 3.6 Transformations of the light field. ............................. 20 3.7 Defocus light field. .................................... 21 4.1 Disk point spread function and its inverse. ........................ 24 4.2 Frequency domain prefiltering solutions using the inverse filter and the Wiener filter. 26 4.3 Spatial domain prefiltering solutions using Richardson-Lucy method. .......... 28 4.4 Prefiltering solution obtained using Levin et al. deconvolution. ............. 29 4.5 Prefiltering using super-resolution technique. ...................... 30 4.6 Convolution weight matrices and their singular values. ................. 31 4.7 Modulation transfer function for the disk PSF. ...................... 32 5.1 Observation of multilayer PSFs and their MTFs. ..................... 34 5.2 Winner-Take-All MTF and frequency assignment .................... 37 5.3 Winner-Take-All binary frequency partitioning. ..................... 38 5.4 Contrast optimization via greedy partition function. ................... 40 5.5 Comparing the perceived images from prefiltering algorithms using the eye chart ex- ample. ........................................... 40 5.6 Prototype multilayer display, front view and side view .................. 43 5.7 Comparing simulated single-layer prefiltering results with multilayer prefiltering results. 45 5.8 Comparing simulated results when brightness are equalized. .............. 46 5.9 Camera photographs of prefiltering results. ........................ 47 5.10 Dynamic range variations of prefiltering. ......................... 48 v 5.11 Dynamic range normalization in video example. ..................... 49 5.12 Sensitivity analysis due to refractive errors and imprecise calibrations. ......... 50 5.13 Contrast over different levels of blurring. ......................... 51 5.14 omparison with prior work. ................................ 52 6.1 Construction of light field displays. ............................ 55 6.2 Deriving image quality as a function of the depth of field. ................ 56 6.3 Depth of field analysis of light field displays. ...................... 58 6.4 Example of vision-correcting algorithms using light field displays. ........... 59 6.5 Light field projection in the frequency domain. ...................... 61 7.1 Light field prefiltering with naive parameter setup. .................... 65 7.2 Conditioning analysis. .................................. 66 7.3 Tradeoff between angular light field resolution and image contrast. ........... 67 7.4 Prototype parallax barrier light field display. ....................... 69 7.5 Optical experiment setup. ................................. 70 7.6 Photographs of results from prototype display. ...................... 71 7.7 Video examples comparing light field prefiltering. .................... 73 7.8 Evaluation and comparison to previous work. ...................... 75 7.9 Comparing with prefiltering and light field based framework over a range. ....... 76 7.10 Accounting for a range of viewing distances. ....................... 77 7.11 Optimization for off-axis viewing. ............................ 78 8.1 Wyant’s ordering of Zerike polynomial. ......................... 81 8.2 ANSI standard Zernike ordering. ............................. 82 8.3 Ray-tracing wavefront ................................... 83 8.4 Derivatives ........................................ 84 8.5 Derivative of Zernike polynomials ............................ 85 8.6 Optical arrangement to illustrate astigmatism. ...................... 86 8.7 Examples showing astigmatism has depth-dependent blur. ................ 87 8.8 Correcting for astigmatism. ................................ 88 8.9 Examples of single term Zernike polynomial point spread