本論文將數位微陣鏡元件 (digital micromirror device，DMD) 應用於數位光學相位共軛 (digital optical phase conjugator，DOPC) 投影系統。利用 DOPC 系統抑制散射能力，將牆面前之聚焦光點重建，配合 DMD 的高切換速率，使重建光點形成 3D 立體實像。在此系統中使用費奈爾反射鏡增加系統準確因子 (system fidelity)，進而提高投影系統之效率。接著我們利用考量系統準確因子之峰值與背景雜訊比 (peak to background ratio，PBR) 與實驗結果做比較，再由比較結果中提出系統之極限。最後我們利用此系統將英文字母投影至 1mm×1mm×20mm 空間中，展示系統結果，並整理此系統極限，將其結果與 LC-SLM 調製的 DOPC 投影系統做比較。

In this thesis, the digital micro-mirror device (DMD) is applied to digital optical phase conjugator (DOPC) projection system. DOPC projection system based on DMD have turbidity suppression and high switching rate, so we can reconstruct focus point in front of the wall and form 3D real image. We improve system efficiency by using Fresnel reflect mirror to increase system fidelity. We present the limit of the system by experiment result and theory which is including system fidelity and PBR. In order to show the result, we project symbol to free space which area is 1mm×1mm×20mm. Finally, we compare limit of DOPC projection system based on DMD or LC-SLM.

1. J. Geng, “Three-dimensional display technologies,” Adv. Opt. Photonics 5, 456-535 (2013).
2. F. Matsuura, and N. Fujisawa, “Anaglyph stereo visualization by the use of a single image and depth information,” J. Vis. 11, 79-86 (2008).
3. I. Ideses, and L. Yaroslavsky, “New methods to produce high quality color anaglyphs for 3-D visualization,” in International Conference Image Analysis and Recognition, A. Campilho and M. Kamel, ed. (2004), pp. 273-280.
4. I. Ideses, and L. Yaroslavsky, “Three methods that improve the visual quality of colour anaglyphs,” J. Opt. A: Pure Appl. Opt. 7, 755 (2005).
5. S. E. B. Sorensen, P. S. Hansen, and N. L. Sorensen, “Method for recording and viewing stereoscopic images in color using multichrome filters,” U.S. patent6,687,003 (February3, 2004).
6. S. Pastoor, and M. Wöpking, “3-D displays: A review of current technologies,” Displays 17, 100-110 (1997).
7. Y. Bastanlar, D. Canturk, and H. Karacan, “Effects of color-multiplex stereoscopic view on memory and navigation,” in Proceedings of IEEE Conference on 2007 3DTV Conference(IEEE2007), pp. 1-4.
8. A. J. Woods, and T. Rourke, “Ghosting in anaglyphic stereoscopic images,” Proc. SPIE 5291, pp. 354-365 (2004).
9. W. Kruger, C.-A. Bohn, B. Frohlich, H. Schuth, W. Strauss, and G. Wesche, “The responsive workbench: A virtual work environment,” Computer 28, 42-48 (1995).
10. C. Cruz-Neira, D. J. Sandin, T. A. DeFanti, R. V. Kenyon, and J. C. Hart, “The CAVE: audio visual experience automatic virtual environment,” Commun. ACM 35, 64-73 (1992).
11. J. Leigh, A. Johnson, L. Renambot, T. DeFanti, M. Brown, B. Jeong, R. Jagodic, C. Krumbholz, D. Svistula, and H. Hur, “Emerging from the CAVE: Collaboration in ultra high resolution environments,” presented at the First International Symposium on Universal Communication, Kyoto, Japan, 14-15 June 2007.
12. T. Shibata, “Head mounted display,” Displays 23, 57-64 (2002).
13. N. Cochrane, “VFX-1 Virtual Reality Helmet by Forte,” GameBytes, (1994).
14. S. Lee, Y. Jo, D. Yoo, J. Cho, D. Lee, and B. Lee, “Tomographic near-eye displays,” Nat. Commun. 10, 1-10 (2019).
15. J. W. Goodman, Introduction to Fourier Optics, 3rd eds. (McGraw (McGraw-Hill, New York, 2002).
16. M. Faraday, “Thoughts on ray vibrations,” Philos. Mag. 28, 345–350 (1846).
17. A. Gershun, “The light field,” Moscow, 1936, P. Moon and G. Timoshenko, translators, J. Math. Phys. XVIII, 51–151 (1939).
18. X. Xia, X. Zhang, L. Zhang, P. Surman, and Y. Zheng, “Time-multiplexed multi-view three-dimensional display with projector array and steering screen,” Opt. Express 26, 15528-15538 (2018).
19. D. Smalley, E. Nygaard, K. Squire, J. Van Wagoner, J. Rasmussen, S. Gneiting, K. Qaderi, J. Goodsell, W. Rogers, and M. Lindsey, “A photophoretic-trap volumetric display,” Nature 553, 486-490 (2018).
20. S. Tay, P.-A. Blanche, R. Voorakaranam, A. Tunç, W. Lin, S. Rokutanda, T. Gu, D. Flores, P. Wang, and G. Li, “An updatable holographic three-dimensional display,” Nature 451, 694-698 (2008).
21. T. Kozacki, M. Kujawińska, G. Finke, W. Zaperty, and B. Hennelly, “Holographic capture and display systems in circular configurations,” J. Disp. Technol. 8, 225–232 (2012).
22. K. Wakunami, P.-Y. Hsieh, R. Oi, T. Senoh, H. Sasaki, Y. Ichihashi, M. Okui, Y.-P. Huang, and K. Yamamoto, “Projection-type see-through holographic three-dimensional display,” Nat. Commun. 7, 1-7 (2016).
23. A. Askin, G. Boyd, J. Dziedzic, R. Smith, A. Ballman, J. Levinstein, and K. Nassau, “Optically-induced refractive index inhomogeneities in LiNbO3 and LiTaO3,” Appl. Phys. Lett 9, 111 (1966).
24. F. S. Chen, J. T. LaMacchia, and D. B. Fraser, “HOLOGRAPHIC STORAGE IN LITHIUM NIOBATE,” Appl. Phys. Lett 13, 223-225 (1968).
25. F. Chen, “Optically induced change of refractive indices in LiNbO3 and LiTaO3,” J. Appl. Phys. 40, 3389-3396 (1969).
26. N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, “Holographic storage in electrooptic crystals. i. steady state,” Ferroelectrics 22, 949-960 (1978).
27. M. Cronin-Golomb, J. O. White, B. Fischer, and A. Yariv, “Exact solution of a nonlinear model of four-wave mixing and phase conjugation,” Opt. Lett. 7, 313-315 (1982).
28. A. Yariv, and D. M. Pepper, “Amplified reflection, phase conjugation, and oscillation in degenerate four-wave mixing,” Opt. Lett. 1, 16-18 (1977).
29. J. Feinberg, “Asymmetric self-defocusing of an optical beam from the photorefractive effect,” J. Opt. Soc. Am. 72, 46–51 (1982)..
30. P. Yeh, “Two-wave mixing in nonlinear media,” IEEE J. Quantum Electron. 25, 484–519 (1989).
31. R. A. Fisher, Optical phase conjugation (Academic Press, 2012).
32. C. C. Sun, R. H. Tsou, W. Shen, H. H. Chan, J. Y. Chan, and M. W. Chan, “Shearing interferometer with a Kitty self-pumped phase-conjugate mirror,” Appl. Opt. 35, 1815-1819 (1996).
33. W. C. Su, C. C. Sun, Y. C. Chen, and Y. Ouyang, “Duplication of phase key for random-phase-encrypted volume holograms,” Appl. Opt. 43, 1728-1733 (2004).
34. C. C. Sun, and W. C. Su, “Three-dimensional shifting selectivity of random phase encoding in volume holograms,” Appl. Opt. 40, 1253-1260 (2001).
35. C. C. Sun, S. Yeh, M. W. Chang, and K. Y. Hsu, “Optimal incident conditions for a Cat-type self-pumped phase-conjugate mirror,” Appl. Opt. 31, 5769-5772 (1992).
36. B. Wang, C. C. Sun, W. C. Su, and A. E. Chiou, “Shift-tolerance property of an optical double-random phase-encoding encryption system,” Appl. Opt. 39, 4788-4793 (2000).
37. W. C. Su, Y. W. Chen, Y. Ouyang, C. C. Sun, and B. Wang, “Optical identification using a random phase mask,” Opt. Commun. 219, 117-123 (2003).
38. C. C. Sun, W. C. Su, B. Wang, and A. E. Chiou, “Lateral shifting sensitivity of a ground glass for holographic encryption and multiplexing using phase conjugate readout algorithm,” Opt. Commun. 191, 209-224 (2001).
39. H. F. Yau, H. C. Kung, H. Y. Lee, C. C. Sun, T. C. Chen, C. C. Chang, Y. P. Tong, and J. Chen, “Ordinary polarized phase conjugator using the photovoltaic effect,” Opt. Commun. 184, 257-263 (2000).
40. Z. Yaqoob, D. Psaltis, M. S. Feld, and C. Yang, “Optical phase conjugation for turbidity suppression in biological samples,” Nat. Photonics 2, 110-115 (2008).
41. I. M. Vellekoop, M. Cui, and C. Yang, “Digital optical phase conjugation of fluorescence in turbid tissue,” Appl. Phys. Lett. 101, 081108 (2012).
42. M. Cui, and C. Yang, “Implementation of a digital optical phase conjugation system and its application to study the robustness of turbidity suppression by phase conjugation,” Opt. Express 18, 3444-3455 (2010).
43. Y. M. Wang, B. Judkewitz, C. A. DiMarzio, and C. Yang, “Deep-tissue focal fluorescence imaging with digitally time-reversed ultrasound-encoded light,” Nat. Commun. 3, 1-8 (2012).
44. B. Judkewitz, Y. M. Wang, R. Horstmeyer, A. Mathy, and C. Yang, “Speckle-scale focusing in the diffusive regime with time reversal of variance-encoded light (TROVE),” Nat. Photonics 7, 300-305 (2013).
45. K. Si, R. Fiolka, and M. Cui, “Fluorescence imaging beyond the ballistic regime by ultrasound-pulse-guided digital phase conjugation,” Nature photonics 6, 657-661 (2012).
46. M. Jang, A. Sentenac, and C. Yang, “Optical phase conjugation (OPC)-assisted isotropic focusing,” Opt. Express 21, 8781-8792 (2013).
47. M. Cui, and C. Yang, “Optical phase conjugation 4Pi microscope,” California Institute of Techology, US Patent US8830573 B2 (2014).
48. I. N. Papadopoulos, S. Farahi, C. Moser, and D. Psaltis, “Focusing and scanning light through a multimode optical fiber using digital phase conjugation,” Opt. Express 20, 10583-10590 (2012).
49. I. N. Papadopoulos, S. Farahi, C. Moser, and D. Psaltis, “High-resolution, lensless endoscope based on digital scanning through a multimode optical fiber,” Biomed. Opt. Express 4, 260-270 (2013).
50. C. L. Hsieh, Y. Pu, R. Grange, and D. Psaltis, “Digital phase conjugation of second harmonic radiation emitted by nanoparticles in turbid media,” Opt. Express 18, 12283-12290 (2010).
51. M. Jang, H. Ruan, H. Zhou, B. Judkewitz, and C. Yang, “Method for auto-alignment of digital optical phase conjugation systems based on digital propagation,” Opt. Express 22, 14054-14071 (2014).
52. D. Wang, E. H. Zhou, J. Brake, H. Ruan, M. Jang, and C. Yang, “Focusing through dynamic tissue with millisecond digital optical phase conjugation,” Optica 2, 728-735 (2015).
53. D. Gabor, “A new microscopic principle,” Nature 161, 777-778 (1948).
54. E. N. Leith, and J. Upatnieks, “Reconstructed wavefronts and communication theory,” J. Opt. Soc. Am. 52, 1123-1130 (1962).
55. E. N. Leith, and J. Upatnieks, “Wavefront reconstruction with continuous-tone objects,” Opt. Soc. Am. 53, 1377-1381 (1963).
56. J. M. Palmer, and B. G. Grant, The art of radiometry, (SPIE, 2009).
57. S. N. Chandrasekaran, H. Ligtenberg, W. Steenbergen, and I. M. Vellekoop, “Using digital micromirror devices for focusing light through turbid media,” Proc. SPIE 8979, 897905 (2014).
58. Y. Liu, C. Ma, Y. Shen, J. Shi, and L. V. Wang, “Focusing light inside dynamic scattering media with millisecond digital optical phase conjugation,” Optica 4, 280-288 (2017).
59. I. M. Vellekoop, “Controlling the propagation of light in disordered scattering media,” Ph.D. thesis (University of Twente, 2008).
60. I. M. Vellekoop, and A. Mosk, “Focusing coherent light through opaque strongly scattering media,” Opt. Lett. 32, 2309-2311 (2007).
61. A. Papoulis, and S. U. Pillai, Probability, random variables, and stochastic processes, (Tata McGraw-Hill Education, 2002).
62. 陳致維，數位光學相位共軛用於立體影像顯示之研究，國立中央大學碩士論文，中華民國一百零八年。
63. Y. W. Yu, C. C. Sun, X. C. Liu, W. H. Chen, S. Y. Chen, Y. H. Chen, C. S. Ho, C. C. Lin, T. H. Yang, and P. K. Hsieh, “Continuous amplified digital optical phase conjugator for focusing through thick, heavy scattering medium,” OSA Continuum 2, 703-714 (2019).
64. P. Mouroulis, J. Macdonald, Geometrical Optics and Optical Design (Oxford U. Press, New York, 1997).
65. 孫慶成，光電工程概論，全華圖書股份有限公司，中華民國一百零一年。
66. 陳宇恆，基於數位光學相位共軛器浮空於多重鏡面之立體投影之研究，國立中央大學碩士論文，中華民國一百零六年。
67. G. Makey, Ö. Yavuz, D. K. Kesim, A. Turnalı, P. Elahi, S. Ilday, O. Tokel, and F. Ö. Ilday, “Breaking crosstalk limits to dynamic holography using orthogonality of high-dimensional random vectors,” Nat. Photonics 13, 251-256 (2019).