本研究探討稜鏡陣列立體拍攝系統優化設計，採用優化技術結合CODE V光學軟體使用者自訂的巨集指令，來設計稜鏡陣列及光學鏡頭達到3D立體拍攝的目的。本文提出兩種設計方法，第一種為稜鏡陣列結合光學鏡頭優化設計，採用視角對稱式稜鏡陣列可以消除軸上色差，輔以光學鏡頭消除離軸色差；在消色差雙稜鏡陣列及光學鏡頭優化設計方面，結果顯示系統優化後的橫向色差最大值為1.3 µm，最大光學畸變絕對值為12.27%。第二種為通用型稜鏡陣列優化設計，此設計係固定鏡頭參數下僅對稜鏡陣列的參數進行優化設計，藉此設計可以適用於各式光學鏡頭，而為達此目的提出立體影像中心法(stereo-image center method)，可以增加稜鏡的視角且可降低色差。若再配合消色差雙片稜鏡陣列組設計，則可大幅降低色差。此外，本文也提出消畸變微結構稜鏡陣列的優化設計方法可以有效改善畸變。

This study presents the optimization design of stereo-photography system based on prism array. The optimization technique combined with CODE V optical software user-defined macro function to design the prism array and optical lenses to achieve the purpose of 3D stereo-photography. In this dissertation, two optical design methods are proposed. The first one is the optimization design of prism array and optical lenses. The viewing-angle symmetric prism array can eliminate the on-axis chromatic aberration, and optical lenses eliminate the off-axis chromatic aberration. In the optimization design of achromatic dual-prism array and optical lenses, the results show that the optical system after optimization has the maximum lateral chromatic aberration of 1.3 m and the absolute maximum optical distortion of 12.27%. The second is an optimization design of general-purpose prism array. The design parameters of the optical lenses were fixed, the prism array was only used to optimize the system design, which can be applied for various types of optical lenses. To achieve this objective, a stereo-image center method was proposed to increase the viewing-angle and to reduce chromatic aberration. If the achromatic double-prism array design was used, the chromatic aberration could be reduced significantly. In addition, the optimization design of the distortion-reduced prism array with micro structure elements was also proposed to improve the distortion effectively.

[1] C. Wheatsone, "On some remarkable, and hitherto unobserved, phenomena of binocular vision", Philos. Trans. R. Soc. Lond., 371-394 (1838).
[2] N. J. Wade and H. Ono, "The stereoscopic views of Wheatstone and Brewster Psychological Research," Psychiatry Res, 47(3), 125-133 (1985).
[3] A. J. Parker, "Binocular depth perception and the cerebral cortex," Nat. Rev. Neuroscience 8, 379-391 (2007).
[4] S. Y. Park, N. Lee, S. Kim, "Stereoscopic imaging camera with simultaneous vergence and focus control," Opt. Eng. 43, 3130-3137 (2004).
[5] M. Inaba, T. Hara and H. Inoue, "A Stereo Viewer Based on a Single Camera with View-Control Mechanism", Proceeding of the IEEE/RSJ International Conference on Intelligent Robots and System, 1857-1863 (1993).
[6] A. Goshtasby and W. A. Gruver, "Design of a single-lens stereo camera system", Pattern Recognition, 26(6), 923-936 (1993).
[7] J. Gluckman and S. K. Navar, “Rectified Catadioptric Stereo Sensors,” IEEE Trans. Pattern Ana. Machine Intelligence, 24, 224-236 (2002).
[8] T. P. Pachidis and J. N. Lygouras, “Pseudo-Stereo Vision System: A Detailed Study,” Journal of Intelligent and Robotic Systems, 42, 135-167 (2005).
[9] L. Yu and B. Pan, “Structure parameter analysis and uncertainty evaluation for single-camera stereo-digital image correlation with a four-mirror adapter,” Applied Optics 55(25), 6936-6946 (2016).
[10] J. Zhu and Y. Li, S. Ye, “Design and calibration of a single-camera-based stereo vision sensor,” Opt. Eng. 45(8), 1-6 (2006).
[11] D. H. Lee and I. S. Kweon, "A Novel Stereo Camera System by a Biprism," IEEE Trans, Robotics Auto., 16(5), 528-541 (2000).
[12] K. B. Lim and Y. Xiao, "Virtual stereovision system: new understanding on single-lens stereovision using a biprism," Journal of Electronic Imaging 14(4), 043020 1-11 (2005).
[13] W. L. Kee, K. B. Lim and D. Wang, "Virtual Epipolar Line Construction of Single-Lens Bi-Prism Stereovision system," Journal of Electronic Science and Technology 10(2), 97-101 (2012).
[14] C. Y. Chen, T. T. Yang and W. S. Sun, "Optics system design applying a micro-prism array of a single lens stereo image pair," Optics Express 16(20), 15495-15505 (2008).
[15] Q. L. Deng, C. Y. Chen, S. W. Cheng, W. S. Sun, B. S. Lin, "Micro-prism type sing-lens 3D aircraft telescope system," Optics Communications, 285(24), 5001-5007 (2012).
[16] W. S. Sun, C. L. Tien, C. Y. Chen, and D. C. Chen, "Single-Lens Camera Based on a Pyramid Prism Array to Capture Four Images," Optical Review, 20(2), 145-152 (2013).
[17] C. Y. Chen, C. F. Su, Q. Y. Cheng, and W. S. Sun, “Design of a Single-Lens Stereoscopic Camera Based on a Micro-Tetrahedron Prism Array,” OPT 10 International Conference on Optics and Photonics in Taiwan, OPT7-P-015 (2010).
[18] W. S. Sun, C. F. Su, “Single-lens stereoscopic camera capture four images on a micro-pyramid prism array,” 8th ODF 12, Saint Petersburg, 3PS-04 (2012).
[19] 蘇靖帆，「使用微型角錐體陣列之單眼立體攝影機光學系統設計」，國立中央大學碩士論文，民國98年。
[20] C. Y. Chen, Q. L. Deng, W. S. Sun, Q.Y. Cheng, B. S. Lin and C. L. Su, "Panoramic stereo photography based on single-lens with a double-symmetric prism," Optics Express 21(7), 8474-8482 (2013).
[21] 鄭喬耀，「角錐體微型陣列板應用於劇場式立體攝影系統」，國立中央大學碩士論文，民國99年。
[22] 楊婷婷，「利用微稜鏡陣列製作單眼立體攝影鏡頭之光學系統設計」，國立雲林科技大學碩士論文，民國97年。
[23] V. N. Mahajan, Optical Imaging and Aberrations part I: ray geometrical optics (SPIE-The International Society for Optical Engineering, 1998).
[24] B. E. Saleh, M. C. Teich, “Ray optics,” in Handbook of Fundamentals of photonics(Wiley,1991), pp. 10-11.
[25] P. M. Hubel, J. Liu, and R. J. Guttosch, “Spatial frequency response of color image sensors: Bayer color filters and Foveon X3,” in Electronic Imaging 2004 Anonymous (International Society for Optics and Photonics, 2004).
[26] 張弘，幾何光學，東華書局，1993。
[27] Schott, Optical Glass Catalogue Excel (Schott Inc., Germany, June, 2012).
[28] M. P. Rimmer, “Relative illumination calculations,” Proc. SPIE 655, 99-104 (1986).
[29] Synopsys, CODE V Electronic Document Library, Version 10.5, Lens System Setup for Reference Manuals, Chap. 1, p 35. (2012).
[30] 李正中，薄膜光學與鍍膜技術，藝軒圖書出版社，第六版。
[31] E. T. Burle, Electro-optics handbook (second edition, McGraw-Hill, New York, 2000).
[32] 李靜君、孫文信、張明文、孫慶成，「稜鏡玻璃選取對色差的影響與校正」, GP-08, Optics and Photonics Taiwan 06，清華大學，台灣, Dec. 15-16 (2006).
[33] W. S. Sun, C. C. Lee, C. C. Sun and S. Y. Chen, “Doublet prisms with an optimal design to correct the chromatic aberration,” IPC2011 International Photonics Conference, PE-TH-32 (2011).
[34] W. S. Sun, C. C. Sun, “Doublet prisms for corrected chromatic aberration,” 8th ODF 12, Saint Petersburg, 3PS-05 (2012).
[35] 李靜君，「稜鏡玻璃選取對色差的影響與校正」，國立中央大學碩士論文，民國95年。
[36] W. S. Sun, C. L. Tien, C. C. Sun, and C. C. Lee, "A Low-cost Optimization Design for Minimizing Chromatic Aberration by Doublet Prisms," Journal of the Optical Society Korea, 16, 336-342 (2012).
[37] W. S. Sun, P. Y. Chu, “Double micro-prism array design for reducing dispersion on prism -based stereo camera system,” Proc. SPIE 8841-19 (2013).
[38] P. Y. Chu, W. S. Sun, Z. Y. H. Hung, “Improvement of chromatic aberration and distortion for the prism-type stereo camera system,” OPTIC’2013 Optics & Photonics Taiwan, International Conference, Taiwan, 2013-THU-S0501-O002 (2013).
[39] W. S. Sun, H. Y. Chen, “Optimize Aberration for Single Lens Camera with Double Micro Prism Array.” OPTIC 2014 Optics & Photonics Taiwan, International Conference, Taiwan, 2014-Fri-S0504-O004 (2014).
[40] 洪兆禹，「稜鏡陣列在單鏡頭立體相機畸變與色差優化設計」，國立中央大學碩士論文，民國95年。
[41] 孫文信，「精調三階像差各分項目標值的鏡組優化設計」，國立中央大學博士論文，民國91年。