本論文主要著重在多LED 光源結構的精準光學模型之研究，我們將從
中場擬合法做延伸性的研究，討論光學模型其中場距離行為的限制，歸納
出準遠場距離約為LED 透鏡直徑的十倍。藉由中場距離的分析去修正傳統
模型法之誤差，我們使用光源強度權重法來建立一個多晶白光單一封裝
LED 光學模型，並在中場距離下做驗證此精準光學模型，相關係數達99.5%
以上。而後我們將討論擴散板之光學腔體效率，建立出LED 陣列搭配擴散
板之光學腔體快速計算效率之模型，並實際驗證該模型的準確性，其誤差
約在5%內。

In this dissertation, we studied the precise optical model of multi-LEDs for different applications. We started from the mid-field algorithm to discuss the limitation of the midfield distance for optical model. In general, the quasi
far-field distance is about 5 to 10 times of the diameter of the encapsulated lens. Based on it, a weighting factor was proposed to modify the light source in the optical model of multi-chips white LED. This optical model was also verified in several midfield distances, and then a precise model of multi-chips white LED was successfully built up. The normalized correlation coefficient is higher than 99.5%.
Then we studied the efficiency of lighting cavities composed of LED arrays. A lighting cavity is a reflecting box with light sources inside, and its exit side is covered with a diffuser plate to mix and distribute light. We derived a simple but precise calculation model for the optical efficiency of diffuser plates attached to a light cavity. Finally, the model was demonstrated in different conditions experimentally. The error between calculation model and experiment is about 5% error.

參考文獻
1. Wikipedia website, http://en.wikipedia.org/wiki/Thomas_Edison.
2. H. J. Round, “A note on carborundum,” Electrical World 19, 309-310 (1907).
3. N. Holonyak, Jr. and S. F. Bevaqua, “Coherent(visible) Light Emission From Ga(As1–xPx) Junctions,” Appl. Phys. Lett. 1, 82-83 (1962).
4. E. F. Schubert, Light-Emitting Diodes, (Cambridge University Press, 2006).
5. S. Nakamura, T. Mukai, and M. Senoh, “Candela-class high-brightness InGaN/AlGaN double-heterostructure blue-light-emitting diodes,” Appl. Phys. Lett. 64, 1687-1689 (1994).
6. S. Nakamura, M. Senoh, N. Iwasa, and S. Nagahama, “High-brightness InGaN blue, green, and yellow light-emitting diodes with quantum well structures,” Jpn. J. Appl. Phys. 34, L797-L799 (1995).
7. LED Magazine, http://www.ledsmagazine.com/news/7/2/7.
8. 孫慶成，2009固態照明研討會，國立中央大學，中華民國九十八年。
9. M. G. Craford, “LEDs for Solid State Lighting and Other Emerging Applications: Status, Trends, and Challenges,” Proc. SPIE 5941, 1-10 (2005).
10. M. S. Kaminski, K. J. Garcia, M. A. Stevenson, M. Frate, and R. J. Koshel, “Advanced Topics in Source Modeling,” Proc. SPIE 4775, 46-57 (2002).
11. C. C. Sun, T. X. Lee, S. H. Ma, Y. L. Lee, and S. M Huang, “Precise optical modeling for LED lighting verified by cross correlation in the midfield region,” Opt. Lett. 31, 2193-2195 (2006).
12. W. G. Chen, C. M. Uang, and C. H. Jou, “Optimal design of an irregular Fresnel lens for multiple light sources using a three-layered Hierarchical Genetic Algorithm,” Opt. Express 15, 9918-9935 (2007)
13. I. Moreno, J. Munoz, and R. Ivanov, “Uniform illumination of distant targets using a spherical light-emitting diode array, ” Opt. Eng. 46, 033001 (2007).
14. M. Burmen, F. Pernus, and B. Likar, “LED light sources: a survey of quality-affecting factors and methods for their assessment,” Meas. Sci. Technol. 19, 122002 (2008).
15. C. C. Sun, C. Y. Chen, H. Y. He, C. C. Chen, W. T. Chien, T. X. Lee, and T. H.Yang, “Precise optical modeling for silicate-based white LEDs,” Opt. Express 16, 20060–20066 (2008).
16. B. Kim, M. Choi, H. Kim, J. Lim, and S. Kang, “Elimination of flux loss by optimizing the groove angle in modified Fresnel lens to increase illuminance uniformity, color uniformity and flux efficiency in LED illumination,” Opt. Express 17, 17916-17927 (2009).
17. F. Chen, S. Liu, K. Wang, Z. Y. Liu, and X. B. Luo, “Free-form lenses for high illumination quality light-emitting diode MR16 lamps,” Opt. Eng. 48, 123002 (2009).
18. Wikipedia website, http://en.wikipedia.org/wiki/Xenon_arc_lamp.
19. Wikipedia website, http://en.wikipedia.org/wiki/Filament_lamp.
20. O. Dross, A. Cvetkovic, J. Chaves, P. Benitez, and J. C. Minano, “LED Headlight Architecture that creates a High Quality Beam Pattern independent of LED Shortcomings,” Proc. SPIE 5942, 1-10 (2005).
21. R. W. G. Hunt, Measuring Colour, (Fountain Press, 1998).
22. G. Wyszecki and W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulae, (John Wiley, 2000).
23. V. N. Mahajan, Optical Imaging and Aberrations - Part I Ray Geometrical Optics, (SPIE PRESS, 1998).
24. R. W. Boyd, Radiometry and the Detection of Optical Radiation, (John Wiley, 1983).
25. A. Zukauskas, M. S. Shur, and R. Caska, Introduction to Solid-State Lighting, (John Wiley, 2002).
26. I. Moreno and C. C. Sun, “Modeling the radiation pattern of LEDs,” Opt. Express 16, 1808-1819 (2008).
27. H. Yang, J. W. M. Bergmans, T. C. W. Schenk, J. P. M. G. Linnartz, and R. Rietman, “An analytical model for the illuminance distribution of a power LED,” Opt. Express 16, 21641-21646 (2008).
28. Y. Ding, X. Liu, Z. R. Zheng, and P. F. Gu, “Freeform LED lens for uniform illumination,” Opt. Express 16, 12958-12966 (2008).
29. A. Pawlak, and K. Zaremba, “Reflector luminaire with high power light-emitting diodes for general lighting,” Appl. Opt. 47, 467-473 (2008).
30. H. Xiang, Z. Zhenrong, L. Xu, and G. Peifu, “Freeform surface lens design for uniform illumination,” J. Opt. A, Pure Appl. Opt. 10, 075005 (2008).
31. D. Feng, J. Yoo, K. Nagatani, W. Kim, and H. C. Kim, “High Illumination Efficiency Linear Light Source Using Light Emitting Diodes,” Jpn. J. Appl. Phys. 46, 563-565 (2007).
32. C. H. Tsuei, J. W. Pen, and W. S. Sun, “Simulating the illuminance and the efficiency of the LED and fluorescent lights used in indoor lighting design,” Opt. Express 16, 18692-18701 (2008).
33. F. Munoz, P. Benı tez, O. Dross, J. C. Minano, and B. Parkyn, “Simultaneous multiple surface design of compact air-gap collimators for light-emitting diodes,” Opt. Eng. 43, 1522-1530 (2004).
34. P. C. P. Chao, C. Y. Shen, C. W. Chiu, J. S. Huang, Y. Y. Kao, T. Y. Tu, C. L. Wang, S. Chi, H. W. Lin, and S. Y. Tsai, “A novel lens cap designed for the RGB LEDs installed in an ultra-thin and directly lit backlight unit of large-sized LCD TVs,” J. Soc. Inf. Disp. 16, 317-327 (2008).
35. K. Wang, X. B. Luo, Z. Y. Liu, B. Zhou, Z. Y. Gan, and S. Liu, “Optical analysis of an 80-W light-emitting diode street lamp,” Opt. Eng. 47, 013002 (2008).
36. H. Yang, J. W. M. Bergmans, T. C. W. Schenk, J. P. M. G. Linnartz, and R. Rietman, “Uniform Illumination Rendering Using an Array of LEDs: A Signal Processing Perspective,” IEEE Trans. Signal Process. 57, 1044-1057 (2009).
37. I. Moreno, M. Avendano-Alejo, and R. I. Tzonchev, “Designing light-emitting diode arrays for uniform nearfield irradiance,” Appl. Opt. 45, 2265-2272 (2006).
38. I. Moreno, C. C. Sun, and R. Ivanov, “Far-field condition for light-emitting diode arrays,” Appl. Opt. 48, 1190-1197 (2009).
39. 謝志欽，LED準遠場之研究與防眩光學之設計，國立中央大學光電所碩士論文，中華民國九十七年。
40. H. Zerfhau-Dreihofer, U. Haack, T. Weber, and D.Wendt, “Light source modeling for automotive lighting devices,” Proc. SPIE 4775, 58-66 (2002).
41. S. Landau and J. Erion, “Car makers embrace LED signals,” Nature Photon. 1, 31-32 (2007).
42. A. Borbely and S. G. Johnson, “Performance of phosphor-coated light-emitting diode optics in ray-trace simulations,” Opt. Eng. 44, 111308-111308-4 (2005).
43. W. T. Chien, C. C. Sun, and I. Moreno, “Precise optical model of multi-chip white LEDs,” Opt. Express 15, 7572–7577 (2007).
44. M. Strojnik and G. Paez, “Radiometry,” in Handbook of Optical Engineering, D. Malacara, B. Thompson, eds., (Marcel Dekker, 2001).
45. N. Narendran, Y. Gu, J. P. Freyssinier-Nova, and Y. Zhu, “Extracting phosphor-scattered photons to improve white LED efficiency,” Phys. Stat. Sol. 202, R60-R62 (2005).
46. T. X. Lee, C. Y. Lin, S. H. Ma, and C. C. Sun, “Analysis of position-dependent light extraction of GaNbased LEDs,” Opt. Express 13, 4175-4179 (2005).
47. J. J. Vos, “On the cause of disability glare and its dependence on glare angle, age and ocular pigmentation,” Clin. Exp. Optom. 86, 363–370 (2003).
48. T. Kasahara, D. Aizawa, T. Irikura, T. Moriyama, M. Toda, and M. Iwamoto, “Discomfort glare caused by white LED light sources,” J. Light Vis. Env. 30, 95-103 (2006).
49. J. A. Wheatley, G. J. Benoit, J. E. Anderson, R. W. Biernath, D. G. Freier, T. R. Hoffend, C. D. Hoyle, T. T. Liu, J. D. Lu, M. A. Meis, V. V. Savvateev, C. R. Schardt, M. E. Sousa, M. F. Weber, and T. J. Nevitt, “Efficient LED light distribution cavities using low loss, angle-selective interference transflectors,” Opt. Express 17, 10612–10622 (2009).
50. A. Travis, T. Large, N. Emerton, and S. Bathiche, “Collimated light from a waveguide for a display backlight,” Opt. Express 17, 19714–19719 (2009).
51. I. Moreno, “Creating a desired lighting pattern with an LED array,” Proc. SPIE 7058, 705811-705811-9 (2008).
52. C. C. Sun, I. Moreno, S. H. Chung, W. T. Chien, C. T. Hsieh, and T. H. Yang, “Brightness management in a direct LED backlight for LCD TVs,” J. Soc. Inf. Disp. 16, 519-526 (2008).
53. 謝志鐸，光學擴散板光學模型之研究，國立中央大學光電所碩士論文，中華民國九十六年。
54. 林孟佳，以多晶片封裝LED為LCTV背光源之背光機構之研究，國立中央大學光電所碩士論文，中華民國九十七年。
55. 蕭書立，散射腔體之光學特性研究，私立元智大學光電所碩士論文，中華民國九十八年。
56. M. Trentacoste, W. Heidrich, L. Whitehead, H. Seetzen, and G. Ward, “Photometric image processing for high dynamic range displays,” J. Vis. Commun. Image Represent. 18, 439–451 (2007).
57. H. F. Chen, T. H. Ha, J. H. Sung, H. R. Kim, and B. H. Han, “Evaluation of LCD local-dimming-backlight system,” J. Soc. Inf. Disp. 18, 57-65 (2010).
58. M. Gebauer, P. Benoit, P. Knoll, and M. Neiger, “P-9: Ray Tracing Tool for Developing LCD-Backlights” SID Symposium Digest of Technical Papers 31, 558-561 (2000).
59. C. H. Tien, and C. H. Hung, “An iterative model of diffuse illumination from bidirectional photometric data,” Opt. Express 17, 723–732 (2009).
60. D. Voigt, I. A. Hagendoorn, and E. W. M. van der Ham, “Compact large-area uniform colour-selectable calibration light source,” Metrologia 46, S243–S247 (2009).
61. M. Nieto-Vesperinas, J. A. Sanchez-Gil, A. J. Sant, and J. C. Dainty, “Light transmission from a randomly rough dielectric diffuser: theoretical and experimental results,” Opt. Lett. 15, 1261–1263 (1990).
62. P. Manninen, P. Karha, and E. Ikonen, “Determining the irradiance signal from an asymmetric source with directional detectors: application to calibrations of radiometers with diffusers,” Appl. Opt. 47, 4714–4722 (2008).
63. P. Manninen, “Characterization of diffusers and light-emitting diodes using radiometric measurements and mathematical modeling,” Doctoral Dissertation Thesis, Helsinki University of Technology, Finland (2008).
64. B. Chevalier, M. G. Hutchins, A. Maccari, F. Olive, H. Oversloot, W. Platzer, P. Polato, A. Roos, J. L. J. Rosenfeld, T. Squire, and K. Yoshimura, “Solar energy transmittance of translucent samples: A comparison between large and small integrating sphere measurements,” Sol. Energy Mater. Sol. Cells 54, 197–202 (1998).
65. I. Moreno, M. Avendano-Alejo, and R. I. Tzonchev, “Designing light-emitting diode arrays for uniform nearfield irradiance,” Appl. Opt. 45, 2265–2272 (2006).
66. Labsphere, Inc., A Guide to Integrating Sphere Theory and Applications, at http://www.labsphere.com/
67. D. Terr, “Weighted Mean” From MathWorld-A Wolfram Web Resource, created by Eric W. Weisstein. http://mathworld.wolfram.com/WeightedMean.html.
68. C. C. Sun, W. T. Chien, I. Moreno, C. C. Hsieh, and Y. C. Lo, “Analysis of the far-field region of LEDs,” Opt. Express 17, 13918–13927 (2009).
69. I. Moreno, and C. C. Sun, “Modeling the radiation pattern of LEDs,” Opt. Express 16, 1808–1819 (2008).
70. I. Schnitzer, E. Yablonovitch, C. Caneau, T. J. Gmitter, and A. Scherer, “30% external quantum efficiency from surface textured, thin-film light-emitting diodes,” Appl. Phys. Lett. 63, 2174 (1993).