本論文中，我們將提出一個架構用以分析並探討白光 LED 中場之色彩分佈，我們將討論當 LED光源上加上二次光學元件時，黃暈的產生之機制，並希望藉此方法於後續的二次光學設計時，可以在設計時就將會導致黃暈的部分進行優化，以達到色彩高均勻度。
在文章中，我們將先對用來量測空間色彩分佈的光譜儀進行校正，接下來針對碗杯型式的封裝體之 LED空間中的色彩變化進行分析，我們使用已建構之YAG螢光粉模型在相同螢光粉濃度下，分別在有無半球形透鏡的條件下建立藍黃光之光學模型，並以實驗驗證其準確性。接著討論將光源加上二次光學透鏡之色彩分佈，並以實驗驗證建立之藍黃光光學模型可用於分析色彩均勻度。而在文章的最後，我們將討論兩種白光 LED 的藍黃光之中場距離分佈。

In this thesis, we propose the framework to analyze and explore the color distribution of the white LED in mid-field. We discuss the mechanism of the yellow ring when the LED light source coupled with secondary optics, and would like to take this approach to the follow-up second optical design. As long we design the part of the second optical elements correctly, the yellow ring can achieve high and uniform color.
In this article, we corrected the spectrometer which is used to measure the color distribution of the space. Furthermore, we studied on the deviation of the color distribution in the space for LEDs in-cup encapsulation. Based on the YAG phosphor model, in the same concentration of the phosphor, we constructed simulation results and verified experiments in the case of that with or without the hemispherical lens. Moreover, we also made simulation results and verified experiments when the light source was coupled with the TIR lens. Finally, we discussed the distance of blue and yellow lights.

[1] N. Holonyak, Jr. and S. F. Bevacqua, “Coherent (visible) light emission from Ga(As1-x Px) junctions,” Appl. Phys. Lett. 1, 82-83 (1962).
[2] S. Nakamura, T. Mukai, and M. Senoh, “Candela-class high-brightness InGaN/AIGaN double-heterostructure blue-light-emitting diodes,” Appl. Phys. Lett. 64, 1687-1689 (1994).
[3] 郭浩中、賴芳儀、郭守義，LED原理與應用，初版，五南出版社，台灣，中華民國九十八年。
[4] Y. Shimizu, K. Sakano, Y. Noguchi, and T. Moriguchi, “Light emitting device having a nitride compound semiconductor and a phosphor containing a garnet fluorescent material,” United States Patent, US 5998925 (1999).
[5] A. Zauskas, F. Ivanauskas, R. Vaicekauskas, M. S. Shur, and R. Gaska, “ Optimization of mulitichip white solid state lighting source with four or more LEDs,” Proc. SPIE 4445, 148-155 (2001).
[6] S. Muthu, F. J. P. Schuurmans, and M. D. Pashley, “Red, green, and blue LEDs for white light illumination,” IEEE J. Sel. Top. Quantum Electronics 8, 333-338 (2002).
[7] Y. Sato, N. Takahashi, and S. Sato, “Full-color fluorescent display devices using a near-UV light-emitting diode,” Jpn. J. Appl. Phys. 35, 838-839 (1996).
[8] T. F. McNulty, B. Lake, D. D. Doxsee, S. Hills, and J. W. Rose, “UV reflectors and UV-based light source having reduced UV radiation leakage incorporating the same,” United States Patent, US 6686676 B2 (2004).
[9] P. Schlotter, R. Schmidt, and J. Schneider, “Luminescence conversion of blue light emitting diodes,” Appl. Phys. A 64, 417-418 (1997).
[10] S. Nakamura and G. Fasol, The Blue Laser Diode: GaN based light emitters and lasers (Spinger, New York, 1997).
[11] A. A. Setlur, A. M. Srivastava, H. A. Comanzo, and D. D. Doxsee, “Phosphor blends for generating white light from near-UV/blue light-emitting devices,” United States Patent, US 6685852 B2 (2004).
[12] C. C. Yang, C. M. Lin, Y. Chen, Y. T. Wu, S. R. Chuang, S. F. Huand, and R. S. Liua, “Highly stable three-band white light from an InGaN-based blue light emitting diode chip precoated with (oxy)nitride green/red phosphors,” Appl. Phys. Lett. 90, 123503 (2007).
[13] Y. H. Won, H. S. Jang, K. W. Cho, Y. S. Song, D. Y. Jeon, and H. K. Kwon, “Effect of phosphor geometry on the luminous efficiency of high-power white light-emitting diodes with excellent color rendering property,” Opt. Lett. 34, 1-3 (2009).
[14] ENERGY STAR, http://www.energystar.gov/index.cfm?c=ssl_res.pt_ssl/.
[15] N. Narendran, Y. Gu, J. P. Freyssinier-Nova, and Y. Zhu, “Extracting phosphor-scattered photons to improve white LED efficiency,” Phys. Stat. Sol. A 202, 60-62 (2005).
[16] H. Luo, J. K. Kim, E. F. Schubert, J. Cho, C. Sone, and Y. Park, “Analysis of high-power packages for phosphor-based white-light-emitting diodes,” Appl. Phys. Lett. 86, 243505 (2005).
[17] S. C. Allen and A. J. Steckl, “A nearly ideal phosphor-converted white light-emitting diode,” Appl. Phys. Lett. 92, 143309 (2008).
[18] B. F. Fan, H. Wu, Y. Zhao, Y. L. Xian, and G. Wang, “Study of phosphor thermal-isolated packaging technologies for high-power white light-emitting diodes,” IEEE Photon. Technol. Lett. 19, 1121-1123 (2007).
[19] Z. Y. Liu, S. Liu, K. Wang, and X. B. Luo, “Optical analysis of color distribution in white LEDs with various packaging methods,” IEEE Photon. Technol. Lett. 20, 2027-2029 (2008).
[20] R. C. Jordan, J. Bauer, and H. Oppermann, “Optimized heat transfer and homogeneous color converting for ultra high brightness LED package,” Proc. SPIE 6198, 61980-B:1-12 (2006).
[21] S. C. Allen and A. J. Steckl, “ELiXIR- solid-state luminaire with enhanced light extraction by internal,” J. Display Technol. 3, 155-159 (2007).
[22] Z. Liu, S. Liu, K. Wang, and X. Luo, “Effects of phosphor’s location on LED packaging performance,” ICEPT-HDP, 1-7 (2008).
[23] Z. Y. Liu, S. Liu, K. Wang, and X. B. Luo, “Studies on Optical Consistency of White LEDs Affected by Phosphor Thickness and Concentration Using Optical Simulation,” IEEE Trans. Compon. Packag. Techol. 33, 680-687 (2010).
[24] J. K. Kim, H. Luo, E. F. Schubert, J. Cho, C. Sone, and Y. Park, “Strongly enhanced phosphor efficiency in GaInN white light-emitting diodes using remote phosphor configuration and diffuse reflector cup,” Jpn. J. Appl. Phys. 44, 649-651 (2005).
[25] H. C. Kuo, C. W. Hung, H. C. Chen, K.J. Chen, C. H. Wang, C. W. Sher, C. C. Yeh, C. C. Lin, C. H. Chen, and Y. J. Cheng, “Patterned structure of REMOTE PHOSPHOR for phosphor-converted white LEDs,” Opt. Express 19, A930-A936 (2011).
[26] K. M. Moon, S. H. An, H. K. Kim, J. H. Chae, and Y. J. Park “Phosphor concentration and geometry for high power white light emitting diode,” Proc. SPIE 7617, 76171Y (2010).
[27] D. A. Steigerwald, J. C. Bhat, D. Collins, R. M. Fletcher, M. O. Holcomb, M. J. Ludowise, P. S. Martin, and S. L. Rudaz, “Illumination with solid state lighting technology,” IEEE J. Select. Topics Quantum Electron. 8, 310-320 (2002).
[28] H. T. Huang, C. C. Tsai, and Y. P. Huang, “Conformal phosphor coating using pulsed spray to reduce color deviation of white LEDs,” Opt. Express 18, A201-A206 (2010).
[29] B. Hou, H. B. Rao, and J. F. Li, “Methods of increasing luminous efficiency of phosphor-converted LED realized by conformal phosphor coating,” J. Display Technol. 5, 57-60 (2009).
[30] Z. Liu, S. Liu, K. Wang, and X. Luo, “Optical Analysis of Color Distribution in White LEDs With Various Packaging Methods ,” IEEE Photon. Technol. Lett 20, 2027-2029 (2008).
[31] K. Wang, D. Wu, F. Chen, Z. Y. Liu, X. B. Luo, and S. Liu, “Angular color uniformity enhancement of white light-emitting diodes integrated with freeform lenses,” Opt. Lett. 35, 1860-1862 (2010).
[32] C. C. Sun, C. Y. Chen, C. C Chen, C. Y. Chiu, Y. N. Peng, Y. H. Wang, T. H. Yang, T. Y. Chung, and C. Y. Chung, “High uniformity in angular correlated-color temperature distribution of white LEDs from 2800K to 6500K,” Opt. Express 20, 6622-6630 (2012)
[33] M. A. Stevenson, M. Cote, C. J. Campillo, D. G. Jenkins, “Computer simulation of asymmetric arc lamp volume emitters,” Proc. SPIE 3780, 226 (2002).
[34] 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).
[35] M. S. Kaminski, K. J. Garcia, M. A. Stevenson, M. Frate, and R. J. Koshel, “Advanced Topics in Source Modeling,” Proc. SPIE 4775, 186 (1999).
[36] H. Zerfhau-Dreihofer, U. Haack, T. Weber, and D.Wendt, “Light source modeling for automotive lighting devices, ”Proc. SPIE 4775, 9 (2002).
[37] W. T. Chien, C. C. Sun, and I. Moreno, “Precise optical model of multi-chip white LEDs,” Opt. Express 15, 7572–7577 (2007).
[38] E. F. Schubert, Light Emitting Diodes (Cambridge University Press, New York, 2006).
[39] J . M . Palmer and B. G. Grant, The art of radiometry (SPIE Press Book, 2006).
[40] G. Wyszecki and W.S. Stiles, Color science : concepts and methods, quantitative data, and formulae (John Wiley & Sons, New York, 1982)
[41] Colour & Vision database, http://cvision.ucsd.edu/.
[42] 大田登，基礎色彩再現工程，全華科技圖書公司，中華民國九十四年。
[43] Wikipedia, http://en.wikipedia.org/.
[44] E. F. Schubert, Light-emitting Diodes (Cambridge University Press, New York, 2006).
[45] D. B. Judd, D. L. Macadam, and G. Wyszecki, “Spectral distribution of typical daylight as a function of correlated color temperature,” J. Opt. Soc. Am. 54, 1031-1036 (1964).
[46] LED照明科技研究中心, http://led.ee.ncku.edu.tw/.
[47] 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 15, 13918-13927 (2009).
[48] Ocean Optics, http://www.oceanoptics.com/.
[49] K. Yamada, Y. Imai, and K. Ishii, “Optical simulation of light source devices composed of blue LEDs and YAG phosphor,” J. Light & Vis. Env. 27, 70-74 (2003).
[50] 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).
[51] 紀葦世，高效能YAG螢光粉之特性量測與模型，元智大學光電所碩士論文，中華民國九十九年。
[52] Cree Inc., http://www.cree.com/.