陽光為萬物生命所需的能量來源，若能將其引入室內以提供照明，有助於減輕對電力的需求，並對人類的生理和心理健康有益。自然光照明系統由三個子系統組成，包括集光、傳光和放光子系統。集光子系統將陽光集中和壓縮，再由傳光子系統傳至室內，最後由放光子系統提供穩定的照明。本論文旨在解決傳光子系統的準直光立方設計問題，透過擴束、縮束和光展量定理的概念優化準直器，以提升光線的準直度，實現遠距離的光線傳輸，並通過模擬分析，評估優化後準直器的準直效率。優化後的準直器在遠距離傳輸方面展現出良好的效能，能夠保留超過一半的能量，提供高能量輸出，同時維持較小的光斑尺寸和全發散角，這顯示出準直器的優異準直效率。

The sunlight serves as the essential energy source for all living beings. If it can be harnessed to provide indoor illumination, it would help alleviate the demand for electrical power and contribute to the physiological and psychological well-being of humans. The Natural Light Illumination System (NLIS) consists of three subsystems: the light collection, light transmission, and light emission subsystems. The light collection subsystem concentrates and compresses sunlight, which is then transmitted indoors through the light transmission subsystem. Finally, the light emission subsystem provides stable illumination.
This paper aims to address the design issues of the collimating LightCube in the light transmission subsystem. By optimizing the collimator's design using concepts such as beam expansion, beam compression, and Etendue, the goal is to enhance the collimation of light and achieve long-distance light transmission. The optimized collimator's collimation efficiency is evaluated through simulation analysis. The results demonstrate that the optimized collimator exhibits superior collimation efficiency compared to the non-optimized counterpart. Even with increasing transmission distances, the optimized collimator maintains higher total energy output, significantly smaller spot size, and reduced full divergence angle, indicating excellent collimation performance.

[1] M. N. Mead, "Benefits of sunlight: a bright spot for human health," (in eng), Environ Health Perspect, vol. 116, no. 4, pp. A160-7, Apr 2008, doi: 10.1289/ehp.116-a160.
[2] R. Stewart and V. Hirani, "Relationship between vitamin D levels and depressive symptoms in older residents from a national survey population," (in eng), Psychosom Med, vol. 72, no. 7, pp. 608-12, Sep 2010, doi: 10.1097/PSY.0b013e3181e9bf15.
[3] K. Al-Obaidi, M. Ismail, and A. Rahman, "A Review of Skylight Glazing Materials in Architectural Designs for a Better Indoor Environment," Modern Applied Science, vol. 8, pp. 68-82, 12/30 2013, doi: 10.5539/mas.v8n1p68.
[4] J. Mardaljevic, M. Andersen, N. Roy, and J. Christoffersen, "Daylighting Metrics for Residential Buildings," 01/01 2011.
[5] W. H. Steel, "Luminosity, Throughput, or Etendue?," Appl. Opt., vol. 13, no. 4, pp. 704-705, 1974/04/01 1974, doi: 10.1364/AO.13.000704.
[6] X. Sun, Z. Zheng, X. Liu, and P. Gu, "Etendue analysis and measurement of light source with elliptical reflector," Displays, vol. 27, pp. 56-61, 03/01 2006, doi: 10.1016/j.displa.2005.10.002.
[7] A. v. Pfeil, F. Wyrowski, A. Drauschke, and H. Aagedal, "Analysis of optical elements with the local plane-interface approximation," Appl. Opt., vol. 39, no. 19, pp. 3304-3313, 2000/07/01 2000, doi: 10.1364/AO.39.003304.
[8] 趙坤峙, "應用於自然光照明系統的多角度準直透鏡," 碩士, 電子工程系, 國立臺灣科技大學, 台北市, 2019. [Online]. Available: https://hdl.handle.net/11296/dg79c7
[9] 張政民, "根基於光立方模組之次世代NLIS系統的設計與研發," 博士, 電子工程系, 國立臺灣科技大學, 台北市, 2021. [Online]. Available: https://hdl.handle.net/11296/b7bs7f
[10] 何友皓, "前集光定日鏡設計應用於自然光照明系統," 碩士, 電子工程系, 國立臺灣科技大學, 台北市, 2015. [Online]. Available: https://hdl.handle.net/11296/jx64y6
[11] 李維, "應用於自然光照明系統之低損耗微稜鏡陣列準直器設計方法," 碩士, 電子工程系, 國立臺灣科技大學, 台北市, 2016. [Online]. Available: https://hdl.handle.net/11296/z68a53
[12] Y. K. Cheng and K. W. E. Cheng, General Study for using LED to replace traditional lighting devices. 2006, pp. 173-177.
[13] D.-H. Kang and M.-S. Jung, "Study on the Design of Asymmetric Lighting with Uniform Illumination Over a Large Area at Short Distance," Korean Journal of Optics and Photonics, vol. 31, no. 4, pp. 183-190, 2020.
[14] 傅玉婷, "應用於傳光系統之高精度自由曲面雙面式準直器," 碩士, 電子工程系, 國立臺灣科技大學, 台北市, 2017. [Online]. Available: https://hdl.handle.net/11296/32wphm
[15] L. International. "Investigation of Ghost Image Effects in Collimation System." https://www.lighttrans.com/use-cases/application/investigation-of-ghost-image-effects-in-collimation-system.html (accessed 7/24, 2023).
[16] A. Srivastava, K. Sati, and S. Kumar, "Optical method for measurement of radius of curvature of large diameter mirrors," vol. 8, 07/01 2017.
[17] A. Rakich, The 100th birthday of the conic constant and Schwarzschild's revolutionary papers in optics (Optics and Photonics 2005). SPIE, 2005.
[18] 劉家佑, "鮑爾透鏡之鏡頭設計與物理光學之詮釋," 碩士, 光電工程系所, 國立交通大學, 新竹市, 2005. [Online]. Available: https://hdl.handle.net/11296/2u579h
[19] D. Schurig and D. Smith, "Universal description of spherical aberration free lenses composed of positive or negative index media," arXiv preprint physics/0307088, 2003.
[20] c. Wikipedia, "Conic constant," in Wikipedia, The Free Encyclopedia., ed.
[21] J. A. Nelder and R. Mead, "A Simplex Method for Function Minimization," The Computer Journal, vol. 7, no. 4, pp. 308-313, 1965, doi: 10.1093/comjnl/7.4.308.
[22] 呂旻奕, "應用於自然光照明系統之自由曲面放光模組設計," 碩士, 色彩與照明科技研究所, 國立臺灣科技大學, 台北市, 2021. [Online]. Available: https://hdl.handle.net/11296/f4j94u
[23] A. J.-W. Whang et al., "Development and Testing of a Modular Sunlight Transport System Employing Free-Form Mirrors," Energies, vol. 15, no. 2, p. 406, 2022. [Online]. Available: https://www.mdpi.com/1996-1073/15/2/406.
[24] L. Wald, "BASICS IN SOLAR RADIATION AT EARTH SURFACE," 2018-01-05, 2018.
[25] L. M. Fraas and L. D. Partain, Solar cells and their applications. John Wiley & Sons, 2010.
[26] C. Gueymard, "Solar Radiation solar radiation Spectrum solar radiation spectrum," 2013, pp. 608-633.
[27] X. Liu, Z. Lu, X. Wang, Z. Jiang, and Y. Li, "Study on the focusing characteristics of off-axis parabolic mirror focusing system," in 2011 Academic International Symposium on Optoelectronics and Microelectronics Technology, 12-16 Oct. 2011 2011, pp. 116-119, doi: 10.1109/AISMOT.2011.6159331.
[28] C. E. Gutiérrez and A. Sabra, "Chromatic aberration in metalenses," Advances in Applied Mathematics, vol. 124, p. 102134, 2021/03/01/ 2021, doi: https://doi.org/10.1016/j.aam.2020.102134.
[29] "The runners-up," Science, vol. 354, no. 6319, pp. 1518-1523, 2016/12/23 2016, doi: 10.1126/science.354.6319.1518.
[30] R. J. Lin et al., "Achromatic metalens array for full-colour light-field imaging," Nature Nanotechnology, vol. 14, no. 3, pp. 227-231, 2019/03/01 2019, doi: 10.1038/s41565-018-0347-0.