微透鏡陣列（Microlens Array, MLA）已廣泛應用於光源均勻化，特別是在照明、抬頭顯示器（HUD）、擴增實境（AR）…等工程領域，這些應用都要求顯示屏幕在短距離內即具備高亮度與高均勻度的光照分佈；然而，傳統規則且週期性的MLA結構應用於同調光源時，易產生干涉條紋與光斑，造成均光性能下降，成為極需克服的難題與挑戰。
本研究利用實驗室自行研發之數位光學式無光罩曝光機，在光阻(Photoresist)上執行高精度劑量控制與複雜圖形的灰階曝光，再經由顯影製程，得到可精確控制形貌的MLA。此一微結構製程除能製作傳統週期性且大面積的MLA，更可以精確調控每一個微透鏡的參數，如其中心位置、距離基準面的高度、與曲率半徑…等等，進而生成非週期、不規則、且參數隨機分布的MLA。藉由打破結構週期性，有效抑制干涉效應，使其光照分布錯位交疊，從而顯著提升投射之光束的均勻性，大幅改善同調光源的均光品質。本論文深入討論各種參數隨機分布之MLA的設計、製作、與光學實驗量測結果，並以量化的方式成功辨識出各個微透鏡參數對於最終均光效果的影響力。
其次，為進一步提高微透鏡均光系統的均勻性與光源利用率，本研究同步發展自由曲面微透鏡陣列。每一微透鏡形貌，皆依其對應至目標均光區的相對位置量身設計。為了消除同調光源的干涉與光斑問題，此一自由曲面MLA的設計也同樣引入隨機參數，隨機改變每一個自由曲面微透鏡的位置、大小、與形狀。根據無光罩曝光機與黃光微影製程所製作之實際成品與光學實測結果顯示，隨機自由曲面MLA相較傳統週期性結構，在光線折射與能量分布上具高度靈活性，能依應用需求產生客製化均光光場，展現優異的光學性能與應用潛力。

Microlens arrays (MLAs) are widely used for light homogenization, especially in applications such as illumination, head-up displays (HUD), and augmented reality (AR), where high brightness and uniformity are required at short distances. However, conventional periodic MLAs tend to produce interference fringes and speckle patterns when used with coherent light sources, posing significant challenges for uniform illumination.
This study utilizes a custom-developed digital maskless lithography system to fabricate microlens arrays on photoresist layers with high-precision grayscale exposure and dose control. In addition to fabricating conventional periodic MLAs, the system enables precise control over individual microlens parameters—such as center position, height, and radius of curvature—allowing the creation of non-periodic, randomly distributed arrays. By breaking the periodicity, interference effects are effectively suppressed, resulting in significantly improved beam uniformity. The influence of various random parameters on light uniformity is quantitatively analyzed in this work.
To further enhance uniformity and light utilization, this study also develops freeform microlens arrays. Each microlens is individually designed based on its position relative to the target illumination area, with randomized variations in position, size, and shape to reduce interference and speckle. Experimental results demonstrate that such random freeform MLAs offer superior control over refraction and energy distribution, enabling customized light fields tailored to specific applications and expanding the potential of high-performance optical systems.

[1] S. Pfadler, F. Beyrau, M. Löffler, and A. Leipertz, “Application of a Beam Homogenizer to Planer Laser Diagnostics,” Optics Express, vol. 14, issue 22, pp. 10171-10180, 2006.
[2] M. Tanaka, H. Kiriyama, Y. Ochi, Y. Nakai, H. Sasao, H. Okada, H. Daido, P. Bolton, and S. Kawanishi, “High-energy, Spatially Flat-Top Green Pump Laser by Beam Homogenization for Petawatt Scale Ti: Sapphire Laser Systems,” Optics Communications, vol. 282, issue 22, pp. 4401-4403, 2009.
[3] A. Köhler, “New Method of Illumination for Photomicrographical Purposes,” J. R. Microsc. Soc., vol. 14, pp. 261-262, 1894.
[4] G. Benner and W. Probst, “Köhler illumination in the TEM: fundamentals and advantages,” J. Microsc., vol. 174, no. 2, pp. 133–142, 1994.
[5] M. Zimmermann, N. Lindlein, R. Voelkel, and K. J. Weible, “Microlens Laser Beam Homogenizer: From Theory to Application,” in Proc. SPIE 6663, Laser Beam Shaping VIII, 666302, 2007.
[6] R. Voelkel and K. J. Weible, “Laser Beam Homogenizing: Limitations and Constraints,” in Proc. SPIE 7102, Optical Fabrication, Testing, and Metrology III, 71020J, 2008.
[7] L. Xue, Y. Pang, W. Liu, L. Liu, H. Pang, A. Cao, L. Shi, Y. Fu, and Q. Deng, “Fabrication of random microlens array for laser beam homogenization with high efficiency,” Micromachines, vol. 11, no. 3, pp. 338, 2020.
[8] S. Tanikawa and J. Yan, “Fabrication of micro-structured surface with controllable randomness by using FTS-based diamond turning,” Precision Engineering, vol. 73, pp. 363-376, 2022.
[9] H. Zhang et al., “Random Silica-Glass Microlens Arrays Based on the Molding Technology of Photocurable Nanocomposites,” ACS Applied Materials & Interfaces, vol. 15, no. 15, pp. 19230-19240, 2023.
[10] J. Zhang, S. Ma, W. Tan, M. Liu, X. Chen, J. Xiao, and J. Xu, "Random spherical microlens array fabricated by elliptical vibration diamond cutting and molding," Appl. Opt., vol. 62, pp. 3445–3453, 2023.
[11] Q. Wang, L. Liu, S. Yang, Z. Yang, X. Xu, S. Wu, X. Su, J. Duan, W. Xiong, and L. Deng, “Maskless fabrication of honeycomb random microlens array by a femtosecond laser,” Opt. Laser Technol., vol. 171, p. 110386, 2024.
[12] L. Sun, S. Jin, and S. Cen, “Free-form microlens for illumination applications,” Applied Optics, vol. 48, no. 28, pp. 5520–5527, 2009.
[13] L. Li and A. Y. Yi, “Design and fabrication of a freeform microlens array for uniform beam shaping,” Microsyst. Technol., vol. 17, no. 11, pp. 1713–1720, 2011.
[14] R. Wu, H. Wang, P. Liu, Y. Zhang, Z. Zheng, H. Li, and X. Liu, “Efficient optimal design of smooth optical freeform surfaces using ray targeting,” Opt. Commun., vol. 300, pp. 100–107, 2013.
[15] R. Wu, P. Liu, Y. Zhang, Z. Zheng, H. Li, and X. Liu, “A mathematical model of the single freeform surface design for collimated beam shaping,” Opt. Express, vol. 21, no. 17, pp. 20974–20989, 2013.
[16] Z. Liu, H. Liu, Z. Lu, Q. Li, and J. Li, “A beam homogenizer for digital micromirror device lithography system based on random freeform microlenses,” Optics Communications, vol. 443, pp. 211–215, 2019.
[17] 許永昕, “利用斜掃描與頻閃技術之高精度無光罩式微影系統的開發與應用,” 國立成功大學機械工程學系博士論文, 2023.
[18] 簡弘量, “光點陣列斜掃描無光罩式微影系統開發,” 國立成功大學機械工程學系博士論文, 2020.
[19] Texas Instruments, “DLP6500 0.65 1080p MVSP Type A DMD,” DLPS040A datasheet, Oct. 2014 [Revised Oct. 2016].
[20] W.F. Lee, C.Y. Wu, and Y.C. Lee, "High performance DMD lithography based on oblique scanning, pulse lighting, and optical distortion calibration," Opt. Laser Technol., vol. 183, p. 112388, 2025.
[21] J. A. Nelder and R. Mead, “A Simplex Method for Function Minimization,” J. Comput., vol. 7, pp. 308-313, 1965.
[22] D. Frisch and U. D. Hanebeck, "Deterministic Gaussian Sampling With Generalized Fibonacci Grids," in Proc. 2021 IEEE 24th Int. Conf. Inf. Fusion (FUSION), Sun City, South Africa, 2021, pp. 1–8.
[23] 張簡翊秀, “無光罩數位微影之光阻曝光模擬與隨機微透鏡陣列製造,” 國立成功大學機械工程學系碩士論文, 2024.
[24] J. W. Goodman, "Some fundamental properties of speckle," J. Opt. Soc. Am., vol. 66, pp. 1145–1150, 1976.
[25] W. Yuan, L. Xue, A. Cao, H. Pang, and Q. Deng, "Close packed random rectangular microlens array used for laser beam homogenization," Opt. Express, vol. 29, pp. 40878–40890, 2021.
[26] 林孟箴, “利用創新製程製作複眼微透鏡與應用於提升有機發光二極體發光效能之研究,” 國立台灣科技大學機械工程學系碩士論文, 2013.
[27] J. Wang, W. Zhou, Y. Liu, G. He, and Y. Yang, “Biomimetic compound eyes with gradient ommatidium arrays,” ACS Appl. Mater. Interfaces, vol. 15, no. 37, pp. 44503–44512, 2023
[28] S. L. Aristizabal, G. A. Cirino, A. N. Montagnoli, A. A. Sobrinho, J. B. Rubert, M. Hospital, and R. D. Mansano, “Microlens array fabricated by a low-cost grayscale lithography maskless system,” Optical Engineering, vol. 52, no. 12, p. 125101, Dec. 2013
[29] 翁朝利, “光學鄰近效應修正方法應用於數位微反射鏡之無光罩微影系統,” 國立成功大學機械工程學系碩士論文, 2024.