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When using a fly’s eye lens system to homogenize highly coherent light sources, the interference effect between the sub-beams can cause a periodic speckle distribution of illumination intensity, thereby disrupting illumination uniformity. It has been shown that using a rotating optical phase-shift plate behind the fly’s eye lens can eliminate interference patterns, but it only demonstrates engineering realizations. And the theoretical analysis and technical guidance on the phase modulation method and statistical averaging method for fly’s eye lens homogenization systems are still lacking. In this work, a simulation model of fly’s eye random phase modulation homogenization system is developed and studied in detail. Each sub-beam of the fly’s eye lens is randomly phase-modulated to break the coherence condition, and the illumination intensity of multiple independent modulations is accumulated to eliminate the interference pattern. The more times the intensity is accumulated, the better the homogenization is. Meanwhile, studied in this paper are the influence of the diffraction effect on homogenization, and the influence of the sub-lens size and focal length on the homogenization, which result in the diffracting-type system and the imaging-type system respectively. For an imaging type system, it is necessary to ensure that the first fly’s eye lens is in the front focal plane of the second fly’s eye lens. By optimizing the parameters of the fly’s eye lens and using an imaging-type system with p = 1.8 mm and fA = 9 mm, a Gaussian beam with the non-uniformity of 117% is homogenized into a flat-topped beam with the non-uniformity of 1.2% in a square illumination area of 100 mm2. This fly’s eye lens random phase modulation homogenization system has a simple structure, low energy loss, and good illumination uniformity, and can be used in systems that require high coherent laser input and high resolution. This technology can be used in the field of deep-ultraviolet mask defect detection.
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Keywords:
- high-coherence light /
- homogenization /
- fly’s eye lens /
- phase modulation
[1] 郁道银, 谈恒英 2006 工程光学 (北京: 机械工业出版社) 第165页
Yu D Y, Tan H Y 2006 Engineering Optics (Beijing: China Machine Press) p165
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Google Scholar
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Goodman J W (translated by Chen J B, Qin K C, Cao Q Z) 2020 Introduction to Fourier Optics (Beijing: Science Press) pp145–151
[25] 李丽, 韩学勤, 赵士伟, 包鸿音, 王兴宾 2014 激光与光电子学进展 51 011401
Li L, Han X Q, Zhao S W, Bao H Y, Wang X B 2014 Laser Optoelectronics Prog. 51 011401
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图 3 传统蝇眼透镜匀化系统仿真结果 (a)衍射型系统照明面一维光强分布图和局部放大图; (b)成像型系统照明面一维光强分布图和局部放大图; (c)干涉图案二维局部放大图
Figure 3. Simulation results of a conventional fly’s eye lens homogenization system: (a) One-dimensional (1D) intensity distribution at the illumination surface of a diffracting-type system and its partial enlarged image; (b) 1D intensity distribution at the illumination surface of a imaging-type system and its partial enlarged image; (c) two-dimensional (2D) localized enlargement of the interference pattern.
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[1] 郁道银, 谈恒英 2006 工程光学 (北京: 机械工业出版社) 第165页
Yu D Y, Tan H Y 2006 Engineering Optics (Beijing: China Machine Press) p165
[2] 许祖彦 2006 激光与红外 36 737
Google Scholar
Xu Z Y 2006 Laser Infrared 36 737
Google Scholar
[3] Deng L X, Dong T H, Fang Y W, Yang Y H, Gu C, Ming H, Xu L X 2021 Opt. Laser Tech. 135 106686
Google Scholar
[4] Wierer J J, Tsao J Y 2015 Phys. Status Solidi A 212 980
Google Scholar
[5] Farshidianfar M H, Khajepouhor A, Gerlich A P 2017 Surf. Coat. Tech. 315 326
Google Scholar
[6] Takada A, Tojo T, Shibuya M 2008 J. Micro-nanolith. Mem. 7 043010
Google Scholar
[7] Dickey F M 2014 Laser Beam Shaping Theory and Techniques (2nd Ed.) (Boca Raton: CRC Press) pp406–414
[8] Deng X M, Liang X C, Chen Z Z, Yu W Y, Ma R Y 1986 Appl. Opt. 25 377
Google Scholar
[9] Streibl N, Nölscher U, Jahns J, Walker S 1991 Appl. Opt. 30 2739
Google Scholar
[10] 郑昕, 戴深宇, 张玉莹, 赵帅 2023 光学学报 43 1014005
Google Scholar
Zheng X, Dai S Y, Zhang Y Y, Zhao S 2023 Acta Opt. Sin. 43 1014005
Google Scholar
[11] Zhang F, Zhu J, Yang B X, Huang L H, Hu X B, Xiao Y F, Huang H J 2013 International Conference on Optical Instruments and Technology: Optoelectronic Measurement Technology and Systems Beijing, China, November 17–19, 2013 p904619
[12] Jin Y H, Hassan A L, Jiang Y J 2016 Opt. Express 24 24846
Google Scholar
[13] Büttner A, Zeitner U D 2002 Opt. Eng. 41 2393
Google Scholar
[14] 傅思祖, 孙玉琴, 黄秀光, 吴江, 周关林, 顾援 2003 中国激光 30 129
Fu S Z, Sun Y Q, Huang X G, Wu J, Zhou G L, Gu Y 2003 Chin. J. Lasers 30 129
[15] Harder I, Lano M, Lindlein N, Schwider J 2004 Photon Management Strasbourg, France, April 26-30, 2004 p99
[16] Wippermann F, Zeitner U D, Dannberg P, Bräuer A, Sinzinger S 2007 Opt. Express 15 6218
Google Scholar
[17] Cao A, Pang H, Wang J Z, Zhang M, Shi L F, Deng Q L 2015 IEEE Photonics J. 7 2400207
Google Scholar
[18] Kopp C, Ravel L, Meyrueis P 1999 J. Opt. A Pure Appl. Opt. 1 398
Google Scholar
[19] 裴宪梓, 梁永浩, 王菲, 朱效立, 谢常青 2019 光子学报 48 314001
Google Scholar
Pei X Z, Liang Y H, Wang F, Zhu L X, Xie C Q 2019 Acta Photonica Sin. 48 314001
Google Scholar
[20] Zhao X H, Gao Y Q, Li F J, Ji L L, Cui Y, Rao D X, Feng W, Ma W X 2019 Appl. Opt. 58 2121
Google Scholar
[21] Li F J, Gao Y Q, Zhao X H, Xia L, Liu D, Ji L L, Feng W, Rao D X, Cui Y, Shi H T, Liu J N, Ma W X, Sui Z 2020 Appl. Opt. 59 2976
Google Scholar
[22] Voelkel R, Weible K J 2008 Optical Fabrication, Testing, & Metrology III Glasgow, Scotland, United Kingdom, September 2–5, 2008 p71020J
[23] Oohashi K, Inoue H, Nomura T, Ono A, Tabata M, Suzuki H 2000 Photomask and Next Generation Lithography Mask Technology VII Kanagawa, Japan, April 12–13, 2000 p452
[24] 古德曼 J W 著 (陈家壁, 秦克诚, 曹其智 译) 2020 傅里叶光学导论(北京: 科学出版社) 第145— 151页
Goodman J W (translated by Chen J B, Qin K C, Cao Q Z) 2020 Introduction to Fourier Optics (Beijing: Science Press) pp145–151
[25] 李丽, 韩学勤, 赵士伟, 包鸿音, 王兴宾 2014 激光与光电子学进展 51 011401
Li L, Han X Q, Zhao S W, Bao H Y, Wang X B 2014 Laser Optoelectronics Prog. 51 011401
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