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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
[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
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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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图 1 传统蝇眼透镜匀化系统光路图 (a)衍射型; (b)成像型
Figure 1. Schematic diagram of conventional fly’s eye lens homogenization system: (a) Diffracting-type; (b) imaging-type.
图 2 蝇眼随机相位调制匀化系统光路图 (a)衍射型; (b)成像型
Figure 2. Schematic diagram of the fly’s eye random phase modulation homogenization system: (a) Diffracting-type; (b) imaging-type.
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.
图 4 衍射型蝇眼随机相位调制匀化系统消相干效果 (a) 累加10次; (b) 累加100次; (c) 累加300次; (d) 累加500次
Figure 4. Decoherence effects of a diffracting type fly’s eye random phase modulation homogenization system: (a) Cumulative 10 times; (b) cumulative 100 times; (c) cumulative 300 times; (d) cumulative 500 times.
图 5 不同子孔径下衍射型系统的匀化效果比较 (a) 不均匀性随子孔径的变化; (b) 不均匀性随叠加次数的变化
Figure 5. Comparison of homogenization effects of diffracting-type systems with different p: (a) The variation of non-uniformity with p; (b) the variation of non-uniformity with cumulative times.
图 6 不同子孔径的衍射型系统的照明面光强分布 (a) p = 0.3 mm; (b) p = 0.9 mm; (c) p = 1.5 mm; (d) p = 2 mm; (e) p = 3 mm; (f) p = 4 mm
Figure 6. Illumination intensity distribution of diffracting-type systems with different p: (a) p = 0.3 mm; (b) p = 0.9 mm; (c) p = 1.5 mm; (d) p = 2 mm; (e) p = 3 mm; (f) p = 4 mm.
图 7 不同子透镜焦距下衍射型系统的匀化效果 (a)不均匀性随子孔径焦距的变化; (b)不均匀性随叠加次数的变化
Figure 7. Comparison of homogenization effects of diffracting-type systems with different fA: (a) The variation of non-uniformity with fA; (b) the variation of non-uniformity with cumulative times.
图 8 不同子透镜焦距的衍射型系统照明光强分布 (a) fA = 5 mm; (b) fA = 25 mm; (c) fA = 45 mm
Figure 8. Illumination intensity distribution of diffracting-type systems with different fA: (a) fA = 5 mm; (b) fA = 25 mm; (c) fA = 45 mm.
图 9 p = 2 mm, fA = 10 mm的衍射型匀化系统的照明光强分布 (a)一维光强分布图; (b)二维光强分布图
Figure 9. llumination intensity distribution of a diffracting-type homogenizing system with p = 2 mm and fA = 10 mm: (a) 1D distribution of intensity; (b) 2D distribution of intensity
图 10 成像型蝇眼随机相位调制匀化系统消相干效果 (a)叠加10次; (b)叠加100次; (c)叠加300次; (a)叠加500次
Figure 10. Decoherence effects of a imaging-type fly’s eye random phase modulation homogenization system: (a) Cumulative 10 times; (b) cumulative 100 times; (c) cumulative 300 times; (d) cumulative 500 times.
图 11 不同子孔径下成像型系统的匀化效果比较 (a) 不均匀性随子孔径的变化; (b) 不均匀性随叠加次数的变化
Figure 11. Comparison of homogenization effects of imaging-type systems with different p: (a) The variation of non-uniformity with p; (b) the variation of non-uniformity with cumulative times.
图 12 不同子孔径的成像型系统的照明面光强分布 (a) p = 0.3 mm; (b) p = 0.9 mm; (c) p = 1.5 mm; (d) p = 2 mm; (e) p = 3 mm; (f) p = 4 mm
Figure 12. Illumination intensity distribution of imaging-type systems with different p: (a) p = 0.3 mm; (b) p = 0.9 mm; (c) p = 1.5 mm; (d) p = 2 mm; (e) p = 3 mm; (f) p = 4 mm.
图 13 不同子透镜焦距下成像型系统的匀化效果 (a)不均匀性随子透镜焦距的变化; (b) 不均匀性随叠加次数的变化
Figure 13. Comparison of homogenization effects of imaging-type systems with different fA : (a) The variation of non-uniformity with fA; (b) the variation of non-uniformity with cumulative times.
图 14 不同子透镜焦距的成像型系统照明光强分布 (a) fA = 5 mm; (b) fA = 25 mm; (c) fA = 45 mm
Figure 14. Illumination intensity distribution of imaging-type systems with different fA: (a) fA = 5 mm; (b) fA = 25 mm; (c) fA = 45 mm.
图 15 传统结构和离焦结构的匀化效果比较 (a)传统结构; (b) fA2 = fA1的离焦结构; (c) fA2 = fA1 + δ的离焦结构
Figure 15. Comparison of homogenization effects between conventional and defocused structures: (a) Conventional structure; (b) defocused structures and fA2 = fA1; (c) defocused structures and fA2 = fA1 + δ.
图 16 离焦量对匀化效果的影响 (a)不均匀性随离焦量的变化; (b) δ= 9 mm的照明面光强分布
Figure 16. Influence of the amount of defocusing on the homogenization effects: (a) The variation of non-uniformity with the amount of defocusing; (b) distribution of intensity on the illuminated surface for δ = 9 mm.
图 17 p = 1.8 mm, fA = 9 mm的衍射型匀化系统的照明光强分布 (a)光强一维分布图; (b)光强二维分布图
Figure 17. llumination intensity distribution of a imaging-type homogenizing system with p = 1.8 mm and fA = 9 mm: (a) 1D distribution of intensity; (b) 2D distribution of intensity.
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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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