基于粒子群算法离轴多反光学系统设计

吴越; 王丽萍; 于杰; 张旭; 金春水

doi:10.37188/CO.2021-0087

基于粒子群算法离轴多反光学系统设计

吴越^{1, 2,},
王丽萍^1, ,,
于杰¹,
张旭^{1, 2},
金春水^1, ,

1.
中国科学院长春光学精密机械与物理研究所，吉林长春 130033
2.
中国科学院大学，北京 100039

详细信息

中图分类号: TN305.7
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出版历程
- 收稿日期: 2021-04-22
- 修回日期: 2021-05-06
- 网络出版日期: 2021-06-22
- 刊出日期: 2021-11-19

Design of off-axis multi-reflective optical system based on particle swarm optimization

doi: 10.37188/CO.2021-0087

WU Yue^{1, 2
,},
WANG Li-ping^{1
, ,},
YU Jie¹,
ZHANG Xu^{1, 2},
JIN Chun-shui^{1
, ,}

1.
Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, Changchun 130033, China
2.
University of Chinese Academy of Sciences, Beijing 100039, China

Funds: Supported by National Science and Technology Major Project (No. 2018ZX02102002)

More Information

Author Bio:
WU Yue (1993—), male, born in Huanggang, Hubei Province, Ph.D. student. He received his bachelor's degree from Northeast Normal University in 2015. He is mainly engaged in the research of optical design. E-mail: wy2398236580@163.com

WANG Li-ping (1981—), female, born in Changchun, Jilin Province. She is a Ph.D., researcher. She received her doctor's degree from Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences in 2009. She is mainly engaged in the research on optics technology of EUV. She has published 17 articles and 26 authorized patents. E-mail: wlp8121@126.com

JIN Chun-shui (1964—), male, born in Changchun, Jilin, Ph.D., researcher, doctoral supervisor. He received his Ph.D. degree from Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences in 2003. He is mainly engaged in the research on UV-EUV imaging optics, UV-EUV optical thin film technology and ultra-high-precision optical metrology. E-mail: jincs@sklao.ac.cn

Corresponding author: wlp8121@126.com; jincs@sklao.ac.cn

摘要

摘要: 满足像差平衡和多约束控制的初始结构构建，是实现极小像差离轴多反光学系统的设计关键。本文基于空间光线追迹与像差矫正相结合的分组设计方法建立离轴多反的初始结构计算数学模型，提出了一种改进的粒子群算法用以解决离轴多反光学系统的初始结构问题，采用带收缩因子的自然选择的粒子群算法提高了计算精度，提升了设计效率，获取了离轴多反光学系统的初始结构。最后，本文以离轴六反的极紫外光刻投影物镜为例，验证此方法的可靠性和有效性，实现了0.33NA极紫外光刻物镜综合波像差优于$1/80\lambda $ RMS光学系统设计。
- 光学设计 /
- 几何光学 /
- 像差理论 /
- 粒子群算法
Abstract: An initial construction satisfying aberration balance and multi-constraint control is essential for the design of an off-axis multi-reflective optical system with minimal aberration. In this paper, a mathematical model for calculating the initial structure of off-axis multi-reflective is established based on the grouping design method combining spatial ray tracing and aberration correction, and an improved Particle Swarm Optimization (PSO) is proposed to solve the initial structure problem of an off-axis multi-reflective optical system. The PSO of natural selection with shrinkage factor is applied to improve calculation accuracy and design efficiency, so as to obtain the initial structure of the off-axis multi-reflection optical system. In the last part of this paper, taking an Extreme UltraViolet (EUV) lithography projection objective with six-mirror reflective aspheric mirrors as an example, the reliability and effectiveness of this method are verified. A 0.33 numerical aperture EUV lithographic objective with wave-front error better than 1/80λ (λ=13.5 nm) RMS is achieved.
- optical design /
- geometric optics /
- aberration theory /
- particle swarm optimization

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图 1 离轴六反光学系统结构示意图

Figure 1. Schematic diagram of the Off-axis six-mirror reflective optical system structure

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图 2 Group 1结构示意图

Figure 2. Group 1 structure schematic diagram

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图 3 Group 2示意图

Figure 3. Schematic diagram of the Group 2

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图 4 针对6组学习因子4种不同算法计算的评价函数的收敛曲线图

Figure 4. Convergence curves of evaluation functions calculated by four different algorithms for 6 groups of learning factors

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图 5 算法流程图

Figure 5. Flow chart of the proposed algorithm

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图 6 离轴六反光学系统初始结构示意图

Figure 6. Schematic diagram of initial structure for the off-axis six-mirror reflective optical system

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图 7 极小像差离轴六反光学系统优化后结构示意图

Figure 7. Schematic diagram of the optimized structure for the off-axis six-mirror reflective optical system

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图 8 离轴六反光学系统全视场畸变分布图

Figure 8. Distortion on full image field for the off-axis six-mirror reflective optical system

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图 9 离轴六反光学系统全视场波像差分布图

Figure 9. Wavefront error RMS on full image for the off-axis six-mirror reflective optical system

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表 1 Evaluation function values calculated by four different algorithms for 6 groups of learning factors

Table 1. Evaluation function values calculated by four different algorithms for 6 groups of learning factors

c₁	c₂	Natural selection PSO algorithm with shrinkage factor	Simulated annealing PSO algorithm with shrinkage factor	Hybrid PSO algorithm with shrinkage factor	Natural selection PSO algorithm with inertial weight
2.05	2.05	0.0106	0.0985	0.0902	0.2415
2.2	1.9	0.0174	0.1148	0.0883	0.0289
2.3	1.8	0.0045	0.0373	0.0498	0.0297
2.4	1.7	0.0255	0.0644	0.0472	0.0584
2.5	1.6	0.0126	0.0533	0.0151	0.0407
2.6	1.7	0.0934	0.1212	0.1041	0.1092

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表 2 Specifications of the off-axis six-mirror reflective optical system

Table 2. Specifications of the off-axis six-mirror reflective optical system

Parameter	Performance
Wavelength/nm	13.5
Numerical Aperture	0.33
Field of view/mm×mm	26×2 Arc
Reduction ratio	4
Wavefront error RMS (λ)	0.011
Chief ray angle on mask (°)	6
Max distortion/nm	1.04
Max image telecentricity/mrad	1.75
Total track/mm	1371
Max asphere departure/μm	60

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参考文献(25)

[1]	WILSON R N. Reflecting Telescope Optics I: Basic Design Theory and its Historical Development[M]. Berlin Heidelberg: Springer, 1996.
[2]	GONG T T, JIN G F, ZHU J. Point-by-point design method for mixed-surface-type off-axis reflective imaging systems with spherical, aspheric, and freeform surfaces[J]. Optics Express, 2017, 25(9): 10663-10676.
[3]	MENG Q Y, WANG H Y, LIANG W J, et al. Design of off-axis three-mirror systems with ultrawide field of view based on an expansion process of surface freeform and field of view[J]. Applied Optics, 2019, 58(3): 609-615.
[4]	PAN J H. The Design, Manufacture and Test of the Aspherical Optical Surfaces[M]. Suzhou: Soochow University Press, 2004. (in Chinese).
[5]	CHEN L, GAO ZH SH, YE J F, et al. Construction method through multiple off-axis parabolic surfaces expansion and mixing to design an easy-aligned freeform spectrometer[J]. Optics Express, 2019, 27(18): 25994-26013.
[6]	YU J, ZHOU F, WANG H, et al. Method for designing error-resistant phase-shifting algorithm[J]. Optics Communications, 2018, 433: 52-59.
[7]	WANG L P. Optical system of extreme ultraviolet lithography[J]. Chinese Journal of Optics and Applied, 2010, 3(5): 452-461. (in Chinese)
[8]	LOWISCH M, KUERZ P, CONRADI O, et al. Optics for ASML’s NXE: 3300B platform[J]. Proceedings of SPIE, 2013, 8679: 86791H.
[9]	CHANG J, ZOU M F, WANG R R, et al. All-reflective optical system design for extreme ultraviolet lithography[J]. Chinese Optics Letters, 2010, 8(11): 1082-1084. doi: 10.3788/COL20100811.1082
[10]	VASILJEVIC D M. Optimization of the Cooke triplet with various evolution strategies and damped least squares[J]. Proceedings of SPIE, 1999, 3780: 207-215.
[11]	LIU J, WEI H, FAN H J. A novel method for finding the initial structure parameters of optical systems via a genetic algorithm[J]. Optics Communications, 2016, 361: 28-35. doi: 10.1016/j.optcom.2015.10.036
[12]	BAL M F. Next-generation extreme ultraviolet lithographic projection systems[D]. Delft: Technique University Delft, 2003.
[13]	BAL M F, BOCIORT F, BRAAT J J M. Analysis, search, and classification for reflective ring-field projection systems[J]. Applied Optics, 2003, 42(13): 2301-2311. doi: 10.1364/AO.42.002301
[14]	LERNER S A, SASIAN J M, DESCOUR M R. Design approach and comparison of projection cameras for EUV lithography[J]. Optical Engineering, 2000, 39(3): 792-802. doi: 10.1117/1.602429
[15]	DELANO E. First-order design and the diagram[J]. Applied Optics, 1963, 2(12): 1251-1256. doi: 10.1364/AO.2.001251
[16]	HUDYMA R, MANN H J, DINGER U. Projection system for EUV lithography: USA, 7375798[P]. 2008-05-20.
[17]	LIU F, LI Y Q. Grouping design of eight-mirror projection objective for high-numerical aperture EUV lithography[J]. Applied Optics, 2013, 52(29): 7137-7144. doi: 10.1364/AO.52.007137
[18]	CAO ZH, LI Y Q, LIU F. Grouping design method with real ray tracing model for extreme ultraviolet lithographic objective[J]. Optical Engineering, 2013, 52(12): 125102.
[19]	WU Y, WANG L P, YU J, et al. Design method for off-axis aspheric reflective optical system with extremely low aberration and large field of view[J]. Applied Optics, 2020, 59(32): 10185-10193. doi: 10.1364/AO.409561
[20]	SHI G H. Find preliminary solution of zoom objective lens using gaussian optics and third-order aberration theory[J]. Chinese Optics, 2018, 11(6): 1047-1060. (in Chinese) doi: 10.3788/co.20181106.1047
[21]	WANG L P, ZHANG L CH, HE F Y, et al. Design of aspheric mirror for panoramic imaging system using multi-population genetic algorithm[J]. Optics and Precision Engineering, 2009, 17(5): 1020-1025. (in Chinese)
[22]	XU F G, HUANG W. Application of genetic algorithm in the design of off-axis four-mirror optical system[J]. Optics and Precision Engineering, 2017, 25(8): 2076-2082. (in Chinese) doi: 10.3788/OPE.20172508.2076
[23]	KENNEDY J, EBERHART R. Particle swarm optimization[C]. Proceedings of International Conference on Neural Networks, IEEE, 1995.
[24]	QIN H, HAN K ZH, LEI CH X. Correction of aberration for three-lens system by particle swarm optimization algorithm[J]. Chinese Optics, 2013, 6(1): 64-72. (in Chinese)
[25]	GONG CH, WANG ZH L. Proficient in MATLAB Optimization Calculation[M]. Beijing: Publishing House of Electronics Industry, 2009. (in Chinese)