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摘要: 为了实现大口径椭圆形光学平面镜的高精度面形测量，提升大口径望远镜系统的像质，本文对椭圆形平面反射镜面形的绝对检测算法进行了研究。首先，对椭圆形镜面进行了多项式正交化拟合研究。接着，对绝对检测算法进行了理论研究，利用正交化绝对检测算法可以有效分离参考镜与待测镜的面形误差，从而实现待测椭圆形平面镜面的高精度面形重构。为了证明上述方法的实际检测精度，本文对250 mm×300 mm的椭圆形镜面进行了绝对检测模拟与检测实验。对参考镜面形精度不高的情况进行了仿真计算，实验中利用光阑在Zygo300 mm口径标准平面镜头中选取250 mm×300 mm椭圆形检测区域，采用150 mm口径Zygo干涉仪对上述椭圆形区域完成绝对检测，并基于上述正交化绝对检测算法对椭圆形平面镜实现了面形重构。实验结果表明，利用本文所述方法可以实现参考镜与椭圆形待测镜面的面形误差分离，绝对检测结果的残差图RMS（Root-mean square）值为0.29 nm，证明了本文所述方法的可行性。利用上述方法可以实现椭圆形平面反射镜的高精度面形重构。Abstract: In order to realize the high-precision surface measurement of large-diameter elliptical optical flat mirrors and improve the image quality of large-aperture telescope systems, the absolute measurement algorithm for flat elliptical mirrors is studied in this paper. Firstly, the orthogonal polynomials fitting of an elliptical optical flat mirror is studied. Then, the absolute testing algorithm is studied theoretically. The orthogonal absolute testing algorithm can effectively separate the surface error of the reference mirror from the mirror to be measured, which can realize the high-precision surface reconstruction of the elliptical flat mirror to be measured. To verify the actual testing accuracy of the above method, we carried out an absolute testing simulation and experiment on a 250 mm×300 mm mirror. In the simulation, the possibility that the reference surface error is high was considered. In the experiment, a 250 mm×300 mm elliptical testing area was selected in the Zygo300 mm standard flat surface. The above-mentioned elliptical area was tested by the 150 mm Zygo interferometer, and the surface reconstruction was realized based on the above-mentioned orthogonal absolute testing algorithm. The experimental results show that the surface error separation between the reference mirror and the elliptical mirror can be achieved by using the method described in this paper, and the residual RMS (Root-Mean Square) value of the absolute testing result is 0.29 nm, which proves the feasibility and accuracy of the method described in this paper. The high-precision surface reconstruction of the elliptical flat mirror can be achieved using the above method.
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Key words:
- interferometry /
- absolute measurement /
- orthogonal /
- fitting /
- elliptical optical flat mirror
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图 12 子孔径检测结果与拼接结果残差图
Figure 12. Difference maps between each subaperture map and its corresponding stitching map
图 14 传统算法测试镜面形重构结果
Figure 14. Reconstructed testing elliptic surface map with the standard Zernike polynomials fitting method
图 15 传统算法参考镜面形重构结果
Figure 15. Reconstructed reference surface map with the standard Zernike polynomials fitting method
图 16 子孔径检测结果与传统绝对检测结果残差图
Figure 16. Difference maps between each subaperture map and its corresponding stitching map using the traditional method
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[1] LI T, LIU Y, SUN Y Y, et al. Vectorial pupil optimization to compensate polarization distortion in immersion lithography system[J]. Optics Express, 2020, 28(4): 4412-4425. doi: 10.1364/OE.382051 [2] VETTER A, KIRNER R, OPALEVS D, et al. Printing sub-micron structures using Talbot mask-aligner lithography with a 193 nm CW laser light source[J]. Optics Express, 2018, 26(17): 22218-22233. doi: 10.1364/OE.26.022218 [3] LI T, LIU Y, SUN Y Y, et al. Multiple-field-point pupil wavefront optimization in computational lithography[J]. Applied Optics, 2019, 58(30): 8331-8338. doi: 10.1364/AO.58.008331 [4] SKIDMORE W. Thirty meter telescope detailed science case: 2015[J]. Research in Astronomy and Astrophysics, 2015, 15(12): 1945-2140. doi: 10.1088/1674-4527/15/12/001 [5] MA D L. Recommended conceptual optical system design for China’s Large Optical-infrared Telescope (LOT)[J]. Optics Express, 2018, 26(1): 108-119. doi: 10.1364/OE.26.000108 [6] LI H Y, WALKER D, YU G Y, et al. Modeling and validation of polishing tool influence functions for manufacturing segments for an extremely large telescope[J]. Applied Optics, 2013, 52(23): 5781-5787. doi: 10.1364/AO.52.005781 [7] JI H R, ZHU ZH B, TAN H, et al. Design of a high-throughput telescope based on scanning an off-axis three-mirror anastigmat system[J]. Applied Optics, 2021, 60(10): 2817-2823. doi: 10.1364/AO.421998 [8] KULAWIEC A, MURPHY P, DEMARCO M. Measurement of high-departure aspheres using subaperture stitching with the Variable Optical Null (VON)[J]. Proceedings of SPIE, 2010, 7655: 765512. doi: 10.1117/12.864962 [9] SUPRANOWITZ C, MCFEE C, MURPHY P, et al. Asphere metrology using variable optical null technology[J]. Proceedings of SPIE, 2012, 8416: 841604. doi: 10.1117/12.2009289 [10] 朱鹏辉, 唐锋, 卢云君, 等. 高精度平面子孔径拼接算法研究[J]. 中国激光,2016,43(11):1104002. doi: 10.3788/CJL201643.1104002ZHU P H, TANG F, LU Y J, et al. Research on high accuracy sub-aperture stitching algorithm for flat optics[J]. Chinese Journal of Lasers, 2016, 43(11): 1104002. (in Chinese) doi: 10.3788/CJL201643.1104002 [11] 王孝坤. 大口径离轴凸非球面系统拼接检验技术[J]. 中国光学,2016,9(1):130-136. doi: 10.3788/co.20160901.0130WANG X K. Measurement of large off-axis convex asphere by systemic stitching testing method[J]. Chinese Optics, 2016, 9(1): 130-136. (in Chinese) doi: 10.3788/co.20160901.0130 [12] 张海东, 王孝坤, 薛栋林, 等. 一种针对超大口径凸非球面的面形检测方法[J]. 中国光学,2019,12(5):1147-1154. doi: 10.3788/co.20191205.1147ZHANG H D, WANG X K, XUE D L, et al. Surface testing method for ultra-large convex aspheric surfaces[J]. Chinese Optics, 2019, 12(5): 1147-1154. (in Chinese) doi: 10.3788/co.20191205.1147 [13] 郑彬, 陈永和, 傅雨田. 拼接式反射镜共焦误差检测[J]. 光学 精密工程,2019,27(1):26-33. doi: 10.3788/OPE.20192701.0026ZHENG B, CHEN Y H, FU Y T. Co-focus error detection of segmented mirrors[J]. Optics and Precision Engineering, 2019, 27(1): 26-33. (in Chinese) doi: 10.3788/OPE.20192701.0026 [14] 李斌, 刘燕德, 谢锋云. 拼接镜新型粗共相检测方法[J]. 光学 精密工程,2018,26(11):2647-2653. doi: 10.3788/OPE.20182611.2647LI B, LIU Y D, XIE F Y. Coarse co-phasing detection of segmented mirrors[J]. Optics and Precision Engineering, 2018, 26(11): 2647-2653. (in Chinese) doi: 10.3788/OPE.20182611.2647 [15] 逯诗桐, 张天一, 张晓辉. 大口径空间巡天望远镜子孔径拼接平场定标法[J]. 中国光学,2020,13(5):1094-1102. doi: 10.37188/CO.2019-0252LU SH T, ZHANG T Y, ZHANG X H. Flat-field calibration method for large diameter survey mirror aperture splicing[J]. Chinese Optics, 2020, 13(5): 1094-1102. (in Chinese) doi: 10.37188/CO.2019-0252 [16] SU P, BURGE J H, PARKS R E. Application of maximum likelihood reconstruction of subaperture data for measurement of large flat mirrors[J]. Applied Optics, 2010, 49(1): 21-31. doi: 10.1364/AO.49.000021 [17] SU D Q, MIAO E L, SUI Y X, et al. Absolute surface figure testing by shift-rotation method using Zernike polynomials[J]. Optics Letters, 2012, 37(15): 3198-3200. doi: 10.1364/OL.37.003198 [18] YANG ZH M, DU J Y, TIAN CH, et al. Generalized shift-rotation absolute measurement method for high-numerical-aperture spherical surfaces with global optimized wavefront reconstruction algorithm[J]. Optics Express, 2017, 25(21): 26133-26147. doi: 10.1364/OE.25.026133 [19] YANG ZH M, GAO ZH SH, ZHU D, et al. Absolute ultra-precision measurement of high-numerical-aperture spherical surface by high-order shift-rotation method using Zernike polynomials[J]. Optics Communications, 2015, 355: 191-199. doi: 10.1016/j.optcom.2015.06.033 [20] MAHAJAN V N, DAI G M. Orthonormal polynomials in wavefront analysis: analytical solution[J]. Journal of the Optical Society of America A, 2007, 24(9): 2994-3016. doi: 10.1364/JOSAA.24.002994 [21] DAI G M, MAHAJAN V N. Nonrecursive determination of orthonormal polynomials with matrix formulation[J]. Optics Letters, 2007, 32(1): 74-76. doi: 10.1364/OL.32.000074 -
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