数字莫尔移相干涉仪误差多点标定与修正研究
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摘要
干涉测量在现有的光学元件面形检测方法中具有测量精度高的优势,应用相对广泛。但干涉仪元件的加工和装调误差会降低面形检测精度。提出一种利用夏克哈特曼波前传感器对实际干涉仪系统进行多点标定的方法,利用波前标定数据在光学设计软件ZEMAX中实现对虚拟干涉仪系统的修正,结合数字莫尔移相算法,消除实际干涉仪加工和装调误差的影响。选取平面镜和可变形镜作为待测镜分别进行面形测量实验,结果表明,标定和修正后的数字莫尔移相干涉仪系统检测精度提高,与Zygo干涉仪的检测结果相比,面形趋势保持一致且峰谷值(PV)值误差相差在0.07λ(λ=532 nm)以内。
Interferometry has a high measurement accuracy and a wide range of applications in the existing surface inspection methods of optical components. Fabrication and alignment errors in the interferometer reduces the accuracy of surface inspection. A multi-point calibration method of an actual interferometer system using a Shaker-Hartmann wavefront sensor is proposed. The correction of the virtual interferometer system is implemented in the optical design software ZEMAX using wavefront calibration data. Combined with digital Moiré phase-shifting algorithm, the influence of the fabrication and alignment errors in the actual interferometer are eliminated. A planar mirror and a deformable mirror are selected as the test mirrors for surface shape measurement experiments. The results show that the measurement accuracy of the digital Moiré phase-shifting interferometer system after calibration and correction is improved. Compared with the measurement results of the Zygo interferometer, the surface shapes are consistent and the peak-to-valley(PV) error difference is within 0.07λ(λ=532 nm).
Interferometry has a high measurement accuracy and a wide range of applications in the existing surface inspection methods of optical components. Fabrication and alignment errors in the interferometer reduces the accuracy of surface inspection. A multi-point calibration method of an actual interferometer system using a Shaker-Hartmann wavefront sensor is proposed. The correction of the virtual interferometer system is implemented in the optical design software ZEMAX using wavefront calibration data. Combined with digital Moiré phase-shifting algorithm, the influence of the fabrication and alignment errors in the actual interferometer are eliminated. A planar mirror and a deformable mirror are selected as the test mirrors for surface shape measurement experiments. The results show that the measurement accuracy of the digital Moiré phase-shifting interferometer system after calibration and correction is improved. Compared with the measurement results of the Zygo interferometer, the surface shapes are consistent and the peak-to-valley(PV) error difference is within 0.07λ(λ=532 nm).
引文
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[17] WANG W, TAN J, WANG T, et al. Reference surface calibration of a Fizeau interferometer through even/odd synthesis[J]. Applied Optics, 2011, 50(20):3482-7.
[18] 皮世威,刘强,孙鹏鹏.基于激光干涉仪的旋转轴误差快速检定方法[J].仪器仪表学报,2017,38(10):2484-2491.PI SH W, LIU Q,SUN P P. Geometric error detection for rotary feed drive based on laser interferometer[J]. Chinese Journal of Scientific Instrumental, 2017,38(10):2484-2491.
[19] 尹志生,李友如,李佩玥,等.高精度六维激光测量系统误差补偿算法研究[J].电子测量与仪器学报,2016,30(8):1275-1281.YING ZH SH,LI Y R,LI P Y, et al. Research on error compensation algorithm for high precision 6-DOF laser measurement system[J]. Journal of Electronic Measurement and Instrumentation, 2016,30(8):1275-1281.
[20] 师途,臧仲明,刘东,等.光学非球面面形非零位检测的回程误差校正[J].光学学报,2016,36(8):155-165.SHI T, ZANG ZH M,LIU D, et al. Retrace error correction for non-noll testing of optical aspheric surface[J]. Acta Optica Sinica, 2016,36(8):155-165.
[21] HAN S, NOVAK E. Retrace error for the measurement of a long-radius optic[C].Congress of the International Commission for Optics. International Society for Optics and Photonics, 1999: 597-598.
[22] DAVIES A. Retrace error evaluation on a figure-measuring interferometer[C].Optics & Photonics. International Society for Optics and Photonics, 2005,5869: 58690V-58690V-8.
[23] 田雨函. 数字莫尔移相干涉仪仪器化研究[D].北京:北京理工大学,2016.TIAN Y H. Research for instrumentation of digital moire phase-shifting interferometer[D]. Beijing:Beijing Institute of Technology,2016.
[24] 罗佳林,许琦欣,侯文玫,等.基于瞳面干涉的自参考干涉仪的研制[J].仪器仪表学报,2016,37(增刊1):74-77.LUO J L, XU J X, HOU W M, et al. Research on self-referencing interferometer based on interfering in the pupil plane [J]. Chinese Journal of Scientific Instrument, 2016,37 (Suppl.1):74-77.
[25] BROOKS A F, KELLY T L, VEITCH P J, et al. Ultra-sensitive wavefront measurement using a Hartmann sensor [J]. Optics Express, 2007, 15(16):10370-10375.
[26] 李新阳,姜文汉. 哈特曼夏克传感器的泽尼克模式波前复原误差[J].光学学报,2002,22(10):1236-1240.LIN X Y, JIANG W H. Zernike modal mavefront reconstruction error of Hartmann-Shack wavefront sensor [J]. Acta Optica Sinica, 2002,22(10):1236-1240.
[27] LIU H L, ZHU Q D, HAO Q, et al. Design of novel part-compensating lens used in aspheric testing[C]. 5th International Symposium on Instrumentation and Control Technology,2003,5253: 480-484.
[2] 谢高容.非球面镜片面形检测技术综述[J]. 光学仪器, 2007, 29(2): 88-90.XIE G R. A summary of aspheric lens surface testing methods [J]. Optical Instruments, 2007,29(2):88-90.
[3] 席庆奎,朱日宏,陈磊,等.计算全息用于非球面检测的方法[J].激光杂志,2004,25(6):67-69.XI Q K, ZHU R H, CHEN L, et al. Methods on testing an aspheric with a computer generated hologram [J]. Laser Journal, 2004,25 (6):67-69.
[4] 王小鹏,朱日宏,王雷,等.数字刀口仪定量检验非球面光学元件面形[J].光学学报, 2011,31(1):148-151.WANG X P, ZHU R H,WANG L, et al. Digitized foucault tester for quantitative evaluation the surface of aspheric optical elements[J]. Acta Optica Sinica, 2011,31(1):148-151.
[5] 倪颖,余景池,郭培基,等.小型非球面轮廓测量仪的原理及应用[J].光学精密工程, 2003,11(6):612-616.NI Y, YU J CH, GUO P J, et al. Principle and application of miniature aspheric surface profilometer [J]. Optics and Precision Engineering,2003,11(6):612-616.
[6] 张磊,田超,刘东,等.非球面非零位环形子孔径拼接干涉检测技术[J].光学学报,2014,34(8):164-172.ZHANG L, TIAN CH, LIU D, et al. Non-null annular subaperture stitching interferometry for aspheric test [J]. Acta Optica Sinica, 2014,34(8):164-172.
[7] 郝群,宁妍,胡摇.基于干涉法的非球面测量技术[J].计测技术, 2018,38(1):1-8.HAO Q, NING Y, HU Y. Interferometric testing of aspheric surface [J].Metrology & Measurement Technology, 2018,38(1):1-8.
[8] 乔玉晶,谭久彬,王伟波.子孔径干涉拼接测量非球面的模型分析[J].仪器仪表学报,2007,28(10):1880-1885.QIAO Y J, TAN J B, WANG W B. Model analysis of sub-aperture stitching interferometry for aspheric surface test [J].Chinese Journal of Scientific Instrumental, 2007,28(10):1880-1885.
[9] 虞祖良,邬敏贤,金国藩.两种利用计算全息检测非球面的方法[J].仪器仪表学报,1981,2(4):64-70.YU Z L, WU M X, JIN G F. Two methods for detecting aspheric surfaces by using computational holography [J]. Chinese Journal of Scientific Instrumental, 1981,2(4):64-70.
[10] 伍凡.非球面干涉仪零检验的补偿器设计[J].应用光学,1997,18(2):10-13.WU F. Design of compensator for null test of aspherical surface interferometer[J].Applied Optics,1997,18(2):10-13.
[11] ZHOU P, BURGE J H. Limits for interferometer calibration using the random ball test[J]. Proceedings of SPIE - The International Society for Optical Engineering, 2009, 7426: 74260U-74260U-12.
[12] BURKE J. Rapid and reliable reference sphere calibration for Fizeau interferometry.[J]. Optics Letters, 2008, 33(21):2536-2538.
[13] SONG W H, LI S, HOU X, et al. Absolute calibration for Fizeau interferometer with the global optimized shift-rotation method[J]. Optics & Lasers in Engineering, 2014, 54(54):49-54.
[14] WU D S, BURKE J. Calibration of spherical reference surfaces for Fizeau interferometry: A comparative study of methods[J]. Applied Optics, 2010, 49(31):6014-6023.
[15] SONG W, WU F, HOU X, et al. Absolute calibration of a spherical reference surface for a Fizeau interferometer with the shift-rotation method of iterative algorithm [J]. Optical Engineering, 2013, 52(3):3601.
[16] BURKE J. Rapid and reliable reference sphere calibration for Fizeau interferometry [J]. Optics Letters, 2008, 33(21):2536-2538.
[17] WANG W, TAN J, WANG T, et al. Reference surface calibration of a Fizeau interferometer through even/odd synthesis[J]. Applied Optics, 2011, 50(20):3482-7.
[18] 皮世威,刘强,孙鹏鹏.基于激光干涉仪的旋转轴误差快速检定方法[J].仪器仪表学报,2017,38(10):2484-2491.PI SH W, LIU Q,SUN P P. Geometric error detection for rotary feed drive based on laser interferometer[J]. Chinese Journal of Scientific Instrumental, 2017,38(10):2484-2491.
[19] 尹志生,李友如,李佩玥,等.高精度六维激光测量系统误差补偿算法研究[J].电子测量与仪器学报,2016,30(8):1275-1281.YING ZH SH,LI Y R,LI P Y, et al. Research on error compensation algorithm for high precision 6-DOF laser measurement system[J]. Journal of Electronic Measurement and Instrumentation, 2016,30(8):1275-1281.
[20] 师途,臧仲明,刘东,等.光学非球面面形非零位检测的回程误差校正[J].光学学报,2016,36(8):155-165.SHI T, ZANG ZH M,LIU D, et al. Retrace error correction for non-noll testing of optical aspheric surface[J]. Acta Optica Sinica, 2016,36(8):155-165.
[21] HAN S, NOVAK E. Retrace error for the measurement of a long-radius optic[C].Congress of the International Commission for Optics. International Society for Optics and Photonics, 1999: 597-598.
[22] DAVIES A. Retrace error evaluation on a figure-measuring interferometer[C].Optics & Photonics. International Society for Optics and Photonics, 2005,5869: 58690V-58690V-8.
[23] 田雨函. 数字莫尔移相干涉仪仪器化研究[D].北京:北京理工大学,2016.TIAN Y H. Research for instrumentation of digital moire phase-shifting interferometer[D]. Beijing:Beijing Institute of Technology,2016.
[24] 罗佳林,许琦欣,侯文玫,等.基于瞳面干涉的自参考干涉仪的研制[J].仪器仪表学报,2016,37(增刊1):74-77.LUO J L, XU J X, HOU W M, et al. Research on self-referencing interferometer based on interfering in the pupil plane [J]. Chinese Journal of Scientific Instrument, 2016,37 (Suppl.1):74-77.
[25] BROOKS A F, KELLY T L, VEITCH P J, et al. Ultra-sensitive wavefront measurement using a Hartmann sensor [J]. Optics Express, 2007, 15(16):10370-10375.
[26] 李新阳,姜文汉. 哈特曼夏克传感器的泽尼克模式波前复原误差[J].光学学报,2002,22(10):1236-1240.LIN X Y, JIANG W H. Zernike modal mavefront reconstruction error of Hartmann-Shack wavefront sensor [J]. Acta Optica Sinica, 2002,22(10):1236-1240.
[27] LIU H L, ZHU Q D, HAO Q, et al. Design of novel part-compensating lens used in aspheric testing[C]. 5th International Symposium on Instrumentation and Control Technology,2003,5253: 480-484.