基于Zernike多项式拟合三平面互检的误差分析
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摘要
基于Zernike多项式拟合三平面互检法,在理论上对光轴偏离、旋转角度以及有效面积对不同面型精度平面的测量误差进行了分析,并分别进行了实验验证.研究结果表明,旋转角度误差和有效面积对测量影响不敏感,可适当降低标定旋转角度成本;而光轴偏离对测量精度影响明显,在高精度面型绝对检测中应对其进行严格校准.
Based on Zernike polynomials fitting,the measurement errors posed by optical axis deviation,rotation angle and active area on different types of high-precision surface were analyzed and the experimental verifications were conducted respectively.The results show that the measurement is not sensitive to the rotation angle and active area,the cost of calibrated rotation angle can therefore be reduced,while the impact of optical axis deviation on measurement precision is rather significant,which should be strictly adjusted before the test on high-precision surface.
Based on Zernike polynomials fitting,the measurement errors posed by optical axis deviation,rotation angle and active area on different types of high-precision surface were analyzed and the experimental verifications were conducted respectively.The results show that the measurement is not sensitive to the rotation angle and active area,the cost of calibrated rotation angle can therefore be reduced,while the impact of optical axis deviation on measurement precision is rather significant,which should be strictly adjusted before the test on high-precision surface.
引文
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[3]VANNONIM.Absolute flatness measurement using oblique incidence setup and an iterative algorithm[J].Optics Express,2014,22(3):3538-3546.
[4]SU Dong-qi,TIAN Wei,MIAO Er-long,et al.Absolute three-flat test in vertical direction with gravity deformation compensation[J].Acta Photonica Sinica,2015,44(11):1112003.苏东奇,田伟,苗二龙,等,基于重力补偿的立式三平板绝对检测[J].光子学报,2015,44(11):1112003.
[5]E Ke-wei,LI Da-hai,ZHANG Chen,et al.Four-step shear method for the absolute measurement of a flat surface based on phase measuring deflectometry[J].Applied Optics,2016,55(30):8419-8425.
[6]SONG Wei-hong,HOU Xi,WU Fan,et al.Simple and rapid data-reduction method with pixel-level spatial frequency of shift-rotation method[J].Applied Optics,2013,24(52):5974-5978.
[7]HAN Dong-song,HE Xin,WEI Zhong-hui,et al.Error correction of interferometer detection with high-accuracy rotation method[J].Optics and Precision Engineering,2015,23(5):1291-1303.韩冬松,何昕,魏仲慧,等,应用高精度旋转法的干涉仪检测误差校正[J].光学精密工程,2015,23(5):1291-1303.
[8]MIAO Er-long.ZHANG Jian,GU Yong-qiang,et al.Measurement error analysis of high precision fizeau interferometer for lithography projection objective[J].Chinese Journal of Lasers,2010,37(8):2029-2034.苗二龙,张健,谷勇强等,用于光刻投影物镜检测的高精度菲佐干涉仪误差分析[J].中国激光,2010,37(8):2029-2034.
[9]GRIESMANN U.Three-flat test solutions based on simple mirror symmetry[J].Applied Optics,2006,45(23):5856-5865.
[10]CHEN Xu,YUAN Wen-quan,FENG Yu-tao,et al.Study of the error of the reference lens in absolute spherical testing and the thermal deformation model establishment[J].Acta Optica Sinica,2011,31(2):0212002陈旭,袁文权,冯玉涛等,绝对检验参考镜误差分析与热变形模型建立[J].光学学报,2011,31(2):0212002.
[11]FUJIMOTO I,TAKATSUJI T,NISHIMURA K,et al.Autonomous calibration method of the reference flat surface of an interferometer without using a standard flat surface[J].Applied Optics,2012,55(30):8419-8425.
[12]ZHU-Shuo.Study on technology for large optic flat mirror testing[D].Beijing:Chinese Academy of Science,2014.朱硕.大口径光学平面镜面形检测技术研究[D].北京:中国科学院大学,2014.
[13]SONG Wei-hong,WU Fan,HOU Xi,et al.Absolute measurement of flats with the method of shift-rotation[J].Optical Review,2013,20(5):374-377.
[14]TIAN Ai-ling,ZHENG Xian-feng,LIU Bing-cai,et al.Absolute measurement of 3D Surface[J].Journal of Xi′an Technological University,2012,32(6):431-436.田爱玲,郑显锋,刘丙才,等,三维面型的绝对测量[J].西安工业大学学报,2012,32(6):431-436.
[15]SCHREINER R,SCHWIDER J,LINDLEIN N,et al.Absolute testing of the reference surface of a Fizeau interferometer through even/odd decompositions[J].Applied Optics,2008,47(32):6134-6141.
[16]YUMOTO H,MATSUYAMA S,MIMURA H,et al.Absolute calibration of optical flats using the three-flat test by considering the relative humidity change[J].Nuclear Inst&Methods in Physics Research A,2013,710(3):2-6.
[17]CHATTERJEE S,KUMAR Y P.Measurement of the surface form error of a spherical surface with a wedge phase shifting Fizeau interferometer[J].Journal of Optics,2013,42(2):122-127.
[18]XU Yang,TANG Feng,WANG Xiang-chao,et al.Measurement error analysis of absolute flatness test[J].Chinese Journal of Lasers,2011,38(10):1008009.徐洋,唐锋,王向朝,等.平面面形绝对检验技术测量误差分析[J].中国激光,2011,38(10):1008009.
[19]FRITZ B S.Absolute calibration of an optical flat[J].Optical Engineering,1984,23(4):379-383.