可调支撑力对光学元件面形的影响
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摘要
可调支撑装置是高精度光学元件的常用支撑结构。分析了可调支撑装置支撑力调节对光学元件面形的影响规律。建立可调支撑装置的力学模型,利用有限元法计算光学元件的变形,并对光学元件面形进行Zernike多项式拟合。不同工况下分析结果表明:均匀支撑时光学元件面形均方根(RMS)最小,可调支撑力变化时,引入的光学元件面形RMS以及主要Zernike多项式系数均与支撑力线性相关,与光学元件的初始支撑状态无关。建立Fringe Zernike系数随任意支撑力变化的敏感度矩阵,采用该矩阵预测随机工况下光学元件支撑力调整后面形,预测调节面形与有限元仿真调节面形基本一致,RMS误差优于0.3%,为可调支撑装置的设计与装调提供理论依据。
Adjustable optic mount is commonly used in the structure design of high precision optical system. Surface shape of optical element influenced by the supporting force adjustment is researched. Mechanical model of the adjustable mount is established, deformation of optical element is calculated with finite element method, and the surface shape is fitted with Zernike polynomials. The analysis results in different working conditions show that the root mean square(RMS) of surface shape is minimized when optical element is under uniform support; when supporting force changes, it causes linear variety of RMS and main Zernike polynomial coefficients of surface shapewhich is independent at the initial working condition of optical element. Finally, sensitivity matrix of Zernike polynomial coefficients changed by every supporting force is established, then estimation of surface shape due to support force adjustment in a new random working condition is made, the estimated result is similar to the finite element analysis surface shape, and the error of RMS is less than 0.3%, so the estimating method is able to guide the design and assembly of adjustable optic mount.
Adjustable optic mount is commonly used in the structure design of high precision optical system. Surface shape of optical element influenced by the supporting force adjustment is researched. Mechanical model of the adjustable mount is established, deformation of optical element is calculated with finite element method, and the surface shape is fitted with Zernike polynomials. The analysis results in different working conditions show that the root mean square(RMS) of surface shape is minimized when optical element is under uniform support; when supporting force changes, it causes linear variety of RMS and main Zernike polynomial coefficients of surface shapewhich is independent at the initial working condition of optical element. Finally, sensitivity matrix of Zernike polynomial coefficients changed by every supporting force is established, then estimation of surface shape due to support force adjustment in a new random working condition is made, the estimated result is similar to the finite element analysis surface shape, and the error of RMS is less than 0.3%, so the estimating method is able to guide the design and assembly of adjustable optic mount.
引文
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12 Yang Guohai,Zhang Guozhi.Generating random variables[J].Application of Statistics and Management,2006,25(2):244-252.杨振海,张国志.随机数生成[J].数理统计与管理,2006,25(2):244-252.
2 Zhang Dejiang,Liu Liren,Xu Rongwei,et al..Finite element analysis for wavefront error of lenses induced by gravity[J].Acta Optica Sinica,2005,25(4):538-541.张德江,刘立人,徐荣伟,等.透镜自重变形引起波像差的有限元分析[J].光学学报,2005,25(4):538-541.
3 Wang Hui,Zhou Feng,Wang Liping,et al..Analysis and metrology of reproducibility of high-precision optic mount[J].Chinese J Lasers,2013,40(12):1208001.王辉,周烽,王丽萍,等.高精度光学元件支撑装置面形复现性分析与测量[J].中国激光,2013,40(12):1208001.
4 Yoder Paul R.Opto-Mechanical Systems Design:Third Edition[M].Bellingham:CRC Press,2006:125-129.
5 Zhao Lei,Gong Yan.Design and analysis for the high-precision lens support structure of objective lens for llithography[J].Acta Optica Sinica,2012,32(9):0922001.赵磊,巩岩.光刻物镜中透镜高精度支撑结构的设计及分析[J].光学学报,2012,32(9):092001.
6 Chen Xindong,Zheng Ligong,Luo Xiao,et al..A deformable mirror with 9 actuated points for low aberration correctiondesign and experiments[J].Acta Optica Sinica,2012,32(3):0322001.陈新东,郑立功,罗霄,等.校正低阶像差的9点促动变形镜-设计与实验[J].光学学报,2012,32(3):0322001.
7 Chen Fulin,Zhang Jingxu,Wu Xiaoxia,et al..Supporting structure of 620 mm thin primary mirror and its active surface correction[J].Optics and Precision Engineering,2011,19(5):1022-1029.陈夫林,张景旭,吴晓霞,等.620 mm薄镜面的主动支撑结构及面形校正[J].光学精密工程,2011,19(5):1022-1029.
8 Guo Kang,Gong Yan.Effect of adjusting force on surface figure of optical element in axial adjustment mechanism[J].Acta Optica Sinica,2013,33(11):1123001.郭抗,巩岩.轴向调节机构中调节力对光学元件面形的影响[J].光学学报,2013,33(11):1123001.
9 Luo Xin,Liu Yuan,Shen Yiping,et al..Influence of non-uniform supporting forces on deformation of large-aperture optical lenses[J].Journal of Huazhong University of Science and Technology(Nature Science Edition),2013,31(8):1-5.罗欣,刘远,沈意平,等.支撑力非均匀性对大口径光学镜片面形的影响[J].华中科技大学学报(自然科学版),2013,31(8):1-5.
10 Shan Baozhong,Wang Shuyan,Niu Hanben,et al..Zernike polynomial fitting method and its application[J].Optics and Precision Engineering,2002,10(3):318-323.单宝忠,王淑岩,牛憨笨,等.Zernike多项式拟合方法及应用[J].光学精密工程,2002,10(3):318-323.
11 Meng Xuan,Qiao Yanfeng,He Fengyun,et al..Analyzing primary mirror deformation of photo-electronic theodolite using Zernike annular polynonial[J].Laser&Optoelectronics Progress,2016,50(7):1-7.孟轩,乔彦峰,何锋赟,等.Zernike环多项式分析光电经纬仪主镜变形[J].激光与光电子学进展,2016,50(7):1-7.
12 Yang Guohai,Zhang Guozhi.Generating random variables[J].Application of Statistics and Management,2006,25(2):244-252.杨振海,张国志.随机数生成[J].数理统计与管理,2006,25(2):244-252.