摘要
针对大口径光学镜片支撑点底面周向均布的柔性支撑系统,采用随机分析方法分析其支撑点上支撑力的随机不均匀性对镜片面形的影响规律.将柔性支撑系统的各点支撑力视为服从均匀分布的独立随机变量,随机产生多组支撑力数据,利用有限元方法分别计算镜片在每组支撑力作用下的镜片变形,求解相应的泽尼克多项式系数,进而对镜片面形变化的峰-谷值及泽尼克多项式系数进行概率密度估计和柯尔莫哥洛夫检验方法检验.实例分析结果表明:采用参数估计方法,镜片在随机支撑力作用下,面形峰-谷值较好地服从正态分布,泽尼克系数较好地服从正态分布;采用非参数估计方法,核概率密度估计的结果可较好反映面形峰-谷值及泽尼克系数的分布特性.
The influence of random perturbation of elastic supporting forces on the surface deformation of a large-aperture lens was analyzed using random analysis method. The elastic supporting forces were spatially evenly arranged along the circumferential direction of the lens′s underside, each of which was generated by an independent elastic mechanism inside the distribution. Multiple groups of supporting forces data were randomly produced, each of which was separately applied to the lens to compute its surface deformations caused by the group of forces data by means of finite element method. The peak-to-valley values （PVs） of the surface deformation and sets of the Zernike polynomial coefficients were evaluated based upon each set of surface deformation results, respectively. The probability density functions of the PVs and the Zernike coefficients were estimated, and the Kolmogorov-Smirnov tests were further performed. The results of the parametric estimation show that the lens′ surface deformation PVs caused by random perturbation of supporting forces shows the gamma distribution, while the Zernike coefficients follow the normal distribution, and the results from non-parametric estimation indicate that both PVs and the Zernike coefficients follow kernel probability density estimation.
出处
《华中科技大学学报（自然科学版）》
EI
CAS
CSCD
北大核心
2013年第8期1-5,共5页
Journal of Huazhong University of Science and Technology(Natural Science Edition)
基金
国家重点基础研究发展计划资助项目(2009CB724205)
关键词
大口径光学镜片
柔性支撑系统
支撑力随机波动
镜片面形
泽尼克多项式
统计假设检验
large-aperture optical lenses
flexible supporting systems
random perturbation of supporting forces
lens deformation
Zernike polynomial
statistical hypothesis test
