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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.
Aiming at the flexible support system with uniform distribution of the bottom of the large-diameter optical lens in the circumferential direction, the influence of the random inhomogeneity of support force on the lens surface shape is analyzed by stochastic analysis method. The support force of each point of the flexible support system is regarded as Obey the uniform random variable, randomly generate multiple sets of support force data, and calculate the lens deformation under the support force of each group by using the finite element method respectively, solve the corresponding Zernike polynomial coefficients, and then change the peak of the lens shape --Top value and Zernike polynomial coefficients were estimated by probability density and Kolmogorov test method.Example analysis results show that the parameters of the lens, under the random support force, the peak-valley value is better According to the normal distribution, the Zernike coefficient obeys the normal distribution well. The non-parametric estimation method can reflect the distribution of the peak-valley and the Zernike coefficient well.