广义最小二乘法在主动光学模式定标中的应用

为了解除4 m轻量化反射镜支撑系统间存在的相互耦合作用, 提出了采用广义最小二乘法进行主动光学的模式定标计算。首先, 介绍了4 m轻量化反射镜的支撑系统, 推导出液压Whiffletree支撑系统工作下主动光学校正力组满足解耦条件的等式约束方程, 将节点面积加权因子修正后的Zernike多项式面形拟合过程作为有限元分析前处理, 建立主动光学的响应矩阵。其次, 采用广义最小二乘法求解同时满足等式和不等式约束下的最佳校正力组。最后, 将提出的方法应用于重力印透效应产生的镜面变形主动力解算, 分析不同阻尼因子对解算结果的影响。结果表明: 阻尼因子取7.4e-9时, 达到了满足约束条件的最佳校正效果, 镜面面形均方根由最初的271.5 nm通过校正后变为8.3 nm。验证了广义最小二乘法应用于4 m轻量化反射镜主动光学校正力组解算的可行性。

Abstract

In order to relieve the coupling effect of 4 m lightweight mirror support system, a generalized least square method was proposed to calibrate active optics. Firstly, the support system of 4 m lightweight mirror was introduced, and the constraints needed to meet in hydraulic Whiffletree passive support system was deduced. Then the Zernike polynomial corrected by node area weighted factor was used to fit the mirror deformation, resulting to influence matrix between Zernike coefficients of mirror deformation and active forces. After that, a generalized least squares method was adopted to obtain the optimal correction forces which simultaneously satisfied the equality and inequality constraints. Finally, the proposed method was applied to the calculation of the optimal active forces to correct the mirror deformation caused by the gravity, and the influence of different damping factors on the calculation results were analyzed. Results show that the optimal correction effect is achieved when the damping factor is 7.4e-9, and the RMS of the mirror deformation is changed from the original 271.5 nm to 8.3 nm after correction, verifying the feasibility of the generalized least squares method to the calibration of the 4 m lightweight mirror active optics.

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兰斌, 吴小霞, 杨洪波, 蒋权, 张正铎. 广义最小二乘法在主动光学模式定标中的应用[J]. 红外与激光工程, 2017, 46(6): 0617001. Lan Bin, Wu Xiaoxia, Yang Hongbo, Jiang Quan, Zhang Zhengduo. Application of generalized least squares method in the calibration of active optics mode[J]. Infrared and Laser Engineering, 2017, 46(6): 0617001.

广义最小二乘法在主动光学模式定标中的应用

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