光学镜面是空间光学遥感器的重要组成部件, 刚体位移和面形 误差是评价其环境适应性的重要指标。介绍了一种从Pantran/Nastran软件的有限元分析结果中提取光 学镜面的刚体位移和面形误差的方法。首先对Patran输出的原始数据进行预处理, 消除原始数据 误差；然后采用坐标变换法计算光学镜面的刚体位移, 并通过法方程法直接进行求解, 没有出现病态矩阵问题； 最后通过球面方程拟合法计算光学镜面的面形误差, 将球面拟合问题转换成3变量最优化问题再进行处 理, 并采用高斯-牛顿法进行数值迭代求解。经工程实践证明, 该方法具有计算简洁准确、计算速度快等特点。

Optical mirrors are the important components of a space remote sensor. Their rigid body displacement and surface figure errors are the key indexes for evaluating their environment adaptability. A method for extracting the rigid body displacement and surface figure errors of mirrors from the Finite Element Analysis (FEA) result by the Pantran/Nastran software is presented. First, the raw data output from Patran/Nastran are preprocessed to eliminate their error. Then, a coordinate transformation method and a method of normal equations are used to calculate the rigid body displacement. No ill conditioned matrix problems are found in calculation. Finally, a spherical fitting method is used to calculate the surface figure error. The spherical fitting problem is converted to the optimization problem with three variables and the Gauss-Newton method is used to carry out numerical calculation. The experimental result shows that this method is concise, accurate and fast.