轴对称二次非球面镜面几何参数的算法

Algorithm for calculating geometric parameter of axial symmetry conic surface

在现代的空间光学遥感器中,越来越多地使用二次非球面光学元件代替以往的球面光学元件,消除球面镜不能消除的像差。二次非球面的几何参数包括其顶点曲率半径和非球面系数,它们对相机的性能有着重要的影响。三座标仪的使用使得二次非球面几何参数的测量变得方便快捷。在三坐标测量数据基础上,给出了一种新型的二次非球面几何参数计算方法,通过采集座标点、寻找旋转轴、计算法线像差等步骤求解出顶点曲率半径和非球面系数。通过仿真分析和实验验证,顶点曲率半径的计算精度可达0.01%,非球面系数的精度可达0.0002。

Modern space telescopes use conic surfaces rather than sphere surfaces in optical systems to avoid the unnecessary aberration brought by sphere surfaces.Geometric parameters of conic surfaces include the vertex radius and aspheric coefficient(e2),they are significant to the performance of the telescopes.As the coordinate measuring machine(CMM)is widely used,the measurement for the geometric parameters of conic surface is much more convenient.We introduced a new algorithm for calculating vertex radius and e2 based on the data measured by the CMM through a few steps:measuring the coordinates,finding the axis and calculating the normal aberration theory.According to the simulation and experiment,the error of vertex radius is less than 0.01%,the error of e2 is less than 0.0002,which can meet the demands for most measurements.