二次非球面镜参数求解模型及求解算法研究

Research on the Model and Algorithm for Computing Surface Parameter of Conic Aspheric Mirror

零位补偿检测的结果常作为非球面元件加工过程中的标准。当零位补偿器可能存在问题时,能否保证非球面顶点曲率及二次曲面常数的精度是一个重要问题。基于二次曲面方程,建立了非球面顶点曲率半径R以及二次曲面常数k的求解模型并推导了基于奇异值分解SVD方法的求解算法。通过对一块孔径为1 229 mm的非球面反射镜进行模拟仿真计算,经过优化,该算法的求解精度可以达到△R=0.1%,△k=0.14%,从而实现对非球面镜零位补偿检测的有效补充。

Null testing is usually used to evaluate the processing quality of aspheric mirrors in fabricating process.When the null compensator emerges a problem,additional method to ensure the accuracy of paraxial radius of curvature and conic constant is required.Based on the equation of conic aspheric,the computing model from which the paraxial radius of curvature R and conic constant k can be obtained was established,and a set of solving algorithm using singular value decomposition（SVD）method was derived.The simulating result of a 1 229 mm.Aspheric mirror is presented and the solving precision reaches △R=0.1%,△k=0.14%,thus the supplement to null testing of aspheric mirror is achieved effectively.