基于曲面拟合的离轴非球面镜顶点半径计算方法

为了解决大口径、离轴非球面顶点半径等参数测量不准的问题，提出了一种基于曲面拟合的非球面参数计算方法。建立了测量坐标系下的非球面准确方程，给出了非线性最小二乘拟合的迭代算法。同时提出了采用补偿器端面数据拟合得到光轴指向，通过测量坐标系下的光轴指向给出合适的拟合初值。对实测数据的实验表明，拟合优度的确定系数接近1，均方根误差约为0.002 6 mm，计算结果的顶点半径偏离设计值0.018 8%。该方法可用于非球面检测阶段的参数计算分析，尤其是计算高精度的顶点半径值，为系统光机装调提供有效的数据支持。

Method to determine vertex radius of off-axis aspheric mirror based on surface fitting

In order to obtain an accurate vertex radius of large-diameter, off-axis aspheric mirrors, a method to determine the geometric parameters of aspheric optical surface based on surface fitting was presented. The accurate aspheric equation under the measuring coordinate system was constructed and an iterative nonlinear least-squares fitting algorithm was given here. Besides, the end surface of the compensator was used to derive the direction of optical axis and then to give appropriate initial values of the surface fitting. The experiments on measured data show that R-square is close to 1 while the root mean square error(RMSE) is about 0.002 6 mm. At the same time, the deviation of the calculated result from the designed value is just 0.018 8% for vertex radius. The method can be utilized to measure and analyze the geometric parameters of aspheric surface-vertex radius for example. It can provide valid data support for the following optical-mechanical assembly.