环形高次非球面在航天遥感器的光学系统中应用越来越广泛, 为了精确测量其非球面参数和矢高, 在探讨三坐标测量机非球面检测扫描路径的基础上, 分析了测试数据与理论数据之间的内在数学关系, 提出了一种基于坐标变换规范测试数据, 通过空间数据转换将测试数据降维, 数据处理由三维空间转换到二维平面, 进而在平面内做多项式拟合求解非球面母线的检测方案。通过泰勒级数展开, 对比分析了母线多项式拟合方程和标准非球面方程之间的系数对应关系, 并对某高次非球面进行实物检测。检测结果表明矢高拟合精度达 0.001 mm, 非球面系数拟合精度达到与设计值数量级一致, 检测方案合理可行, 为类似高次非球面的检测提供了一条有效可行的检测途径。

In order to measure the asphricial parameters and arc hight, taken the lens distance measurement as goal, a method is presented in this article which can calculate the generatrix equation through polynomial fitting. Through discussing the scanning path of aspheric surface, analyzing the relationship between the measurement data and the theoretical data, normalizing the measurement data based on coordinate transform, the data processing is transferred from space into plane in which the generatrix is solved. The relationship between the parameters of the generatrix fitting equation and the standard equation is comparative analyzed. The mathematical expression of high-order aspheric parameters is derived. The testing result of an high-order aspheric surface indicated that the scheme is reasonable and feasible. The fitting precision of rise can reach 0.001 mm which meets the testing requirement.