Abstract: To evaluate the axisymmetric aspherical parts efficiently and accurately,an improved sequential quadratic programming algorithm and Newton-Raphson method of nonlinear equations was proposed to evaluate the profile error of aspherical parts.Regarding the issue that the design coordinate system failed to coincide with the measurement coordinate system in the detection of measuring instruments,a coordinate transformation matrix was used to eliminate the position error in the measurement coordinate system.Binary nonlinear equation was constructed to represent the projection points of aspheric surface based on its characteristics and Newton-Raphson method was applied to accurately calculate the projection distance.The improved sequential quadratic programming algorithm was adopted to establish error sub-problem solution to solve the computational intractability,and Quasi-Newton method was applied to solve the problem of large-scale unconstrained nonlinear.The simulation and experimental analysis were performed with various aspheric lenses and compared with the methods of least square and entropy function.The experimental results showed that the proposed algorithm effectively improved the data processing efficiency and accuracy when calculating the profile error.

Key words: optical aspheric surface, profile error, seqential quadratic programming, Newton-Raphson method, minimum zone

摘要： 为了高效率、高精度的评定轴对称非球面零件,提出一种改进序列二次规划算法并结合非线性方程组牛顿迭代法来评定非球面的轮廓度误差。对于测量仪器检测时存在的设计坐标系与测量坐标系不重合的问题,使用坐标变换矩阵来消除测量坐标系存在的位置误差;针对非球面的特点,构建二元非线性方程组来表示非球面的投影点,并采用牛顿迭代法精准计算投影距离;为解决计算的复杂性,采用改进序列二次规划算法构建误差子问题求解,并利用拟牛顿法求解大规模无约束非线性问题。最后,对多种非球面镜片进行仿真和实验分析,并与最小二乘法和熵函数法对比。结果表明,所设计的算法有效提高了计算轮廓度误差过程中的数据处理效率和精度。

关键词: 光学非球面, 轮廓度误差, 序列二次规划, 牛顿迭代法, 最小区域准则