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

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