Tian Chao, Yang Yongying, Wei Tao, Zhuo Yongmo
State Key Laboratory of Modern Optical Instrumentation, Zhejiang University, 38 Zheda Road, Hangzhou 310027, China.
Appl Opt. 2011 Jul 10;50(20):3559-69. doi: 10.1364/AO.50.003559.
The nonnull interferometric method that employs a partial compensation system to compensate for the longitude aberration of the aspheric under test and a reverse optimization procedure to correct retrace errors is a useful technique for general aspheric testing. However, accurate system modeling and simulation are required to correct retrace errors and reconstruct fabrication error of the aspheric. Here, we propose a ray-tracing-based method to simulate the nonnull interferometer, which calculates the optical path difference by tracing rays through the reference path and the test path. To model a nonrotationally symmetric fabrication error, we mathematically represent it with a set of Zernike polynomials (i.e., Zernike deformation) and derive ray-tracing formulas for the deformed surface, which can also deal with misalignment situations (i.e., a surface with tilts and/or decenters) and thus facilitates system modeling extremely. Simulation results of systems with (relatively) large and small Zernike deformations and their comparisons with the lens design program Zemax have demonstrated the correctness and effectiveness of the method.
采用部分补偿系统来补偿被测非球面的纵向像差以及采用反向优化程序来校正回程误差的非零干涉测量方法，是一种用于一般非球面检测的有用技术。然而，需要精确的系统建模和仿真来校正回程误差并重建非球面的制造误差。在此，我们提出一种基于光线追迹的方法来模拟非零干涉仪，该方法通过跟踪光线穿过参考光路和测试光路来计算光程差。为了对非旋转对称的制造误差进行建模，我们用一组泽尼克多项式（即泽尼克变形）对其进行数学表示，并推导了变形表面的光线追迹公式，该公式还可以处理对准误差情况（即具有倾斜和/或偏心的表面），从而极大地促进了系统建模。具有（相对）大、小泽尼克变形的系统的仿真结果以及它们与透镜设计程序Zemax的比较，证明了该方法的正确性和有效性。
