基于Levenberg-Marquardt算法的大型非球面镜轮廓数据处理方法  

Large optical aspheric mirror profile data evaluation method based on Levenberg-Marquardt algorithm

作　　者：金秋宇 马飞[1] 刘恩涛[1] 王允[1] 赵维谦[1] 

机构地区：[1]北京理工大学光电学院精密光电测试仪器及技术北京市重点实验室,北京100081

出　　处：《应用光学》2016年第4期555-560,共6页Journal of Applied Optics

基　　金：民用航天"十二五"预研项目资助课题

摘　　要：大型非球面镜通过加工-检测-再加工-再检测的制造工艺以满足面形精度要求,根据检测后的轮廓数据准确评定面形是提高再加工精度的关键。为解决抛光前镜面的面形评定问题,采用基于信赖域法则的Levenberg-Marquardt算法对参数进行拟合、误差补偿以及面形评定。利用Code V仿真分析算法性能,构建大型非球面轮廓仪测试抛物面加工件,对实测数据经过32次迭代得到元件参数及轮廓残差曲线,收敛精度为1.16×10-21。实验表明:该算法可对大型非球面镜轮廓数据进行高效准确的拟合、评定,为进一步提高再加工精度提供可靠依据。Large optical aspheric mirrors are manufactured by the technology of processing,measuring,re-processing and re-measuring in order to meet the profile accuracy requirements,so an accurate evaluation of surface shape based on profile data after measuring is the key to improve the precision of reprocessing.To solve the problem of evaluating rough machining surface of mirrors,the Levenberg-Marquardt（LM）algorithm based on the trust-region rule was applied to data fitting,error compensation and surface shape evaluation.Simulation by Code V was carried out to analyze the algorithm performance,and a paraboloid workpiece was measured in surface profiler which was designed by ourselves.The parameters and residual variance curve of surface were obtained through 32 times of iteration and the convergence precision is 1.16×10-21.Experiments show that the algorithm can efficiently and accurately evaluate the contour data of large aspherics,which can provide the reliable foundation for surface shape convergence in the process of rough machining.

关 键 词：大型非球面镜 LEVENBERG-MARQUARDT 误差补偿 非线性拟合 轮廓数据评定 

分 类 号：TN206[电子电信—物理电子学] TH741[机械工程—光学工程]