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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

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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。

Abstract

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.

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中图分类号:TN206;TH741

DOI:10.5768/jao201637.0402004

所属栏目:光电信息获取与处理

基金项目:民用航天“十二五”预研项目资助课题

收稿日期:2016-04-25

修改稿日期:2016-06-04

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作者单位    点击查看

金秋宇: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
马 飞: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
刘恩涛: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
王 允: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
赵维谦: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

联系人作者:金秋宇(somnr_m@icloud.com)

备注:金秋宇(1992-), 男, 四川成都人, 硕士研究生, 主要研究方向为精密光电仪器测控技术。

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引用该论文

Jin Qiuyu,Ma Fei,Liu Entao,Wang Yun,Zhao Weiqian. Large optical aspheric mirror profile data evaluation method based on Levenberg-Marquardt algorithm[J]. Journal of Applied Optics, 2016, 37(4): 555-560

金秋宇,马 飞,刘恩涛,王 允,赵维谦. 基于Levenberg-Marquardt算法的大型非球面镜轮廓数据处理方法[J]. 应用光学, 2016, 37(4): 555-560

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