| 基于Levenberg-Marquardt算法的大型非球面镜轮廓数据处理方法 |
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| 引用本文： | 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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| 作者姓名： | 金秋宇 马飞 刘恩涛 王允 赵维谦 |
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| 作者单位： | 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 |
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| 基金项目： | 民用航天“十二五”预研项目资助课题 |
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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1.1610-21。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。
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| 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 |
| 收稿时间： | 2016-04-25 |
Large optical aspheric mirror profile data evaluation method based on Levenberg Marquardt algorithm |
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| 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. |
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| Authors: | Jin Qiuyu;Ma Fei;Liu Entao;Wang Yun;Zhao Weiqian |
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| Affiliation: | 1.Beijing Key Lab for Precision Optoelectronic Measurement Instrument and Technology,School of Opto electronics,Beijing Institute of Technology,Beijing 100081,China |
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| 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 1.1610-21. 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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