Large optical aspheric mirror profile data evaluation method based on LevenbergMarquardt 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LevenbergMarquardt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 /
- LevenbergMarquardt /
- 误差补偿 /
- 非线性拟合 /
- 轮廓数据评定
Abstract: Large optical aspheric mirrors are manufactured by the technology of processing，measuring，reprocessing and remeasuring 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 LevenbergMarquardt (LM) algorithm based on the trustregion 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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期刊类型引用(3)
1. 李想，赵强，郭磊，李颖. 高斯光束理论及非线性拟合在准直器自动生产中的应用. 中国激光. 2025(02): 165-170 . 
百度学术
2. 和士琦，刘伟. 数字化信息平台Oracle数据库空闲碎片整合研究. 自动化与仪器仪表. 2020(08): 158-161 . 百度学术
3. 田晗，冯朝一. 残缺指纹激光数据的走势推定. 激光杂志. 2018(02): 122-125 . 百度学术
其他类型引用(1)
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