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

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．