Large-diameter Planar Surface Shape Measure Technology Based On Sub-aperture Stitching

With the rapid development of high-precision optical component manufacturing technology,large-aperture optical components have been widely used in various national science and engineering projects.As a result,higher requirements have been placed on the surface shape measure technology of large-aperture optical components.Existing optical component measure technology is difficult to simultaneously meet the measure requirements of large aperture and high precision.Sub-aperture stitching measure method is a high-precision and low-cost surface shape measure technology.This method uses small-aperture standard optical components to detect large-aperture optical components,which reduces the difficulty of measure while also have the high-precision advantages of interference measurement.It can improve the lateral resolution and obtain wavefront mid-frequency errors information.In this dissertation,focuses on the research of large-aperture flat surface shape measure technology based on sub-aperture stitching.The main work includes:（1）The sub-aperture division and stitching mode are studied,and two sub-aperture stitching algorithms,the dual objective function method and the global optimized stitching method,are modeled and simulated to verify the simulation results of the two stitching algorithms,It is determined that the global optimized stitching algorithm has higher stitching accuracy,and its theoretical stitching accuracy can reach 1×10^-12.（2）There are positioning errors and standard mirror system errors in sub-aperture stitching interferometry.A positioning error solved model based on marker points was established to address the positioning error problem.The impact of positioning errors on the accuracy of sub-aperture stitching algorithms was analyzed through simulation,and the results showed that the accuracy of sub-aperture stitching algorithms decreases as the positioning errors increase.The standard mirror surface shape in sub-aperture stitching interferometry can cause cumulative errors in the sub-stitching algorithm.To address the standard mirror system error,In this dissertation,uses the translation difference method to solve the standard mirror surface shape information.Numerical simulations were conducted to verify that the translation difference method can effectively compensate for the standard mirror error in the sub-aperture measurement results,thereby improved the full aperture surface reconstruction accuracy.（3）The sub-aperture overlap region fusion algorithm is proposed to address the problems of stitching traces and missing middle and high frequency errors in sub-aperture overlap region fusion.The low-frequency errors of the surface shapes are fused by weighted average of spatial Euclidean distances,and the mid-frequency errors of the surface shapes are fused by a fusion method based on regional characteristics.The results show that the proposed fusion algorithm can effectively preserve the medium and high frequency errors of the face shape while eliminated the stitching traces,and realize the measure and evaluation of the face shape of large-aperture planar optical elements in a wide frequency band.Experiments on the sub-aperture stitching measure of typical optical components are carried out,and the experimental results are in agreement with the full-aperture measure results,RMS deviation value close toλ/1000.