Sub-aperture weighted stitching algorithm for absolute measurement of cylindrical surface

The sub-aperture stitching interferometry method requires a certain overlapping region between adjacent sub-apertures. By removing the phase deviations of corresponding points in the overlapping regions, a complete surface map was stitched together. A weighted fusion stitching algorithm was proposed. By calculating the weights of each group of measurement results in the overlapping area, the splicing traces produced when the averaging method taking values in the overlapping area were improved, achieving a smoother splicing effect. Additionally, by combining the cylindrical two-position absolute measurement method, the influence of the reference mirror surface shape was eliminated, simplifying the process for rotation in the cylindrical three-position interferometric measurement method. The influence of misalignment errors on measurement results during sub-aperture adjustment was also reduced. The measurement data of sub-aperture were obtained at the confocal and focal line positions, and after stitching, the Chebyshev polynomial fitting was applied to derive the absolute surface shape of the entire cylindrical aperture. This method not only reduces dependence of cylindrical measurement on the reference mirror aperture and focal length, but also ensures measurement accuracy.