Stitching arithmetic of the sub-aperture testing of large convex aspheric surface

When using an interferometer tests a large convex aspheric surface in sub-aperture, the subapertures and the mirror under test are off-axis. So when stitching the measurements, the full aperture map is got, besides the piston and tilt that are usual in plane testing, there is lateral misalignment need to be removed as well. Based on the least squared fit process of the plane sub-aperture testing, the stitching arithmetic is improved to apply to the sub-aperture off-axis testing. In order to prove the validity of the arithmetic, the Matlab is used to emulate the stitching process of sub-aperture testing for lm convex aspheric surface. The results indicate that the improved arithmetic is effective, and its stitching precision can reach 0.0048A.