Iterative algorithm for subaperture stitching

The configuration parameters gb defocus г,, and Zernike polynomial coefficients Cq are unknown in Eq. (37) and are best estimated by minimizing the overlapping inconsistency. This is called the configuration optimization subproblem. On the other hand, the overlapping point pairs must first be determined. We call it an overlapping calculation subproblem. These two subproblems couple with each other. The overlapping correspondence changes with the configuration, which is difficult to be explicitly formulated. Therefore, the two subproblems are solved alternatingly. Such an iterative process repeats until it converges at the acceptable tolerance. The optimal configuration gi and defocus coefficients г, are then obtained. Therefore, all measuring points are now correctly transformed into the global frame, and the normal distances as well as the overlapping deviations are finally determined in the same frame. A full-aperture surface error map is thus obtained, and the stitching is completed.

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