Vol. 6, issue 12, article # 12

Abstract:

The present approach to segmented mirror control used for phase compensation is to measure phase tilts with a wavefront sensor, apply these tilts to the segments, and then adjust the pistons to minimize the edge mismatch by bringing adjacent segment edge midpoints together. Matching the heights of adjacent segment edge midpoints leads to a linear system of equations for the segment pistons U_i , in terms of the segment tilts t_i , which looks like a discretized Poisson equation, С²U = – Сt . We demonstrate that the discrete linear system is ill–posed in 2 dimensions. Moreover, diffractive effects that arise from the segmentation must be accounted for in the wavefront control.