An efficient iterative algorithm for subaperture stitching interferometry for aspheric surface

The subaperture stitching testing method provides a cost-effective means for large field of view, high spatial resolution interferometer. Current approaches to subaperture stitching are mostly limited to plano optics, where only the piston and the tilts are considered. Another implied assumption is that pixels corresponding to the overlapping region between pairs of subapertures are exactly known and given by the nominal translation within a spatial tolerance. This is obviously impractical in the case of aspheric surface. We address the problem here and introduce a geometrical approach to formulate it mathematically. It is essentially a large-scale nonlinear optimization problem, which is very complicated and time-consuming to be solved by conventional method. By virtue of the alternating optimization technique and the successive linearization method, we present a novel iterative algorithm for subaperture stitching interferometry for aspheric surface. It differs from others in that the CAD model of the tested surface is used to determine the overlapping region precisely and efficiently. Subapertures are then simultaneously stitched by minimizing deviations among them, as well as deviations from the nominal surface. As a result, precise prior knowledge of the nulling and alignment motion, which is of six degrees of freedom, is no longer required. Numerical simulations are given to test the validity and computational efficiency of the proposed algorithm.