Fast, precise, and shape-flexible registration of wavefronts

A fast and precise algorithm for wavefront reconstruction by the registration of wavefront segments is presented. If the wavefront exceeds the sensor aperture or the dynamic range of the sensor, a Shack-Hartmann sensor can measure only segments of an optical wavefront. The algorithm registers the wavefront segments in parallel, where they are simultaneously transformed to minimize their overlap mismatch for precise reconstruction of the entire wavefront. The original nonlinear optimization problem is approximated by a convex optimization problem that can be solved more efficiently. A simulation-based analysis of the algorithm and a comparison to a previously proposed parallel registration (PR) algorithm as well as to the iterative closest point (ICP) algorithm are presented. It is shown that despite measurement noise, the algorithm can precisely register plane as well as divergent wavefronts with root mean square registration errors smaller than 10 nm. Particularly for the divergent wavefront, this enables a reduction of the registration error by a factor of up to 750 as compared to the established algorithms. Analysis and comparison to the ICP and PR algorithm also show that the computation time of the proposed algorithm can be from one to three orders of magnitude smaller.