Figuring algorithm for high-gradient mirrors with axis-symmetrical removal function

Abstract

Figuring technologies based on intracone and intercone stitching for high-gradient mirrors are discussed. Based on the conventional computer-controlled optics shaping principle, a process model for a single cone with intracone stitching is constructed. With the circular stitching property of the model, a modified Bayesian-based Richardson-Lucy (RL) algorithm is deduced to deconvolute dwell time for single cone. Building on this algorithm, with the introduction of intercone stitching, a process model for a complex cone is built. Then another modified Bayesian-based RL algorithm is deduced to deconvolute the dwell time for a complex cone from the properties of intracone stitching and intercone stitching. With a velocity realization method for dwell time on a spiral path of the cone and the determination criterion of the path parameter, figuring technologies for single and complex cones are presented. Simulation and experiment demonstrate that theories and methods discussed can solve key problems of figuring high-gradient mirrors; the figuring technologies are novel methods for high-gradient mirrors and can be used to figure mirrors finely.