Advanced matrix-based algorithm for ion-beam milling of optical components

Abstract

Control of an ion beam for milling optical surfaces is a nontrivial problem in two-dimensional deconvolution. The ion milling operation is performed by moving an ion beam gun through a grid of points over the surface of an optical workpiece. The control problem is to determine the amount of time to dwell at each point in the grid to obtain a desired surface profile. This research treats the problem in linear algebra terms. The required dwell times are the solutions to a large, sparse system of linear equations. Traditional factorization methods such as Gaussian elimination cannot be used because the linear equations are severely ill conditioned. Theoretically, a least-squares solution to this problem exists. Practical approaches to finding a minimal least-squares solution are discussed.