title: Numerical reconstruction of optical surfaces.
abstract: There are several problems in optics that involve the reconstruction of surfaces such as wavefronts, reflectors, and lenses. The reconstruction problem often leads to a system of first-order differential equations for the unknown surface. We compare several numerical methods for integrating differential equations of this kind. One class of methods involves a direct integration. It is shown that such a technique often fails in practice. We thus consider one method that provides an approximate direct integration; we show that it is always converging and that it provides a stable, accurate solution even in the presence of measurement noise. In addition, we consider a number of methods that are based on converting the original equation into a minimization problem.
authors.affiliation: Mathematics Department, Indiana University, Bloomington, Indiana 47405, USA.
authors.forename: Jayoung
authors.initials: J
authors.lastname: Nam
authors.forename: Jacob
authors.initials: J
authors.lastname: Rubinstein