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.

© 2008 Optical Society of America

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