Optimization of the optical sparse array configuration

Abstract

One feature of systems with sparse optical aperture is the possible existence of zero-value regions of the optical transfer function. In using fast-convergent gradient methods for nonlinear constrained optimization with criteria based on the optical transfer function or the modulation transfer function, the gradient of the minimized function can also contain zero-value regions. Such situations can result in a suspension of the calculation if an intermediate solution falls into such a region. We show that, using gradient methods, it is possible to avoid this calculation problem if we redefine the subaperture step pupil functions—in particular, approximate them by continuously differentiable functions having no zero-value regions. This is demonstrated on examples of apertures consisting of circular and annular subapertures. This approach can be used for both types of multiaperture optical telescopes, the Michelson and Fizeau, and for both space and earth science missions.