Abstract

The optical systems with distributed/sparse apertures have a number of distinctive features in comparison with the systems with monolithic ones. Among them the possible existence of zero-value regions of the optical transfer function (OTF) and the existence of a beam combination system which forms a combined image in a common focal plane. Using the fast-convergent gradient methods for nonlinear constrained optimization, the first feature can result in a suspension of a calculation process if an intermediate solution falls into a zero-value region of the OTF. The second feature gives rise to introducing of some optical errors influencing the quality of the combined image due to the limited accuracy of a beam combination control system. In this thesis, the possibility of applying a gradient optimization method to optimize the distributed/sparse optical aperture configuration is shown. An appropriate approach based on approximation of the step pupil functions with zero-value regions by continuously differentiable functions with non zero-value regions is proposed. This method is demonstrated using examples of circular and annular subapertures. Further, the influence of the residual random image alignment (IA) and optical path difference (OPD) errors of the beam combination system on the OTF is investigated. On the basis of the Fraunhofer approach to the Kirchhoff diffraction theory, an analytical expression showing the dependence of an instantaneous OTF on the IA and OPD errors is derived. Using the Gaussian probability distributions for the random errors, an analytical expression determining an average OTF (AOTF) depending on statistical parameters of the errors is obtained. The calculation results permit to produce the necessary requirements to the accuracy of the beam combination control system. Finally, possible optimization variants utilizing the step pupil function approximation and the AOTF conception are presented. They use a gradient constrained optimization method with objective functions depending on a signal-to-noise ratio which is expressed in terms of the optimized parameters, in particular, the parameters of the aperture configuration, the effective focal length, and the geometrical parameters of a charge coupled device. Presented results show optimal solutions of the considered optimization problems for the distributed apertures consisting of two and three annular subapertures.