Influence of the random image alignment and optical path difference errors of a beam combination system on the optical transfer function of the optical sparse array

Abstract

The presence of a beam combination system that forms a united image in a common focal plane is one of the features of systems with an optical sparse array. Any control system of a beam combiner has a limited accuracy and, as a result, introduces some optical errors that influence the quality of the united image. This especially concerns systems with a dynamic aperture reconfiguration during an active process of observation. We present analytical expressions for the instantaneous spectral optical transfer function (OTF) of the optical sparse array consisting of N circular and annular subapertures depending on the residual random image alignment and optical path difference errors, and the average OTF for the Gaussian probability distributions depending on the statistical parameters of the last. The formulas are deduced on the basis of the Fraunhofer approach to the Kirchhoff diffraction theory. The results can be used for both space and earth sciences applications.