Point spread function and optical transfer function of a misaligned hypertelescope

Abstract

Analytical expressions for an instantaneous spectral point spread function (PSF) and an instantaneous spectral optical transfer function of a misaligned hypertelescope without delay lines, and containing circular and/or annular collecting mirrors, are presented. The formulas are deduced on the basis of the Fresnel approach to the Kirchhoff diffraction theory. Numerical results obtained for the system containing 60 identical annular mirrors, illustrate the pupil densification properties of the hypertelescope and the influence of random spatial and angular positioning errors of the optical elements on the average PSF (APSF), and on the average modulation transfer function (AMTF) calculated for the errors obeying specified probability distributions. The APSF and the AMTF give the opportunity to estimate the influence of the alignment errors on the resulting image quality in the hypertelescope image plane. This estimation can be used to produce the necessary requirements to the accuracy of the mirror control system and to the accuracy of the optical element alignment in dependence on the values of the exit pupil densification and the desirable resolution capability of the hypertelescope. The notion of the PSF and the modulation transfer function for off-axis beams can be useful for evaluation of a hypertelescope field of view.