Two-dimensional PSF prediction of multiple-reflection optical systems with rough surfaces

The focusing accuracy in reective optical systems, usually expressed in terms of the Point Spread Function (PSF) is chiey determined by two factors: the deviation of the mirror shape from the nominal design and the surface finishing. While the effects of the former are usually well described by the geometrical optics, the latter is diffractive/interferential in nature and determined by a distribution of defects that cover several decades in the lateral scale (from a few millimeters to a few microns). Clearly, reducing the level of scattered light is crucial to improve the focusing of the collected radiation, particularly for astronomical telescopes that aim to detect faint light signals from our Universe. Telescopes are typically arranged in multiple reections configuration and the behavior of the multiply-scattered radiation becomes difficult to predict and control. Also it is difficult to disentangle the effect of surface scattering from the PSF degradation caused by the shape deformation of the optical elements. This paper presents a simple and unifying method for evaluating the contribution of optical surfaces defects to the two-dimensional PSF of a multi-reections system, regardless of the classification of a spectral range as "geometry" or "roughness". This method, entirely based on Huygens-Fresnel principle in the far-field approximation, was already applied in grazing-incidence X-ray mirrors and experimentally validated for a single reection system, accounting for the real surface topography of the optics. In this work we show the extension of this formalism to a double reection system and introducing real microroughness data. The formalism is applied to a MAGIC-I panel mirror that was fully characterized, allowing us to predict the PSF and the validation with real measurements of the double reection ASTRI telescope, a prototype of CTA-SST telescope.