Self-consistent computation of x-ray mirror point spread functions from surface profile and roughness

The angular resolution degradation of an X-ray mirror, represented by its Point Spread Function (PSF), is usually simulated accounting for geometrical deformations and microroughness of its surface. When the surface profile is analyzed in terms of Fourier components, figure errors comprise the spectral regime of long spatial wavelengths, whilst microroughness falls in the regime of high spatial frequencies. The first effect is in general simulated along with geometrical optics, while the second contribution - that heavily depends on the energy of X-rays - is derived from the first order scattering theory. A drawback of this method, indeed, is that the separation between the geometrical and physical optics regime is not abrupt. Moreover, it is not clear how one should merge the PSFs derived from the two computations to retrieve an affordable reconstruction of the PSF of the mirror. In this paper we suggest a method to compute the mirror PSF from longitudinal profiles of a grazing incidence mirror, based uniquely on physical optics. The treatment makes use of Fresnel diffraction from measured/simulated profiles, accounting for the surface roughness in terms of its PSD (Power-Spectral-Density). Even though this approach was already adopted in the past to simulate the sole X-ray scattering, in this work we show, along a series of simulations, that it can be applied to reproduce the effect of scattering, aperture diffraction and figure errors as well. The computation returns the PSF at any X-ray energy, it is self-consistent and does not require setting any boundary between figure errors and roughness.