Unification Of Geometric And Diffractive Scattering From Random Rough Surfaces

The point spread function (PSF) of an X-ray mirror is determined by its surface topography. A new attempt is made to cover the full range of random surface roughness from macroscopic to microscopic imperfections, which has not been possible in the past. The angular deflections imposed by geometric slope errors are compared with diffraction angles which are calculated for each spatial frequency of the Fourier spectrum of the surface profile. A critical frequency has been found at which the regimes of geometric and diffraction optics separate, enabling easy calculation of the full PSF. The well-known expression of the Rayleigh scattering factor is shown to hold also separately for each spatial frequency. Furthermore, for frequencies greater than the. critical frequency the total microroughness is shown to be as low as to allow the application of the existing scattering theories in the smooth surface limit. At lower spatial frequencies geometric slope errors dominate.