Grazing-incidence small-angle X-ray scattering from a random rough surface: a self-consistent wavefunction approximation

An attempt is made to go beyond the distorted-wave Born approximation by using the integral wave equation adjusted with the Green function formalism in application to the grazing-incidence small-angle X-ray (GISAX) scattering from a random rough surface. The self-consistent approximation for the wavefunction is applied to obtain a basic solution of the non-averaged integral wave equation. The analytical expressions for the reflected GISAX specular and diffuse scattering intensities are obtained using the statistical model of a random Gaussian surface in terms of the r.m.s. roughness and two-point cumulant correlation function.