New method to model x-ray scattering from random rough surfaces

Abstract

This paper presents a method for modeling the X-ray scattering from random rough surfaces. An actual rough surface is (incompletely) described by its Power Spectral Density (PSD). For a given PSD, model surfaces with the same roughness as the actual surface are constructed by preserving the PSD amplitudes and assigning a random phase to each spectral component. Rays representing the incident wave are reflected from the model surface and projected onto a flat plane, which approximates the model surface, as outgoing rays and corrected for phase delays. The projected outgoing rays are then corrected for wave densities and redistributed onto an uniform grid where the model surface is constructed. The scattering is then calculated by taking the Fast Fourier Transform (FFT) of the resulting distribution. This method is generally applicable and is not limited to small scattering angles. It provides the correct asymmetrical scattering profile for grazing incident radiation. We apply this method to the mirrors of the Chandra X-ray Observatory and show the results. We also expect this method to be useful for other X-ray telescope missions.