The scattering of x rays from nonideal multilayer structures

Abstract

A general theory is developed for the scattering of x rays from a single nonideal interface between two dielectric media. It is then extended to describe the scattering of x rays from a multilayer structure composed of many nonideal interfaces. The most unique feature of this theory is that there are no constraints on the physical structure of the interfaces; the interfaces can have any form of roughness or compositional inhomogeneity. A simple analytical expression is derived for both the near and far radiation field to first order, assuming that the scattering is weak. The theory is valid for arbitrary polarization and at all angles of incidence (measured from the normal) less than the critical angle for total external reflection. Finally, the results are applied to study the effect of different interface structures on the performance of multilayer x-ray optics.