Analysis of X-ray scattering from a rough multilayer mirror in the first-order perturbation theory

The scattering of X-rays from a rough multilayer structure is analyzed in the framework of the first-order scalar perturbation theory. As known, the scattering diagram from a multilayer mirror is expressed as a double sum of partial scattering amplitudes from each interface. In the present work the summation is performed in an explicit form. The simple analytic formulas are deduced, which are well suited for analysis of physical phenomena observed in experiments and describe all the features of X-ray scattering.