Small-angle x-ray scattering under grazing incidence: The cross section in the distorted-wave Born approximation

The specular and nonspecular intensity of x rays scattered from a rough surface with fluctuations in the electron density is calculated in the distorted-wave Born approximation. The contributions to the nonspecular intensity of roughness and density fluctuations can be separated. The structure factor is given by a convolution integral of the Fourier transform of the density correlation function. Special geometries of density fluctuations are discussed.