This paper discusses the interpretation of arc-second x-ray scattering of mirror surfaces in terms of the power spectral densities of their topographic roughness. Such scattering depends on surface spatial wave-lengths of the order of mm to cm; much longer than those involved in conventional visible-light scattering and profile measurements. Key features are: 1) Expressions are developed for analyzing smooth-surface scattering in the Fresnel regime at angles comparable with the point-spread function of the measuring apparatus. 2) A sampling-theorem representation is used to describe the scattering in terms of a discrete rather than a continuous convolution with the system point-spread function. 3) Corrections are included to account for finite-record-length effects. And 4), results are illustrated for simple power-law power spectra.
E. L. Church,
"Interpretation Of High-Resolution X-Ray Scattering Measurements", Proc. SPIE 0257, Radiation Scattering in Optical Systems, (3 March 1981); doi: 10.1117/12.959623; https://doi.org/10.1117/12.959623