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In the framework of the scalar theory of diffraction, we determine the rms width of the angle spread function degraded by surface roughness in reflective grazing-incidence optics of cylindrical symmetry for X-ray astronomy. Our derivation does not rely on the small roughness approximation, is thus valid for arbitrary roughness values, and takes into full consideration the cylindrical symmetry of the mirrors. The dependence of the rms beam width on both the grazing-incidence angles and the radiation wavelength is studied for both single and double reflection optics, the latter being more relevant to X-ray telescopes. When the small roughness approximation is applicable, we also derive an expression for the angle spread function of the optical system in the presence of roughness scattering that provides the correct expression for the rms beam width.

Roughness scattering in X-ray grazing-incidence telescopes