The main problems and the approach used by the authors for roughness metrology of super-smooth surfaces designed for diffraction-quality X-ray mirrors are discussed. The limitations of white light interferometry and the adequacy of the method of atomic force microscopy for surface roughness measurements in a wide range of spatial frequencies are shown and the results of the studies of the effect of etching by argon and xenon ions on the surface roughness of fused quartz and optical ceramics, Zerodur, ULE and Sitall, are given. Substrates of fused quartz and ULE with the roughness, satisfying the requirements of diffraction-quality optics intended for working in the spectral range below 10 nm, are made.
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