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.

We have studied the surface treatment of polished fused silica by neutralized Ar ions with energy of 500-1500 eV and incidence angles of 0-90°. We found the following regularities: for samples that passed the standard procedure of deep polishing (initial effective roughness σ(eff)∼0.5  nm), the effective roughness decreases to the ultrasmooth level (i.e., σ(eff)∼0.25  nm in the range of spatial frequencies q∈[4.9×10(-2)-63]  μm(-1)). The effect begins to be noticeable at the material removal of 150 nm and reaches saturation at depths of removal greater than 1 μm. For supersmooth samples (σ(eff)<0.3  nm), the effective roughness keeps the initial level at material removal down to tens of micrometers. The optimal ion energy range is 800-1300 eV (maximum smoothing effect); at higher energy some surface roughness degradation is observed. All the smoothing effects are observed at the incidence angle range θ(in)=0-35°. Increasing the ion energy above 1300 eV increases the etching rate by up to 4 μm per hour (J(ion)=0.8  mA/cm2), which allows for deep aspherization of sized substrates. The technique allows for manufacturing the optical elements for extreme ultraviolet and soft x-ray wavelength ranges with a numerical aperture of up to 0.6.

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A description of a stand based on atomic force microscopy (AFM) for roughness measurements of large optical components with arbitrary surfaces is given. The sample under study is mounted on a uniaxial goniometer which allows the sample to be tilted in the range of ±30°. The inclination enables the local normal along the axis of the probe to be established at any point of the surface under study. A comparison of the results of the measurement of noise and roughness of a flat quartz sample, in the range of spatial frequencies 0.025-70 μm(-1), obtained from "standard" AFM and developed versions is given. Within the experimental error, the measurement results were equivalent. Examples of applications of the stand for the study of substrates for X-ray optics are presented.

Multilayer structures with short periods have been systematically investigated using a tunable soft X-ray synchrotron, BESSY II, and X-ray tube radiation. Multilayer X-ray mirrors of W/B(4)C, W/Sc, Mo/B(4)C, Mo/C, La/B(4)C, Cr/C and Cr/Sc, with periods from 0.8 nm to 3.5 nm and number of periods up to 300-400, were constructed and investigated. The high reflectivity and spectral resolution of the mirrors allow them to be used to create multimirror systems for X-ray diagnostics of high-temperature plasma, for X-ray astronomy and microscopy.