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.

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The possibilities of applying the point diffraction interferometry (PDI) method for the detection of the middle spatial frequency roughness of superpolished optical surfaces are analyzed. The point source used in the experiment is based on a single mode optical fiber with the subwavelength exit aperture size, which is about 0.25 μm. In a numerical aperture of 0.01 the reference wave root-mean-square deformation is less than 0.005 nm. It is theoretically shown that the possible diffraction-limited lateral resolution of PDI while measuring a spherical substrate of 100 mm curvature radius is about 8 μm. The experiment demonstrated the possibility of obtaining roughness spectra in the range 0.001-0.05  μm(-1). The surface map obtained by PDI, and the roughness spectra obtained by both the PDI and atomic-force microscopy methods are shown.

The behavior of sputtering yield and the surface roughness of monocrystalline silicon of orientations ⟨ 100 ⟩ , ⟨ 110 ⟩ , and ⟨ 111 ⟩ under the ion-beam bombardment by neutralized Ar ions with energies of 200–1000 eV is studied. The significant dependence (modulation) of sputtering yield on incidence angle due to crystalline structure is observed. It is shown that a sharp increase in the sputtering yield and a decrease in the effective surface roughness at energies above 400 eV occurs. At energies of more than 400 eV for orientations ⟨ 100 ⟩ , ⟨ 110 ⟩ , and ⟨ 111 ⟩ at normal ion incidence, smoothing of the effective roughness in the range of spatial frequencies ν ∈ [ 4 . 9 ⋅ 1 0 − 2 − 6 . 3 ⋅ 1 0 1 µ m − 1 ] up to a value of 0.17 nm is observed. This makes it possible to use the ion-beam etching technique for finishing polishing, aspherization, and correction of local shape errors of single-crystal silicon substrates, which are of the greatest interest for synchrotrons of the 3rd+ and 4th generation and x-ray free electron lasers.