We present research investigations in the eld of multilayer optics in X-ray and extreme ultra-violet ranges (XUV), aimed at the development of optical elements for applications in experiments in physics and in scienti c instrumentation. We discuss normal incidence multilayer optics in the spectral region of \water window", multilayer optics for collimation and focusing of hard X-rays, multilayer dispersing elements for X-ray spectroscopy of high-temperature plasma, multilayer dispersing elements for analysis of low Z-elements. Our research pays special attention to optimization of multilayer optics for projection EUV-lithography ( ¶ = 13nm) and short period multilayer optics.

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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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The effect of Be layers on the reflection coefficients of Mo/Be/Si multilayer mirrors in the extreme ultraviolet (EUV) region is reported. Samples were studied using laboratory and synchrotron based reflectometry, and high-resolution transmission electron microscopy. The samples under study have reflection coefficients above 71% at 13.5 nm and more than 72% at 12.9 nm in a near normal incidence mode. Calculations show that by optimizing the thickness of the Be layer it should be possible to increase the reflection coefficient by another 0.5-1%. These results are of considerable interest for EUV lithography.