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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