Precision imaging multilayer optics for soft X-rays and extreme ultraviolet bands

Optical methods that provide high diffraction image quality with a spatial resolution of several to tens of nanometers and are in demand in such areas as projection lithography, X-ray microscopy, astrophysics, and fundamental research on the interaction of matter (vacuum) with ultrahigh ($10^{20}$–$10^{23}$ W cm$^{-2}$) electromagnetic fields are reviewed in terms of fabrication and testing technologies and possible use in the $2$–$60$ nm wavelength range. The current worldwide status of and recent achievements by the Institute for Physics of Microstructures of the Russian Academy of Sciences (RAS) in the field are discussed.