Diffractional focusing of x-rays by a cylindrically bent crystal: the Johann scheme and backscattering

An analytical formula for a diffraction region size in the Johann scheme with a point source is obtained. It is demonstrated that taking terms similar tox(3) and similar tox(4) in the expansion of a wave phase for an incident wave into account, one can derive analytical expressions for the spatial distribution of intensity near a focus (the Airy function and the Pearsey integral respectively). On the basis of these expressions, a focusing Johann spectrometer is considered. The theoretical limit for the spectral resolution that this spectrometer can attain is similar to10(-7). The influence of the x-ray radiation nonmonochromaticity and of the source size on the focusing coherence is analysed.