Coherence properties of focused X-ray beams at high-brilliance synchrotron sources

An analytical approach describing properties of focused partially coherent X-ray beams is presented. The method is based on the results of statistical opticsand gives both the beam size and transverse coherence length at any distancebehind an optical element. In particular, here Gaussian Schell-model beams andthin optical elements are considered. Limiting cases of incoherent and fullycoherent illumination of the focusing element are discussed. The effect of thebeam-defining aperture, typically used in combination with focusing elements atsynchrotron sources to improve transverse coherence, is also analyzed in detail. As an example, the coherence properties in the focal region of compoundrefractive lenses at the PETRA III synchrotron source are analyzed