• X-ray lenses;
  • partial coherence

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