  We simulate the focusing of a partially-coherent X-ray beam emitted by an
undulator in a fourth-generation storage ring performing coherent mode
decomposition and wave optics propagation. The focus position is shifted, and
its size is enlarged when an entrance slit crops the beam. This is the usual
case when a slit is used to select the coherent fraction. The pairing of two
focusing elements (mirrors, lenses or transfocators) to ensure a fixed focal
position is also analyzed. Our results show that the image of a partially
coherent source, such an undulator in a low-emittance storage ring, is a
non-trivial function of the aperture used to control the coherence fraction.

Optics;Accelerator Physics