Crystal optics elements in a coherent x-ray scattering experiment

We describe wave propagation from a partially coherent x-ray source taking into account the free-space wave propagation and the Bragg diffraction on a collimating crystal. We find conditions when the free-space propagation becomes irrelevant and the coherence length is given by the extinction length of the corresponding Bragg reflection. We show that a wide wavelength range can be retained if the collimating crystal is illuminated by a convergent beam. The increase of the coherence length by Bragg diffraction is demonstrated in a laboratory experiment on periodic surface gratings with different periods.