Influence of diffraction in crystals on the coherence properties of X-ray free-electron laser pulses

The spatial and temporal evolution of the field of random X-ray femtosecond pulses and their coherent properties upon pulse propagation in free space and under dynamical diffraction in perfect crystals in the Bragg and Laue geometries has been analyzed on the basis of the formalism developed in statistical optics. Particular attention is paid to the influence of large pulse propagation distances, which are characteristic of lengthy channels of X-ray free-electron lasers.