The diffraction of long-wavelength X rays with the energy corresponding to the region of anomalous dispersion near the Si L2,3 absorption edges transmitted through microchannel plates has been studied both experimentally and theoretically. The radiation of a finite antenna array, as well as the processes of excitation of X-ray fluorescence and propagation of waves in hollow waveguide structures, has been mathematically simulated. The model describes a polycapillary structure consisting of noninteracting emitters, which are hollow channels of a microchannel plate. It has been shown that coherently excited X-ray fluorescence propagates primarily in the direction of the zeroth diffraction order.