Dynamical X-ray diffraction in a crystal with the spatial modulation of incident and reflected waves

A new approach has been proposed to the problem of dynamical scattering of spatially limited X-ray beams. The dynamical diffraction theory in a crystal with the lateral modulation of incident and reflected X-ray waves has been developed within this approach. The unusual angular distribution of the diffracted intensity from the crystal with an absorbing surface grating has been physically explained and numerically simulated. The effect of the instrument function on the formed diffraction pattern has been demonstrated.