Formulae in the paper by Balyan (2015) [J. Synchrotron Rad. 22, 1410–1418] are corrected.

The double-slit dynamical diffraction of X-rays in curved crystals is theoretically investigated. It is shown that interference fringes similar to Young's fringes are formed which can be used for determination of the curvature radius.

X-ray third-order nonlinear asymmetrical Bragg diffraction is investigated.

The two-wave dynamical diffraction Talbot effect inside a crystal for the case of spherical-wave illumination of a periodic object is investigated.

The rocking-curve dependence on the deviation of an incident X-ray plane wave from the exact Bragg orientation in and perpendicular to the diffraction plane for the asymmetrical Bragg case is investigated.

The dependence of X-ray rocking curves on the deviation angle from the exact Bragg orientation in the diffraction plane and in the direction perpendicular to the diffraction plane is investigated for the asymmetrical Laue case.

A new exact solution for the case of third-order nonlinear two-wave X-ray dynamical diffraction is obtained and the third-order nonlinear dynamical diffraction phenomenon is investigated. The solution is presented via Jacobi elliptic functions and takes into account the intensity of the incident wave as well as the deviation from the Bragg exact orientation.

The X-ray integer and fractional Talbot effect is studied under two-wave dynamical diffraction conditions in a perfect crystal, for the symmetrical Laue case of diffraction. The dynamical diffraction fractional Talbot effect is investigated for the first time.

The double-slit dynamical diffraction of X-rays in perfect crystals is theoretically investigated. It is shown that interference fringes similar to Young's fringes are formed on the exit surface of a crystal.

For the first time the third-order nonlinear time-dependent Takagi's equations of X-rays in crystals are obtained. The third-order nonlinear and linear time-dependent dynamical diffraction of X-rays spatially restricted in the diffraction plane pulses in crystals is investigated. The results of analytical and numerical calculations are presented.

Two-wave third-order nonlinear symmetric Bragg-case dynamical diffraction of a plane X-ray wave in a perfect crystal is investigated theoretically. An analytical solution is found and results of numerical calculations are presented.

On the basis of the eikonal approximation, X-ray Bragg-case focusing by a perfect crystal with parabolic-shaped entrance surface is investigated theoretically.

Taking into account background correction and using Fourier analysis, a numerical method of reconstructed object image correction using a dynamical diffraction Fraunhofer hologram is discussed.

A numerical method of reconstruction of an object image using a dynamical diffraction Fraunhofer hologram is discussed.

An X-ray LLL interferometer with a wedge-shaped mirror plate is experimentally and theoretically investigated.

A new type of X-ray LLL interferometer, a `hard' interferometer, which has both a base and a `ceiling', is tested for experimental investigations. The tested interferometer has no preliminary uncontrollable moiré and can be used for object and deformation investigations.

The current work shows the calculation and study of an X-ray one-dimensionally focusing system composed of Bragg double-asymmetric-reflecting two-crystal plane parallel plates and a double-concave cylindrical parabolic lens placed in the gap between the plates. The focusing distance is calculated, intensity distribution curves are given in the focusing plane and on the focusing line, and the intensity at the focus point and the longitudinal and transverse sizes of the focus are defined.