Dark-field x-ray microscopy (DFXM) is a non-destructive microscopy technique for the three-dimensional mapping of orientations and stresses of materials. If the sample is large and near-perfect, multiple scattering effects (dynamical diffraction) may become important, and the incident x-ray may not penetrate the entire sample. To get a three-dimensional mapping, one tries to avoid dynamical effects relying on the “weak beam approximation”, however, the further from the Bragg condition, the weaker the diffraction is. Particularly, in the DFXM based on x-ray free electron laser, the photon number is limited, so that the weak beam approximation may not be applicable. If dynamical effects are not avoided, the multiple scatterings may yield different results to a single scattering. That is why computer simulation of dynamical diffraction is needed for studying DFXM. A previous study utilized Takagi-Taupin equations which is suitable for near-perfect crystals. For strongly deformed crystals, the diffraction is more diffused. The previous method may bring errors from the neglecting of second order derivatives of Maxwell’s equations. For example, in the limit of weak scattering, the Takagi-Taupin equations are not equivalent to the equations of kinematic diffraction theory. To cover the limit of kinematic diffraction, we developed an alternative method. The new method solves a wave field composed of plane waves which satisfy the vacuum dispersion relation. In a similar way to Carlson’s finite difference scheme, two dimensional Fourier transformations are used to solve the equations. Wherein, for a rapid convergence, a continuous Fourier transformation is calculated with a Taylor expansion approximation. The method was compared to Carlson’s method with a near perfect crystal. DFXM of strongly deformed crystals were studies, while the results of the current method were compared to results of the kinematic diffraction theory.
 

dynamical diffraction,kimenatic diffraction,dark-field x-ray microscopy