A varying-step algorithm for numerical integration of Takagi–Taupin equations

Abstract

The numerical integration of the Takagi-Taupin equations using a constant step of integration does not allow the simulation of traverse topographs since the accuracy of the computation is rather poor. A new algorithm is described in which the step of integration varies inside the crystal, following the oscillations of the amplitudes of the wavefields. The precision becomes good enough to simulate either section topographs, taking into account the real width of the incident beam, or traverse topographs. Moreover in most cases the time of computation is decreased by a factor of two to three.