Formulation of perfect-crystal diffraction from Takagi-Taupin equations. Numerical implementation in the crystalpy library

The Takagi-Taupin equations are solved in their simplest form (zero deformation) to obtain the Bragg-diffracted and transmitted complex amplitudes. The case of plane-parallel crystal plates is discussed using a matrix model. The equations are implemented in an open-source python library crystalpy adapted for numerical applications such as crystal reflectivity calculations and ray tracing.