Extending the Takagi-Taupin equations for x-ray nanobeam Bragg coherent diffraction

We present an approach for simulating x-ray nanobeam Bragg coherent diffraction patterns based on the Takagi-Taupin equations. Compared to conventional methods, the current approach can be universally applied to any weakly strained system including semi-infinite crystals that diffract dynamically. It addresses issues such as the curved wave front and redivergence of the focused incident beam. We show excellent agreement with experimental data for a strained ${\mathrm{La}}_0.7{\mathrm{Sr}}_0.3{\mathrm{MnO}}₃$ thin film on a ${\mathrm{SrTiO}}₃$ substrate and a path to extracting physical information using automatic differentiation.