A finite difference scheme for integrating the Takagi-Taupin equations on an arbitrary orthogonal grid

X-ray Free Electron Laser based Dark-Field X-ray Microscopy

“…To demonstrate the contrast we have relied on two DFXM forward simulations tools [26,27]. This work corroborates the validity of these models, as -although they were constructed independently, using different physical approaches, they arrive at qualitatively similar results.…”

“…Ref. [27]. The scattered field is propagated through the CRL and to the detector using Fourier propagation methods described in Ref.…”

“…We simulate longitudinal sound wave propagation in a diamond single crystal using the thermomechanical Python modeling package udkm1Dsim [24,25]. Forward simulations of DFXM data are performed using both geometrical optics [26] and wavefront propagation optics [27] to explore the DFXM parameter-space and optimize the experimental configuration. Using a setup relevant for an experiment at the XCS instrument at the Linac Coherent Light Source (LCLS) as an example, the simulations show the propagation of a longitudinal strain wave with both a clear contrast and a good signalto-noise from a single pulse, thereby opening the door to investigating the materials science entailed in dynamic imaging of phonon propagation [28][29][30].…”

Simulating dark-field x-ray microscopy images with wave front propagation techniques

“…With the sample structure and the boundary conditions given, the TTEs constitute an initial value problem, where the initial value is the amplitude of the incident x-rays on the z = 0 surface. This can be solved by an appropriate finite difference scheme to yield the amplitudes of both the transmitted and scattered beams on the exit-surface z = L. Details of the applied finite difference scheme are given in [21].…”