X-ray free-electron laser based dark-field X-ray microscopy: a simulation-based study

Abstract

Dark-field X-ray microscopy (DFXM) is a nondestructive full-field imaging technique providing three-dimensional mapping of microstructure and local strain fields in deeply embedded crystalline elements. This is achieved by placing an objective lens in the diffracted beam, giving a magnified projection image. So far, the method has been applied with a time resolution of milliseconds to hours. In this work, the feasibility of DFXM at the picosecond time scale using an X-ray free-electron laser source and a pump–probe scheme is considered. Thermomechanical strain-wave simulations are combined with geometrical optics and wavefront propagation optics to simulate DFXM images of phonon dynamics in a diamond single crystal. Using the specifications of the XCS instrument at the Linac Coherent Light Source as an example results in simulated DFXM images clearly showing the propagation of a strain wave.

Analytical Methods for Superresolution Dislocation Identification in Dark-Field X-ray Microscopy

“…The success of our position estimation algorithms applied to real DFXM images will depend on the fidelity of the simulation model and noise models. More recent implementations of the forward model have been developed for X-ray free electron laser experiments [28], and using wavefront propagation methods, which offer more accurate results (including dynamical diffraction), though at a higher computational cost [29]. As models of the imaging process are refined, we expect the utility of the numerical methods leveraging those models to increase.…”

Simultaneous Dark- and Bright-Field X-ray Microscopy at X-ray Free Electron Lasers

“…Given the complexity of the DFXM experiments, we detail a conversion from the synchrotron to XFEL systems here. For full understanding of how these coordinate systems convert to intensity and contrast mechanisms, see our previous work in 27,29,30 . The full microscope setup in this orientation is shown in Figure 1, with diffraction in the horizontal scattering geometry, as we used at XFELs.…”

“…The experiment used a channel-cut Si monochromator to reduce the bandwidth to ∆E/E ∼ 10 −4 , and a divergence of 1.1 × 1.1µrad 2 . A monochromatic beam with a stable spectrum is essential for interpretable results from DFXM because fluctuations in the incident beam's photon energy change the d-spacing and orientation that are imaged by DFXM 29,30 . We discuss the tradeoffs for this in Section 3.5.…”

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

“…Simulations based on the propagation of coherent wavefronts are becoming an increasingly common tool for the development of X-ray diffraction imaging techniques, where they are regularly used to evaluate the viability of new methods (Pedersen et al, 2018;Holstad et al, 2022) and to investigate the effect of experimental errors (Shabalin et al, 2017;Carnis et al, 2019). Furthermore, by accurately predicting coherent interference, such simulation methods are particularly relevant given the recent arrival of highly coherent X-ray sources, such as fourth-generation synchrotrons and freeelectron lasers.…”

“…One often tries to avoid these dynamical effects [even if occasionally they are the subject of interest (Rodriguez-Fernandez et al, 2021)] by using highly deformed samples, small grains or relying on the 'weak beam approximation', i.e. measuring at the tails of the rocking curve (Shabalin et al, 2017;Holstad et al, 2022). However, in many cases dynamical effects are unavoidable and must be accounted for in the simulation framework by solving the Takagi-Taupin equations (TTEs): a set of coupled, first-order PDEs (partial differential equations) that, in general, must be integrated numerically (Takagi, 1962;Taupin, 1967).…”