Simulations of dislocation contrast in dark-field X-ray microscopy.

Dark-field X-ray microscopy (DFXM) is a full-field imaging technique that non-destructively maps the structure and local strain inside deeply embedded crystalline elements in three dimensions. In DFXM, an objective lens is placed along the diffracted beam to generate a magnified projection image of the local diffracted volume. This work explores contrast methods and optimizes the DFXM setup specifically for the case of mapping dislocations. Forward projections of detector images are generated using two complementary simulation tools based on geometrical optics and wavefront propagation, respectively. Weak and strong beam contrast and the mapping of strain components are studied. The feasibility of observing dislocations in a wall is elucidated as a function of the distance between neighbouring dislocations and the spatial resolution. Dislocation studies should be feasible with energy band widths of 10-2, of relevance for fourth-generation synchrotron and X-ray free-electron laser sources.

Non-imaging metasurface design for collimated beam shaping.

Non-imaging optical lenses can shape the light intensity from incoherent sources to a desired target intensity profile, which is important for applications in lighting, solar light concentration, and optical beam shaping. Their surface curvatures are designed to ensure optimal transfer of energy from the light source to the target. The performance of such lenses is directly linked to their asymmetric freeform surface curvature, which is challenging to manufacture. Metasurfaces can mimic any surface curvature without additional fabrication difficulty by imparting a spatially-dependent phase delay using optical antennas. As a result, metasurfaces are uniquely suited to realize non-imaging optics, but non-imaging design principles have not yet been established for metasurfaces. Here, we take an important step in connecting non-imaging optics and metasurface optics, by presenting a phase-design method for beam shaping based on the concept of optimal transport. We establish a theoretical framework that enables a collimated beam to be redistributed by a metasurface to a desired output intensity profile. The optimal transport formulation leads to metasurface phase profiles that transmit all energy from the incident beam to the output beam, resulting in an efficient beam shaping process. Through a variety of examples, we show that our approach accommodates a diverse range of different input and output intensity profiles. Last but not least, a full field simulation of a metasurface has been done to verify our phase-design framework.

Simulating dark-field X-ray microscopy images with wavefront propagation techniques.

Dark-field X-ray microscopy is a diffraction-based synchrotron imaging technique capable of imaging defects in the bulk of extended crystalline samples. Numerical simulations are presented of image formation in such a microscope using numerical integration of the dynamical Takagi-Taupin equations and wavefront propagation. The approach is validated by comparing simulated images with experimental data from a near-perfect single crystal of diamond containing a single stacking-fault defect in the illuminated volume.

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

Calculating dynamical diffraction patterns for X-ray diffraction imaging techniques requires numerical integration of the Takagi-Taupin equations. This is usually performed with a simple, second-order finite difference scheme on a sheared computational grid in which two of the axes are aligned with the wavevectors of the incident and scattered beams. This dictates, especially at low scattering angles, an oblique grid of uneven step sizes. Here a finite difference scheme is presented that carries out this integration in slab-shaped samples on an arbitrary orthogonal grid by implicitly utilizing Fourier interpolation. The scheme achieves the expected second-order convergence and a similar error to the traditional approach for similarly dense grids.

Fourier ptychographic dark field x-ray microscopy.

Dark-field x-ray microscopy (DFXM) is an x-ray imaging technique for mapping three-dimensional (3D) lattice strain and rotation in bulk crystalline materials. At present, these maps of local structural distortions are derived from the raw intensity images using an incoherent analysis framework. In this work, we describe a coherent, Fourier ptychographic approach that requires little change in terms of instrumentation and acquisition strategy, and may be implemented on existing DFXM instruments. We demonstrate the method experimentally and are able to achieve quantitative phase reconstructions of thin film samples and maps of the aberrations in the objective lens. The method holds particular promise for the characterization of crystalline materials containing weak structural contrast.