Direct 3D Tomographic Reconstruction and Phase-Retrieval of Far-Field Coherent Diffraction Patterns

We present an alternative numerical reconstruction algorithm for direct tomographic reconstruction of a sample refractive indices from the measured intensities of its far-field coherent diffraction patterns. We formulate the well-known phase-retrieval problem in ptychography in a tomographic framework which allows for simultaneous reconstruction of the illumination function and the sample refractive indices in three dimensions. Our iterative reconstruction algorithm is based on the Levenberg-Marquardt algorithm. We demonstrate the performance of our proposed method with simulation studies

X-ray ptychography on low-dimensional hard-condensed matter materials

Tailoring structural, chemical, and electronic (dis-)order in heterogeneous media is one of the transformative opportunities to enable new functionalities and sciences in energy and quantum materials. This endeavor requires elemental, chemical, and magnetic sensitivities at the nano/atomic scale in two- and three-dimensional space. Soft X-ray radiation and hard X-ray radiation provided by synchrotron facilities have emerged as standard characterization probes owing to their inherent element-specificity and high intensity. One of the most promising methods in view of sensitivity and spatial resolution is coherent diffraction imaging, namely, X-ray ptychography, which is envisioned to take on the dominance of electron imaging techniques offering with atomic resolution in the age of diffraction limited light sources. In this review, we discuss the current research examples of far-field diffraction-based X-ray ptychography on two-dimensional and three-dimensional semiconductors, ferroelectrics, and ferromagnets and their blooming future as a mainstream tool for materials sciences

Three-dimensional magnetization structures revealed with X-ray vector nanotomography

In soft ferromagnetic materials, the smoothly varying magnetization leads to the formation of fundamental patterns such as domains, vortices and domain walls<sup>1</sup>. These have been studied extensively in thin films of thicknesses up to around 200 nanometres, in which the magnetization is accessible with current transmission imaging methods that make use of electrons or soft X-rays. In thicker samples, however, in which the magnetization structure varies throughout the thickness and is intrinsically three dimensional, determining the complex magnetic structure directly still represents a challenge<sup>1, 3</sup>. We have developed hard-X-ray vector nanotomography with which to determine the three-dimensional magnetic configuration at the nanoscale within micrometre-sized samples. We imaged the structure of the magnetization within a soft magnetic pillar of diameter 5 micrometres with a spatial resolution of 100 nanometres and, within the bulk, observed a complex magnetic configuration that consists of vortices and antivortices that form cross-tie walls and vortex walls along intersecting planes. At the intersections of these structures, magnetic singularities—Bloch points—occur. These were predicted more than fifty years ago<sup>4</sup> but have so far not been directly observed. Here we image the three-dimensional magnetic structure in the vicinity of the Bloch points, which until now has been accessible only through micromagnetic simulations, and identify two possible magnetization configurations: a circulating magnetization structure<sup>5</sup> and a twisted state that appears to correspond to an ‘anti-Bloch point’. Our imaging method enables the nanoscale study of topological magnetic structures<sup>6</sup> in systems with sizes of the order of tens of micrometres. Knowledge of internal nanomagnetic textures is critical for understanding macroscopic magnetic properties and for designing bulk magnets for technological applications<sup>7</sup>

Fourier ptychography: current applications and future promises

Traditional imaging systems exhibit a well-known trade-off between the resolution and the field of view of their captured images. Typical cameras and microscopes can either “zoom in” and image at high-resolution, or they can “zoom out” to see a larger area at lower resolution, but can rarely achieve both effects simultaneously. In this review, we present details about a relatively new procedure termed Fourier ptychography (FP), which addresses the above trade-off to produce gigapixel-scale images without requiring any moving parts. To accomplish this, FP captures multiple low-resolution, large field-of-view images and computationally combines them in the Fourier domain into a high-resolution, large field-of-view result. Here, we present details about the various implementations of FP and highlight its demonstrated advantages to date, such as aberration recovery, phase imaging, and 3D tomographic reconstruction, to name a few. After providing some basics about FP, we list important details for successful experimental implementation, discuss its relationship with other computational imaging techniques, and point to the latest advances in the field while highlighting persisting challenges

Multimodal x-ray and electron microscopy of the Allende meteorite.

Multimodal microscopy that combines complementary nanoscale imaging techniques is critical for extracting comprehensive chemical, structural, and functional information, particularly for heterogeneous samples. X-ray microscopy can achieve high-resolution imaging of bulk materials with chemical, magnetic, electronic, and bond orientation contrast, while electron microscopy provides atomic-scale spatial resolution with quantitative elemental composition. Here, we combine x-ray ptychography and scanning transmission x-ray spectromicroscopy with three-dimensional energy-dispersive spectroscopy and electron tomography to perform structural and chemical mapping of an Allende meteorite particle with 15-nm spatial resolution. We use textural and quantitative elemental information to infer the mineral composition and discuss potential processes that occurred before or after accretion. We anticipate that correlative x-ray and electron microscopy overcome the limitations of individual imaging modalities and open up a route to future multiscale nondestructive microscopies of complex functional materials and biological systems