Geometric reconstruction methods for electron tomography

Electron tomography is becoming an increasingly important tool in materials science for studying the three-dimensional morphologies and chemical compositions of nanostructures. The image quality obtained by many current algorithms is seriously affected by the problems of missing wedge artefacts and nonlinear projection intensities due to diffraction effects. The former refers to the fact that data cannot be acquired over the full $180^\circ$ tilt range; the latter implies that for some orientations, crystalline structures can show strong contrast changes. To overcome these problems we introduce and discuss several algorithms from the mathematical fields of geometric and discrete tomography. The algorithms incorporate geometric prior knowledge (mainly convexity and homogeneity), which also in principle considerably reduces the number of tilt angles required. Results are discussed for the reconstruction of an InAs nanowire

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>

Multimodal Differential Emission Measure in the Solar Corona

The Atmospheric Imaging Assembly (AIA) telescope on board the Solar Dynamics Observatory (SDO) provides coronal EUV imaging over a broader temperature sensitivity range than the previous generations of instruments (EUVI, EIT, and TRACE). Differential emission measure tomography (DEMT) of the solar corona based on AIA data is presented here for the first time. The main product of DEMT is the three-dimensional (3D) distribution of the local differential emission measure (LDEM). While in previous studies, based on EIT or EUVI data, there were 3 available EUV bands, with a sensitivity range $\sim 0.60 - 2.70$ MK, the present study is based on the 4 cooler AIA bands (aimed at studying the quiet sun), sensitive to the range $\sim 0.55 - 3.75$ MK. The AIA filters allow exploration of new parametric LDEM models. Since DEMT is better suited for lower activity periods, we use data from Carrington Rotation 2099, when the Sun was in its most quiescent state during the AIA mission. Also, we validate the parametric LDEM inversion technique by applying it to standard bi-dimensional (2D) differential emission measure (DEM) analysis on sets of simultaneous AIA images, and comparing the results with DEM curves obtained using other methods. Our study reveals a ubiquitous bimodal LDEM distribution in the quiet diffuse corona, which is stronger for denser regions. We argue that the nanoflare heating scenario is less likely to explain these results, and that alternative mechanisms, such as wave dissipation appear better supported by our results.Comment: 52 pages, 18 figure

GENFIRE: A generalized Fourier iterative reconstruction algorithm for high-resolution 3D imaging

Tomography has made a radical impact on diverse fields ranging from the study of 3D atomic arrangements in matter to the study of human health in medicine. Despite its very diverse applications, the core of tomography remains the same, that is, a mathematical method must be implemented to reconstruct the 3D structure of an object from a number of 2D projections. In many scientific applications, however, the number of projections that can be measured is limited due to geometric constraints, tolerable radiation dose and/or acquisition speed. Thus it becomes an important problem to obtain the best-possible reconstruction from a limited number of projections. Here, we present the mathematical implementation of a tomographic algorithm, termed GENeralized Fourier Iterative REconstruction (GENFIRE). By iterating between real and reciprocal space, GENFIRE searches for a global solution that is concurrently consistent with the measured data and general physical constraints. The algorithm requires minimal human intervention and also incorporates angular refinement to reduce the tilt angle error. We demonstrate that GENFIRE can produce superior results relative to several other popular tomographic reconstruction techniques by numerical simulations, and by experimentally by reconstructing the 3D structure of a porous material and a frozen-hydrated marine cyanobacterium. Equipped with a graphical user interface, GENFIRE is freely available from our website and is expected to find broad applications across different disciplines.Comment: 18 pages, 6 figure

Splitting times of doubly quantized vortices in dilute Bose-Einstein condensates

Recently, the splitting of a topologically created doubly quantized vortex into two singly quantized vortices was experimentally investigated in dilute atomic cigar-shaped Bose-Einstein condensates [Y. Shin et al., Phys. Rev. Lett. 93, 160406 (2004)]. In particular, the dependency of the splitting time on the peak particle density was studied. We present results of theoretical simulations which closely mimic the experimental set-up. Contrary to previous theoretical studies, claiming that thermal excitations are the essential mechanism in initiating the splitting, we show that the combination of gravitational sag and time dependency of the trapping potential alone suffices to split the doubly quantized vortex in time scales which are in good agreement with the experiments. We also study the dynamics of the resulting singly quantized vortices which typically intertwine--especially, a peculiar vortex chain structure appears for certain parameter values.Comment: 5 pages, 5 figure

Estimation of the hydraulic parameters of unsaturated samples by electrical resistivity tomography

In situ and laboratory experiments have shown that electrical resistivity tomography (ERT) is an effective tool to image transient phenomena in soils. However, its application in quantifying soil hydraulic parameters has been limited. In this study, experiments of water inflow in unsaturated soil samples were conducted in an oedometer equipped to perform three-dimensional electrical measurements. Reconstructions of the electrical conductivity at different times confirmed the usefulness of ERT for monitoring the evolution of water content. The tomographic reconstructions were subsequently used in conjunction with a finite-element simulation to infer the water retention curve and the unsaturated hydraulic conductivity. The parameters estimated with ERT agree satisfactorily with those determined using established techniques, hence the proposed approach shows good potential for relatively fast characterisations. Similar experiments could be carried out on site to study the hydraulic behaviour of the entire soil deposi