Developments in acquisition technology and a growing need for time-resolved experiments pose great computational challenges in tomography. In addition, access to reconstructions in real time is a highly demanded feature but has so far been out of reach. We show that by exploiting the mathematical properties of filtered backprojection-type methods, having access to real-time reconstructions of arbitrarily oriented slices becomes feasible. Furthermore, we present RECAST3D, software for visualization and on-demand reconstruction of slices. A user of RECAST3D can interactively shift and rotate slices in a GUI, while the software updates the slice in real time. For certain use cases, the possibility to study arbitrarily oriented slices in real time directly from the measured data provides sufficient visual and quantitative insight. Two such applications are discussed in this article.

The 3D spatial resolution, the material contrast and the evolution of the noise are analyzed in the reconstructed volume of a combined scanning transmission electron microscopy (HAADF-STEM) and energy dispersive x-ray spectroscopy (EDS) tomography experiment. Standard simultaneous iterative reconstruction technique and HAADF-EDS bimodal tomographic reconstruction are considered for the +/−90°tomography series of a pillar shaped sample embedding a full nanowire device. With a high number of iterations, a spatial resolution for both HAADF and EDS down to 5 nanometer can be reached for this volume. Best material's contrast and minimum noise are obtained for medium number of iterations. Improvement of the signal-tonoise and contrast can be obtained by filtering the EDS data while the spatial resolution is not impacted. A fast and reliable preparation methodology for rectangularly shaped pillar samples for tomography analysis is discussed.

Users of X-ray (micro-)CT in research environments often study many different types of objects, with many different research questions. For each new scan, the settings of the scan (number of angles, dose, cone angle) are chosen by the user, often based on how much time is available, the dose sensitivity of the sample, and geometrical characteristics of the particular CT-scanner that is used. The FDK algorithm is the most common reconstruction method used for circular cone-beam data. Its filter is typically chosen based on characteristics of the object, the scan parameters, and task-specific metrics. This imposes a problem for case-by-case research use, as selecting an optimal filter requires manual and subjective user choices as well as considerable expertise. In this paper we present a computationally efficient and automated method to compute an FDK-filter for a given measured projection dataset that is optimal with respect to an objectively defined quality criterion that is based on the difference between the measured projection data and the computed projections of the reconstructed volume. We show that for a variety of objects, scan settings (number of angles and noise levels), and tasks (porosity quantification, threshold-based segmentation), the FDK-filters computed by our approach yield accurate results in terms of several different metrics that are comparable to filters manually selected for the experiments.

Combined tilt- and focal series scanning transmission electron microscopy is a recently developed method to obtain nanoscale three-dimensional (3D) information of thin specimens. In this study, we formulate the forward projection in this acquisition scheme as a linear operator and prove that it is a generalization of the Ray transform for parallel illumination. We analytically derive the corresponding backprojection operator as the adjoint of the forward projection. We further demonstrate that the matched backprojection operator drastically improves the convergence rate of iterative 3D reconstruction compared to the case where a backprojection based on heuristic weighting is used. In addition, we show that the 3D reconstruction is of better quality.

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