Iterative reconstruction algorithms are becoming increasingly important in electron tomography of biological samples. These algorithms, however, impose major computational demands. Parallelization must be employed to maintain acceptable running times. Graphics Processing Units (GPUs) have been demonstrated to be highly cost-effective for carrying out these computations with a high degree of parallelism. In a recent paper by Xu et al.[1], a GPU implementation strategy was presented that obtains a speedup of an order of magnitude over a previously proposed GPU-based electron tomography implementation. In this technical note, we demonstrate that by making alternative design decisions in the GPU implementation, an additional speedup can be obtained, again of an order of magnitude. By carefully considering memory access locality when dividing the workload among blocks of threads, the GPU's cache is used more efficiently, making more effective use of the available memory bandwidth.Keywords: Electron Tomography, Reconstruction, GPU Recently, iterative algebraic methods, such as ART and SIRT, have gained popularity in the electron tomography community due to their flexibility with respect to the geometric parameters of the tilt series, and their ability to handle noisy projection data. The use of algebraic reconstruction methods imposes major computational demands. Depending on the number of iterations, reconstructing a large 3D volume with a sequential implementation can easily take days on a normal PC. This obstacle can be largely overcome by parallelizing the computations, in particular the projection and backprojection steps. Graphics Processing Units (GPUs) have recently emerged as powerful parallel processors for general-purpose computations. Their architecture allows operations to be performed on a large number of data elements simultaneously.Several algorithmic strategies have already been proposed for implementing algebraic methods for electron tomography on the GPU. In [2], it was demonstrated by Castaño-Diez et al. that at that time, a GPU implementation of the SIRT algorithm could achieve similar performance to a CPU implementation running on a medium sized cluster. Xu et al. recently proposed a different implementation strategy [1] that leads to a speedup of an order of magnitude compared to the results from [2]. They attribute this speedup to improvements in three categories: minimizing synchronization overhead, encouraging latency hiding, and exploiting RGBA channel parallelism. The first two design goals are interdependent and cannot be optimized separately. In this technical note, we argue that by exploiting data locality more effectively, the runtime of the projection and back projection operations can be substantially reduced, even though the required number of thread synchronization steps will increase. We demonstrate that a significant speedup can be gained in this manner. Exploiting data localityThe Graphics Processing Unit (GPU) is well suited for carrying out the computations involved in ...

Colloidal core-shell semiconductor nanocrystals form an important class of optoelectronic materials, in which the exciton wave functions can be tailored by the atomic configuration of the core, the interfacial layers, and the shell. Here, we provide a trustful 3D characterization at the atomic scale of a free-standing PbSe(core)-CdSe(shell) nanocrystal by combining electron microscopy and discrete tomography. Our results yield unique insights for understanding the process of cation exchange, which is widely employed in the synthesis of core-shell nanocrystals. The study that we present is generally applicable to the broad range of colloidal heteronanocrystals that currently emerge as a new class of materials with technological importance.

Diffraction contrast tomography is a near‐field diffraction‐based imaging technique that provides high‐resolution grain maps of polycrystalline materials simultaneously with the orientation and average elastic strain tensor components of the individual grains with an accuracy of a few times 10−4. Recent improvements that have been introduced into the data analysis are described. The ability to process data from arbitrary detector positions allows for optimization of the experimental setup for higher spatial or strain resolution, including high Bragg angles (0 < 2θ < 180°). The geometry refinement, grain indexing and strain analysis are based on Friedel pairs of diffraction spots and can handle thousands of grains in single‐ or multiphase materials. The grain reconstruction is performed with a simultaneous iterative reconstruction technique using three‐dimensional oblique angle projections and GPU acceleration. The improvements are demonstrated with the following experimental examples: (1) uranium oxide mapped at high spatial resolution (300 nm voxel size); (2) combined grain mapping and section topography at high Bragg angles of an Al–Li alloy; (3) ferrite and austenite crystals in a dual‐phase steel; (4) grain mapping and elastic strains of a commercially pure titanium sample containing 1755 grains.

Electron tomography is a powerful imaging technique in electron microscopy that can be used to investigate the 3D structure of nanomaterials. At present, most reconstruction algorithms are based on either backprojection or algebraic reconstruction techniques (see, e.g. [1]). A drawback of these methods is that they require a large number of images (> 50-100) to obtain sufficient accuracy in the reconstructions. Even then, artifacts are often visible in the reconstructed volume, e.g. due to the limited tilt-range and tilt-step during data acquisition.Recently, new reconstruction algorithms have been developed in the context of Discrete tomography [2,3,4]. Discrete tomography focuses on the reconstruction of images that contain only a small, discrete set of gray values. In the context of electron tomography this corresponds directly to samples that consist only of a few different materials. If these materials are known in advance, this knowledge can be used by the reconstruction algorithm in addition to the tomographic projection data, which may yield a vast reduction in the number of projections that is required to compute an accurate reconstruction.Many challenges in materials science involve complex structured samples, which nevertheless consist only of a limited number of separated, well-defined materials. Using discrete tomography for such samples may have several advantages. Besides a reduction of the required number of projections and suppression of certain types of artifacts, a main advantage of discrete tomography is that the reconstruction is already segmented into the different materials. In contrast, if a conventional reconstruction algorithm is used, such as filtered backprojection or SIRT, the segmentation is often difficult and time consuming.As an example, we consider the 3D reconstruction of nanoparticles formed by doping of SiC with Er followed by high-temperature annealing [5,6]. Previous analysis showed that the sample mainly consists of ErSi 2 nanocrystals in a SiC matrix. The reconstructed image should be a binary image, consisting of only two gray values for the interior of the ErSi 2 nanocrystals and the surrounding SiC matrix (see Fig. 1, 2). Investigating the distribution and shape of such particles in 3D is of great interest to understand the formation and growth mechanism as well as the electronic properties of the nanocrystals.Preliminary results will be presented on the application of discrete tomography to the ErSi 2 /SiC example, in order to investigate the number of required projections, the segmentation capabilities and the ability to reduce the artifacts present with conventional reconstruction methods.

We demonstrate the ability to record a tomographic tilt series containing 3487 images in only 3.5 s by using a direct electron detector in a transmission electron microscope. The electron dose is lower by at least one order of magnitude when compared with that used to record a conventional tilt series of fewer than 100 images in 15–60 minutes and the overall signal-to-noise ratio is greater than 4. Our results, which are illustrated for an inorganic nanotube, are important for ultra-low-dose electron tomography of electron-beam-sensitive specimens and real-time dynamic electron tomography of nanoscale objects with sub-ms temporal resolution.

Discrete electron tomography is a new approach for three-dimensional reconstruction of nanoscale objects. The technique exploits prior knowledge of the object to be reconstructed, which results in an improvement of the quality of the reconstructions. Through the combination of conventional transmission electron microscopy and discrete electron tomography with a model-based approach, quantitative structure determination becomes possible. In the present work, this approach is used to unravel the building scheme of Zeotile-4, a silica material with two levels of structural order. The layer sequence of slab-shaped building units could be identified. Successive layers were found to be related by a rotation of 120 degrees, resulting in a hexagonal space group. The Zeotile-4 material is a demonstration of the concept of successive structuring of silica at two levels. At the first level, the colloid chemical properties of Silicalite-1 precursors are exploited to create building units with a slablike geometry. At the second level, the slablike units are tiled using a triblock copolymer to serve as a mesoscale structuring agent.

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