High-level algorithm prototyping: An example extending the TVR-DART algorithm

Operator Discretization Library (ODL) is an open-source Python library for prototyping reconstruction methods for inverse problems, and ASTRA is a high-performance Matlab/Python toolbox for large-scale tomographic reconstruction. The paper demonstrates the feasibility of combining ODL with ASTRA to prototype complex reconstruction methods for discrete tomography. As a case in point, we consider the total-variation regularized discrete algebraic reconstruction technique (TVR-DART). TVR-DART assumes that the object to be imaged consists of a limited number of distinct materials. The ODL/ASTRA implementation of this algorithm makes use of standardized building blocks, that can be combined in a plug-and-play manner. Thus, this implementation of TVR-DART can easily be adapted to account for application specific aspects, such as various noise statistics that come with different imaging modalities

Three-dimensional visualization and characterization of polymeric self-assemblies by Transmission Electron Microtomography

Self-assembling structures and their dynamical processes in polymeric systems have been investigated using three-dimensional transmission electron microscopy (3D-TEM). Block copolymers (BCPs) self-assemble into nanoscale periodic structures called microphase-separated structures, a deep understanding of which is important for creating nanomaterials with superior physical properties, such as high-performance membranes with well-defined pore size and high-density data storage media. Because microphase-separated structures have become increasingly complicated with advances in precision polymerization, characterizing these complex morphologies is becoming increasingly difficult. Thus, microscopes capable of obtaining 3D images are required. In this article, we demonstrate that 3D-TEM is an essential tool for studying BCP nanostructures, especially those self-assembled during dynamical processes and under confined conditions.The first example is a dynamical process called order-order transitions (OOTs). Upon changing temperature or pressure or applying an external field, such as a shear flow or electric field, BCP nanostructures transform from one type of structure to another. The OOTs are examined by freezing the specimens in the middle of the OOT and then observing the boundary structures between the preexisting and newly formed nanostructures in three-dimensions. In an OOT between the bicontinuous double gyroid and hexagonally packed cylindrical structures, two different types of epitaxial phase transition paths are found. Interestingly, the paths depend on the direction of the OOT. The second example is BCP self-assemblies under confinement that have been examined by 3D-TEM. A variety of intriguing and very complicated 3D morphologies can be formed even from the BCPs that self-assemble into simple nanostructures, such as lamellar and cylindrical structures in the bulk (in free space).Although 3D-TEM is becoming more frequently used for detailed morphological investigations, it is generally used to study static nanostructures. Although OOTs are dynamical processes, the actual experiment is done in the static state, through a detailed morphological study of a snapshot taken during the OOT. Developing time-dependent nanoscale 3D imaging has become a hot topic. Here, the two main problems preventing the development of in situ electron tomography for polymer materials are addressed. First, the staining protocol often used to enhance contrast for electrons is replaced by a new contrast enhancement based on chemical differences between polymers. In this case, no staining is necessary. Second, a new 3D reconstruction algorithm allows us to obtain a high-contrast, quantitative 3D image from fewer projections than is required for the conventional algorithm to achieve similar contrast, reducing the number of projections and thus the electron beam dose. Combini

In-situ STEM imaging of growth and phase change of individual CuAlX precipitates in Al alloy

Age-hardening in Al alloys has been used for over a century to improve its mechanical properties. However, the lack of direct observation limits our understanding of the dynamic nature of the evolution of nanoprecipitates during age-hardening. Using in-situ (scanning) transmission electron microscopy (S/TEM) while heating an Al-Cu alloy, we were able to follow the growth of individual nanoprecipitates at atomic scale. The heat treatments carried out at 140, 160, 180 and 200 °C reveal a temperature dependence on the kinetics of precipitation and three kinds of interactions of nano-precipitates. These are precipitate-matrix, precipitate-dislocation, and precipitate-precipitate interactions. The diffusion of Cu and Al during these interactions, results in diffusion-controlled individual precipitate growth, an accelerated growth when interactions with dislocations occur and a size dependent precipitate-precipitate interaction: growth and shrinkage. Precipitates can grow and shrink at opposite ends at the same time resulting in an effective displacement. Furthermore, the evolution of the crystal structure within an individual nanoprecipiate, specifically the mechanism of formation of the strengthening phase, θ′, during heat-treatment is elucidated by following the same precipitate through its intermediate stages for the first time using in-situ S/TEM studies

Automated discrete electron tomography – Towards routine high-fidelity reconstruction of nanomaterials

Electron tomography is an essential imaging technique for the investigation of morphology and 3D structure of nanomaterials. This method, however, suffers from well-known missing wedge artifacts due to a restricted tilt range, which limits the objectiveness, repeatability and efficiency of quantitative structural analysis. Discrete tomography represents one of the promising reconstruction techniques for materials science, potentially capable of delivering higher fidelity reconstructions by exploiting the prior knowledge of the limited number of material compositions in a specimen. However, the application of discrete tomography to practical datasets remains a difficult task due to the underlying challenging mathematical problem. In practice, it is often hard to obtain consistent reconstructions from experimental datasets. In addition, numerous parameters need to be tuned manually, which can lead to bias and non-repeatability. In this paper, we present the application of a new iterative reconstruction technique, named TVR-DART, for discrete electron tomography. The technique is capable of consistently delivering reconstructions with significantly reduced missing wedge artifacts for a variety of challenging data and imaging conditions, and can automatically estimate its key parameters. We describe the principles of the technique and apply it to datasets from three different types of samples acquired under diverse imaging modes. By further reducing the available tilt range and number of projections, we show that the proposed technique can still produce consistent reconstructions with minimized missing wedge artifacts. This new development promises to provide the electron microscopy community with an easy-to-use and robust tool for high-fidelity 3D characterization of nanomaterials

Prospects of three-dimensional microstructural analysis using discrete tomography

In electron tomography, three-dimensional datasets are reconstructed with various reconstruction algorithms. The accuracy and requirements on the projection geometry depend on kind of algorithms used for reconstruction. In this report, we discuss the comparison between the filtered back-projection (FBP) technique, most commonly used algorithm, and recently developed algorithm such as discrete algebraic reconstruction technique (DART). A hexagonally packed cylindrical structure was used as a model for such comparison. DART successfully reproduced the model even at the geometry where the model was poorly reconstructed by FBP. The influence of the maximum tilt angle to the quality of reconstructed image was also investigated. Reasonable quality of reconstruction has been obtained in a limited angular range by DART, while FBP generate only qualitative images