Abstract: By combining statistical parameter estimation and model-order selection using a Bayesian framework, the maximum a posteriori (MAP) probability rule is proposed in this chapter as an objective and quantitative method to detect atom columns from high-resolution scanning transmission electron microscopy (HRSTEM) images. The validity and usefulness of this approach is demonstrated to both simulated and experimental annular dark-field (ADF) STEM images, but also to simultaneously acquired annular bright-field (ABF) and ADF STEM image data.

Abstract: An efficient model-based estimation algorithm is introduced to quantify the atomic column positions and intensities from atomic-resolution (scanning) transmission electron microscopy ((S)TEM) images. This algorithm uses the least squares estimator on image segments containing individual columns fully accounting for overlap between neighboring columns, enabling the analysis of a large field of view. To provide end-users with this well-established quantification method, a user friendly program, StatSTEM, is developed which is freely available under a GNU public license. In this chapter, this efficient algorithm is applied to three different nanostructures for which the analysis of a large field of view is required.

Abstract: The maximum a posteriori (MAP) probability rule for atom column detection can also be used as a tool to evaluate the relation between scanning transmission electron microscopy (STEM) image quality and atom detectability. In this chapter, a new image-quality measure is proposed that correlates well with atom detectability, namely the integrated contrast-to-noise ratio (ICNR). Furthermore, the working principle of the MAP probability rule is described in detail showing a close relation to the principles of model-selection methods.

Abstract: In this chapter, the principles of detection theory are used to quantify the probability of error for atom counting from high-resolution scanning transmission electron microscopy (HRSTEM) images. Binary and multiple hypothesis testing have been investigated in order to determine the limits to the precision with which the number of atoms in a projected atomic column can be estimated. The probability of error has been calculated when using STEM images, scattering cross-sections or peak intensities as a criterion to count atoms. Based on this analysis, we conclude that scattering cross-sections perform almost equally well as images and perform better than peak intensities. Furthermore, the optimal STEM detector design can be derived for atom counting using the expression of the probability of error. We show that for very thin objects the low-angle annular dark-field (LAADF) regime is optimal and that for thicker objects the optimal inner detector angle increases.

Abstract: A small sample tilt away from a main zone axis orientation results in an elongation of the atomic columns in ADF STEM images. An often posed research question is therefore whether the ADF STEM image intensities of tilted nanomaterials should be quantified using a parametric imaging model consisting of elliptical rather than the currently used symmetrical peaks. To this purpose, simulated ADF STEM images corresponding to different amounts of sample tilt are studied using a parametric imaging model that consists of superimposed 2D elliptical Gaussian peaks on the one hand and symmetrical Gaussian peaks on the other hand. We investigate the quantification of structural parameters such as atomic column positions and scattering cross sections using both parametric imaging models. In this manner, we quantitatively study what can be gained from this elliptical model for quantitative ADF STEM, despite the increased parameter space and computational effort. Although a qualitative improvement can be achieved, no significant quantitative improvement in the estimated structure parameters is achieved by the elliptical model as compared to the symmetrical model. The decrease in scattering cross sections with increasing sample tilt is even identical for both types of parametric imaging models. This impedes direct comparison with zone axis image simulations. Nonetheless, we demonstrate how reliable atom-counting can still be achieved in the presence of small sample tilt.

Abstract: We introduce a Bayesian genetic algorithm for reconstructing atomic models of monotype crystalline nanoparticles from a single projection using Z-contrast imaging. The number of atoms in a projected atomic column obtained from annular dark field scanning transmission electron microscopy images serves as an input for the initial three-dimensional model. The algorithm minimizes the energy of the structure while utilizing a priori information about the finite precision of the atom-counting results and neighbor-mass relations. The results show promising prospects for obtaining reliable reconstructions of beam-sensitive nanoparticles during dynamical processes from images acquired with sufficiently low incident electron doses.

Abstract: This paper investigates the possible benefits for counting atoms of different chemical nature when analysing multiple 2D scanning transmission electron microscopy (STEM) images resulting from independent annular dark field (ADF) detector regimes. To reach this goal, the principles of statistical detection theory are used to quantify the probability of error when determining the number of atoms in atomic columns consisting of multiple types of elements. In order to apply this theory, atom-counting is formulated as a statistical hypothesis test, where each hypothesis corresponds to a specific number of atoms of each atom type in an atomic column. The probability of error, which is limited by the unavoidable presence of electron counting noise, can then be computed from scattering-cross sections extracted from multiple ADF STEM images. Minimisation of the probability of error as a function of the inner and outer angles of a specified number of independent ADF collection regimes results in optimal experimental designs. Based on simulations of spherical Au@Ag and Au@Pt core–shell nanoparticles, we investigate how the combination of two non-overlapping detector regimes helps to improve the probability of error when unscrambling two types of atoms. In particular, the combination of a narrow low angle ADF detector with a detector formed by the remaining annular collection regime is found to be optimal. The benefit is more significant if the atomic number Z difference becomes larger. In
addition, we show the benefit of subdividing the detector regime into three collection areas for heterogeneous nanostructures based on a structure consisting of three types of elements, e.g., a mixture of Au, Ag and Al atoms. Finally, these results are compared with the probability of error resulting when one would ultimately use a pixelated 4D STEM detector and how this could help to further reduce the incident electron dose.

Abstract: Advanced electron microscopy techniques, including scanning electron microscopes (SEM), scanning transmission electron microscopes (STEM), and transmission electron microscopes (TEM), have revolutionized imaging capabilities. However, achieving high-quality experimental images remains a challenge due to various distortions stemming from the instrumentation and external factors. These distortions, introduced at different stages of imaging, hinder the extraction of reliable quantitative insights. In this paper, we will discuss the main sources of distortion in TEM and S(T)EM images, develop models to describe them, and propose a method to correct these distortions using a convolutional neural network. We validate the effectiveness of our method on a range of simulated and experimental images, demonstrating its ability to significantly enhance the signal-to-noise ratio. This improvement leads to a more reliable extraction of quantitative structural information from the images. In summary, our findings offer a robust framework to enhance the quality of electron microscopy images, which in turn supports progress in structural analysis and quantification in materials science and biology.

Abstract: To understand the structure–property relationship of nanostructures, reliably quantifying parameters, such as the number of atoms along the projection direction, is important. Advanced statistical methodologies have made it possible to count the number of atoms for monotype crystalline nanoparticles from a single ADF STEM image. Recent developments enable one to simultaneously acquire multiple ADF STEM images. Here, we present an extended statistics-based method for atom counting from a combination of multiple statistically independent ADF STEM images reconstructed from non-overlapping annular detector collection regions which improves the accuracy and allows one to retrieve precise atom-counts, especially for images acquired with low electron doses and multiple element structures.

Abstract: Microplasmas can be used for a wide range of technological applications and to improve the understanding of fundamental physics. Scanning electron microscopy, on the other hand, provides insights into the sample morphology and chemistry of materials from the mm‐ down to the nm‐scale. Combining both would provide direct insight into plasma‐sample interactions in real‐time and at high spatial resolution. Up till now, very few attempts in this direction have been made, and significant challenges remain. This work presents a stable direct current glow discharge microplasma setup built inside a scanning electron microscope. The experimental setup is capable of real‐time in situ imaging of the sample evolution during plasma operation and it demonstrates localized sputtering and sample oxidation. Further, the experimental parameters such as varying gas mixtures, electrode polarity, and field strength are explored and experimental<italic>V</italic>–<italic>I</italic>curves under various conditions are provided. These results demonstrate the capabilities of this setup in potential investigations of plasma physics, plasma‐surface interactions, and materials science and its practical applications. The presented setup shows the potential to have several technological applications, for example, to locally modify the sample surface (e.g., local oxidation and ion implantation for nanotechnology applications) on the µm‐scale.

Abstract: Electron tomography is essential for investigating the three-dimensional (3D) structure of nanomaterials. However, many of these materials, such as metal-organic frameworks (MOFs), are extremely sensitive to electron radiation, making it difficult to acquire a series of projection images for electron tomography without inducing electron-beam damage. Another significant challenge is the high contrast in high-angle annular dark field scanning transmission electron microscopy that can be expected for nanocomposites composed of a metal nanoparticle and an MOF. This strong contrast leads to so-called metal artifacts in the 3D reconstruction. To overcome these limitations, we here present low-dose electron tomography based on four-dimensional scanning transmission electron microscopy (4D-STEM) data sets, collected using an ultrafast and highly sensitive direct electron detector. As a proof of concept, we demonstrate the applicability of the method for an Au nanostar embedded in a ZIF-8 MOF, which is of great interest for applications in various fields, including drug delivery.

Abstract: The present contribution gives a review of recent quantification work of atom displacements, atom site occupations and level of crystallinity in various systems and based on aberration corrected HR(S)TEM images. Depending on the case studied, picometer range precisions for individual distances can be obtained, boundary widths at the unit cell level determined or statistical evolutions of fractions of the ordered areas calculated. In all of these cases, these quantitative measures imply new routes for the applications of the respective materials.