Abstract: Transmission electron microscopy (TEM) is a technique that uses an electron beam to analyze materials. This analysis is based on the interaction between the electron beam and the sample, such as photon emission and electron diffraction pattern, to name a few. Sample damage, however, also occurs when such interaction alters the structure of the sample. To ensure information from the undamaged material can be acquired, the electron expense to probe the material is thus limited. In this work, we propose efficient methods for acquiring and processing the information originating from the electron-sample interaction so that the study of the material and the conducting of the TEM experiment can be less hindered by the limited dose usage. In the first part of the work, the relationship between the scattering of the electron and the local physical property of the sample is studied. Based on this relationship, two reconstruction schemes are proposed capable of producing high-resolution images at low-dose conditions. Besides, the proposed reconstructions are not restricted to complete datasets but instead work on pieces of data, therefore allowing live feedback during data acquisition. Such feature of the methods allows the whole TEM experiment to be carried out under low dose conditions and thus further reduces possible beam damage on the studied material. In the second part of the work, we discuss our approach to modulating the electron beam and its benefits. An electrostatic device that can alter the wavefront of the passing electron wave is introduced and characterized. The beam-modulation ability is demonstrated by creating orthogonal beam sets, and applications that exploit the adaptability of the wave modulator are demonstrated with both simulation and experiments.

Abstract: In this chapter, a statistical model-based method to count the number of atoms of monotype crystalline nanostructures from high-resolution annular dark-field (ADF) scanning transmission electron microscopy (STEM) images is discussed in detail together with a thorough study on the possibilities and inherent limitations. We show that this method can be applied to nanocrystals of arbitrary shape, size, and atom type. The validity of the atom-counting results is confirmed by means of detailed image simulations and it is shown that the high sensitivity of our method enables us to count atoms with single atom sensitivity.

Abstract: This chapter provides an overview of statistical and quantitative methodologies that have pushed (scanning) transmission electron microscopy ((S)TEM) toward accurate and precise measurements of unknown structure parameters for understanding the relation between the structure of a material and its properties. Hereby, statistical parameter estimation theory has extensively been used which enabled not only measuring atomic column positions, but also quantifying the number of atoms, and detecting atomic columns as accurately and precisely as possible from experimental images. As a general conclusion, it can be stated that advanced statistical techniques are ideal tools to perform quantitative electron microscopy at the atomic scale. In the future, statistical methods will continue to be developed and novel quantification procedures will open up new possibilities for studying material structures at the atomic scale.

Abstract: In this chapter, the principles of statistical parameter estimation theory for a quantitative analysis of atomic-resolution electron microscopy images are introduced. Within this framework, electron microscopy images are described by a parametric statistical model. Here, parametric models are introduced for different types of electron microscopy images: reconstructed exit waves, annular dark-field (ADF) scanning transmission electron microscopy (STEM) images, and simultaneously acquired ADF and annular bright-field (ABF) STEM images. Furthermore, the Cramér-Rao lower bound (CRLB) is introduced, i.e. a theoretical lower bound on the variance of any unbiased estimator. This CRLB is used to quantify the precision of the structure parameters of interest, such as the atomic column positions and the integrated atomic column intensities.

Abstract: The idea of this Review is to introduce newly developed possibilities of advanced electron microscopy to the materials science community. Over the last decade, electron microscopy has evolved into a full analytical tool, able to provide atomic scale information on the position, nature, and even the valency atoms. This information is classically obtained in two dimensions (2D), but can now also be obtained in 3D. We show examples of applications in the field of nanoparticles and interfaces.

Abstract: The concept of resolution in high-resolution electron microscopy (HREM) is the power to resolve neighboring atoms. Since the resolution is related to the width of the point spread function of the microscope, it could in principle be determined from the image of a point object. However, in electron microscopy there are no ideal point objects. The smallest object is an individual atom. If the width of an atom is much smaller than the resolution of the microscope, this atom can still be considered as a point object. As the resolution of the microscope enters the sub-Å regime, information about the microscope is strongly entangled with the information about the atoms in HREM images. Therefore, we need to find an alternative method to determine the resolution in an object-independent way. In this work we propose to use the image wave of a crystalline object in zone axis orientation. Under this condition, the atoms of a column act as small lenses so that the electron beam channels through the atom column periodically. Because of this focusing, the image wave of the column can be much more peaked than the constituting atoms and can thus be a much more sensitive probe to measure the resolution. Our approach is to use the peakiness of the image wave of the atom column to determine the resolution. We will show that the resolution can be directly linked to the total curvature of the atom column wave. Moreover, we can then directly obtain the resolution of the microscope given that the contribution from the object is known, which is related to the bounding energy of the atom. The method is applied on an experimental CaTiO3 image wave.

Abstract: In the present paper, a statistical model-based method to count the number of atoms of monotype crystalline nanostructures from high resolution high-angle annular dark-field (HAADF) scanning transmission electron microscopy (STEM) images is discussed in detail together with a thorough study on the possibilities and inherent limitations. In order to count the number of atoms, it is assumed that the total scattered intensity scales with the number of atoms per atom column. These intensities are quantitatively determined using model-based statistical parameter estimation theory. The distribution describing the probability that intensity values are generated by atomic columns containing a specific number of atoms is inferred on the basis of the experimental scattered intensities. Finally, the number of atoms per atom column is quantified using this estimated probability distribution. The number of atom columns available in the observed STEM image, the number of components in the estimated probability distribution, the width of the components of the probability distribution, and the typical shape of a criterion to assess the number of components in the probability distribution directly affect the accuracy and precision with which the number of atoms in a particular atom column can be estimated. It is shown that single atom sensitivity is feasible taking the latter aspects into consideration.