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: 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.