In this work, a recently developed quantitative approach based on the principles of detection theory is used in order to determine the possibilities and limitations of High Resolution Scanning Transmission Electron Microscopy (HR STEM) and HR TEM for atom-counting. So far, HR STEM has been shown to be an appropriate imaging mode to count the number of atoms in a projected atomic column. Recently, it has been demonstrated that HR TEM, when using negative spherical aberration imaging, is suitable for atom-counting as well. The capabilities of both imaging techniques are investigated and compared using the probability of error as a criterion. It is shown that for the same incoming electron dose, HR STEM outperforms HR TEM under common practice standards, i.e. when the decision is based on the probability function of the peak intensities in HR TEM and of the scattering cross-sections in HR STEM. If the atom-counting decision is based on the joint probability function of the image pixel values, the dependence of all image pixel intensities as a function of thickness should be known accurately. Under this assumption, the probability of error may decrease significantly for atom-counting in HR TEM and may, in theory, become lower as compared to HR STEM under the predicted optimal experimental settings. However, the commonly used standard for atom-counting in HR STEM leads to a high performance and has been shown to work in practice.@en

In the present paper, the optimal detector design is investigated for both detecting and locating light atoms from high resolution scanning transmission electron microscopy (HR STEM) images. The principles of detection theory are used to quantify the probability of error for the detection of light atoms from HR STEM images. To determine the optimal experiment design for locating light atoms, use is made of the so-called Cramér–Rao Lower Bound (CRLB). It is investigated if a single optimal design can be found for both the detection and location problem of light atoms. Furthermore, the incoming electron dose is optimised for both research goals and it is shown that picometre range precision is feasible for the estimation of the atom positions when using an appropriate incoming electron dose under the optimal detector settings to detect light atoms.@en