title: Optimal experimental design for nano-particle atom-counting from high-resolution STEM images.
abstract: In the present paper, the principles of detection theory are used to quantify the probability of error for atom-counting from high resolution scanning transmission electron microscopy (HR STEM) 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 for the probability of error. We show that for very thin objects LAADF is optimal and that for thicker objects the optimal inner detector angle increases.
authors.affiliation: Electron Microscopy for Materials Science (EMAT), University of Antwerp, Groenenborgerlaan 171, B-2020 Antwerp, Belgium.
authors.forename: A
authors.initials: A
authors.lastname: De Backer
authors.affiliation: Electron Microscopy for Materials Science (EMAT), University of Antwerp, Groenenborgerlaan 171, B-2020 Antwerp, Belgium.
authors.forename: A
authors.initials: A
authors.lastname: De Wael
authors.affiliation: Electron Microscopy for Materials Science (EMAT), University of Antwerp, Groenenborgerlaan 171, B-2020 Antwerp, Belgium.
authors.forename: J
authors.initials: J
authors.lastname: Gonnissen
authors.affiliation: Electron Microscopy for Materials Science (EMAT), University of Antwerp, Groenenborgerlaan 171, B-2020 Antwerp, Belgium. Electronic address: sandra.vanaert@uantwerpen.be.
authors.forename: S
authors.initials: S
authors.lastname: Van Aert
keywords: Data processing/image processing; Electron microscope design and characterisation; High-resolution scanning transmission electron microscopy (HR STEM); Quantitative ADF STEM