Determination of three-dimensional atomic positions from tomographic reconstruction using ensemble empirical mode decomposition

Abstract

Tomographic reconstruction from a tilt series of electron micrographs has raised great interest in materials, chemical, and condensed matters science because of its capability of revealing 3D local atomic structures within nanomaterials. Previous breakthroughs have demonstrated that the positions of individual atoms can not only be visualized but also determined by combining a scanning transmission electron microscope with a high-angle annular dark-field detector, equally sloped tomography, and the filtering/denoising method. However, the filtering/denoising approach—whether imposed on 2D projections or 3D reconstruction—raises concerns regarding the robustness of image processing, the accuracy of atomic positions, and the artificial atoms introduced during filtering. In this article, we report a general method that overcomes these limitations. By removing unphysical oscillations in 2D projections through ensemble empirical mode decomposition and applying a standard Wiener filter to the 3D reconstruction, we are able to determine atomic structures with higher accuracy.