Model-based deconvolution for particle analysis applied to a through-focus series of HAADF-STEM images

This paper presents an approach for determining the sizes and three-dimensional (3D) positions of nanoparticles from a through-focus series of high-angle annular dark-field scanning transmission electron microscopy images. By assuming spherical particles with uniform density, the sizes and 3D positions can be derived via Wiener deconvolution using a series of kernels prepared by the convolution of the 3D point spread function of the electron beam and the 3D density distribution of spheres with different radii. This process is referred to as a model-based deconvolution. Four 3D datasets with a volume size of 148 × 148 × 560 nm3 were obtained from the four sets of 256 high-angle annular dark-field scanning transmission electron microscopy images of 256 × 256 pixels taken from the same field of view under the through-focus condition. The 3D positions and radii of 14 particles in each 3D dataset were derived using the model-based deconvolution for ∼8 min. The observation errors of the 3D position were estimated as σx ≅ σy ≅ 0.3 nm and σz < 1.6 nm.