Mpfit: a robust method for fitting atomic resolution images with multiple Gaussian peaks

Greg Stone,Leixin Miao,Nasim Alem,Debangshu Mukherjee

doi:10.1186/s40679-020-0068-y

Abstract

The standard technique for sub-pixel estimation of atom positions from atomic resolution scanning transmission electron microscopy images relies on fitting intensity maxima or minima with a two-dimensional Gaussian function. While this is a widespread method of measurement, it can be error prone in images with non-zero aberrations, strong intensity differences between adjacent atoms or in situations where the neighboring atom positions approach the resolution limit of the microscope. Here we demonstrate mpfit, an atom finding algorithm that iteratively calculates a series of overlapping two-dimensional Gaussian functions to fit the experimental dataset and then subsequently uses a subset of the calculated Gaussian functions to perform sub-pixel refinement of atom positions. Based on both simulated and experimental datasets presented in this work, this approach gives lower errors when compared to the commonly used single Gaussian peak fitting approach and demonstrates increased robustness over a wider range of experimental conditions.

Highlights

The development of spherical aberration-correction for scanning transmission electron microscopy (STEM) imaging has been one of the biggest triumphs of electron microscopy over the past several decades, allowing the sub-ångström resolution imaging of crystal structures [1,2,3]
Such an imaging setup uses a ring shaped annular detector with the outer and inner detector collection circles centered along the microscope optic axis. Such a configuration will have an inner collection angle of approximately 85–90 mrad to capture only the incoherently scattered electrons, and is conventionally referred to as high angle annular dark field STEM (HAADF-STEM) imaging [5, 21]. This mode of imaging is referred to as dark field imaging since atom columns themselves are bright due to electrons preferentially scattering from atomic nuclei as a consequence of Rutherford scattering from proton–electron Coulombic forces [22, 23]
Fitting atom positions with Gaussians The best modern aberration-corrected microscopes can generate electron probes that are free of aberrations up to 30 mrad, which corresponds to beam diameters that are of the order of 0.5 Å, or 50 pm at 200 kV [8, 10]

Summary

Introduction

The development of spherical aberration-correction for scanning transmission electron microscopy (STEM) imaging has been one of the biggest triumphs of electron microscopy over the past several decades, allowing the sub-ångström resolution imaging of crystal structures [1,2,3]. While the Gaussian function fitting approach is an extraordinarily powerful technique, one noted shortcoming is that it assumes well-separated atoms with no overlap, or negligible aberrations in the beam itself—conditions that are only available under a certain limited set of imaging conditions [16, 17] Such an imaging setup uses a ring shaped annular detector with the outer and inner detector collection circles centered along the microscope optic axis. Such a configuration will have an inner collection angle of approximately 85–90 mrad to capture only the incoherently scattered electrons, and is conventionally referred to as high angle annular dark field STEM (HAADF-STEM) imaging [5, 21].

Methods

Results

Conclusion