Abstract
Accurate quantum mechanical scanning transmission electron microscopy image simulation methods such as the multislice method require computation times that are too large to use in applications in high-resolution materials imaging that require very large numbers of simulated images. However, higher-speed simulation methods based on linear imaging models, such as the convolution method, are often not accurate enough for use in these applications. We present a method that generates an image from the convolution of an object function and the probe intensity, and then uses a multivariate polynomial fit to a dataset of corresponding multislice and convolution images to correct it. We develop and validate this method using simulated images of Pt and Pt–Mo nanoparticles and find that for these systems, once the polynomial is fit, the method runs about six orders of magnitude faster than parallelized CPU implementations of the multislice method while achieving a 1 − R2 error of 0.010–0.015 and root-mean-square error/standard deviation of dataset being predicted of about 0.1 when compared to full multislice simulations.
Highlights
As the uses of scanning transmission electron microscopy (STEM) in applications of high-resolution materials imaging continue to expand, methods for simulating STEM images become increasingly important
We report pixel-wise cross validation (CV) fractional root-mean-square (RMS) error and CV 1 − R2 error, where R2 is the coefficient of determination between the predicted and multislice pixel intensities [34]
CV fractional RMS error results for image-based twofold cross validation are reported in Additional file 1: Section S2.1
Summary
As the uses of scanning transmission electron microscopy (STEM) in applications of high-resolution materials imaging continue to expand, methods for simulating STEM images become increasingly important. The simplest is the convolution method, an incoherent linear image model that convolves the probe point-spread function with simple atomic potentials for the specimen [14] This method assumes that there is no dynamic scattering and no interference between scattered and unscattered electrons [15]. The multislice method can require significant computation times, on the order of weeks of central processing unit (CPU) time [O(106 s/image), where we use O(X) to represent “on the order” of X] to simulate a typical STEM image [20]. With significant parallelization, this is not a major limitation when calculating just a few images.
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