The introduction of spherical aberration corrector to the scanning transmission electron microscopy (STEM) has enabled the observation of local crystallographic structure at the atomic scale. Beyond an ordinary visualization of atomic structures, now the quantitative analysis of atomic positions e.g., strain, polarization, and oxygen octahedral tilt, have garnered an increasing interest. However, these structural transitions generally occur at several picometer scale, which is a sub-pixel level information in the STEM images. Thus, a precise acquisition of atomic position has become the principal issue of the structural analysis.
In the STEM image, atomic positions are obtained through the intensity value of the atomic columns; hence the noise reduction, segmentation of atomic column, and fitting atomic position are the key parts. Although various algorithms have been reported including the techniques for each of these steps and comprehensive programs, an exact performance comparison has not been made and it is not known which algorithm is an optimal solution. Therefore, we report a method to improve image quality and to find atomic columns dedicated to STEM images, and benchmark with other reported techniques.
Fig.1: Algorithm for STEM analysis. Entire workflow of precise atomic peak analysis in parallelly acquired HAADF–STEM and ABF–STEM images of La-doped SrTiO3 along the zone axis of . Preprocessing steps reduce noise and enhance the peak contrast. Segmentation steps achieve the coordinate information of atomic columns.
Fig. 1 shows the flowchart of our proposed method. The proposed method consists of three steps: preprocessing step, segmentation step and analyzation step. In the preprocessing step, the BM3D method is performed to remove the noise in the STEM image. Then, background stains and bias are removed through morphological filtering. In the segmentation step, the preprocessed STEM image is binarized through K-means clustering method. And then, atomic positions are detected by center of mass of each binarized atom. The atomic position information obtained in the previous step is used in the analyzation step. This step provides various analysis information such as displacement, polarization, bucking angle, and c/a ratio.
Fig. 2: Benchmarks for accuracy of atomic position acquisition. a Accuracy of acquired atomic positions from our proposed method, depending on the input noise. Error bars indicate the standard deviations of errors. Benchmark results for the accuracy test from b our proposed method, c 9-point 2D quadratic fitting, d multiple ellipse fitting, and e 2D Gaussian fitting. Each colored dot denotes the deviation from the ground truth. The top and right graphs present the normal distribution of errors in each x- and y-component. The black lines indicate the standard deviations of errors.
We conducted the accuracy test on the atomic positions acquired from simulation images with various noise levels and our proposed method shows a sub-pixel accuracy in average, even with the high Poisson noise (Fig. 2a). The same evaluation was conducted on other reported programs (Fig. 2b-e) and only 2D Gaussian fitting with PCA noise reduction (Fig. 2e) had comparable performance with our proposed method (Fig. 2b), while the former had a bias on y-axis.