Quantitative Analysis Of Transmission Electron Microscopy Images

Ferroelectric vortex refers to electric dipole moments with continuous rotation in nanostructures.If we consider using these structures to store data,theoretically their storage density is several orders of magnitude higher than the current technology of ferroelectric storage.Our group creatively used spherical aberration correction TEM with resolution better than 0.1nm and custom-built in situ TEM holder to study the behavior of the polar vortices under stress.However,because the average length of polarization vector is very short,it needs very good experience and takes a lot of time to observe the polarization vectors and lattice constants in TEM images directly.Therefore,it is important to process these images quantitatively,especially in batches.Because of the defect of TEM lens and the quality of sample,the shape of the atoms observed in TEM is never the perfect Gaussian-shaped,and the brightest pixel is not located in the center of the atom.Therefore,we need to use 2D-Gaussian curve fitting to determine the exact center position of every atoms.This paper is to complete these tasks through the self-designed algorithm.The algorithm in this paper is written in Python language.Based on the Open CV Library for computer vision and Sci Py Library for scientific computing,the accurate position of atoms can be quickly obtained through these two steps: "preliminary identification" and "accurate calculation".Specifically,in the "preliminary recognition" step,we apply several sort image enhancement technologies to make the atoms image clearer and more normal,and then separate the atoms from the background through adaptive segmentation method.At last,the method of contour recognition is adopted before we obtain the rough positions of all atoms.In the "accurate calculation" step.we look up for each atomic regions in the original TEM image according to those rough positions.Then,the pixel values in each small region are fitted with 2D-Gaussian curve by least square method,and finally the precise atomic position is obtained.In the latter part of the algorithm,we solve two quantitative problems of lattice constant distribution and polarization vector distribution.In cubic crystal,the lattice constant is equal to the length of each side of the lattice.Instead,the average of the distances between the atom and its four nearest neighbor is taken in order to reduce the random error.Electric polarization refers to the physical phenomenon that the center of positive point and the center of positive point do not coincide.In practical algorithm,we always take the smallest square formed by four adjacent cations as a cell,and then take the displacement of cation center relative to anion center in the cell as micro polarization vector.In the process of solving these two problems,we always use kd tree technology to accelerate the search of adjacent atoms.In addition,we evaluated the results of the two targets respectively,and compare them with the results of some wellaccepted algorithms.Besides,we estimate that the fitting error of the atomic position in our algorithm is within 0.9 pixels.In addition,we also completed a batch processing of a group of TEM images with a large difference in magnification,and the algorithm achieved good results for all.On the other hand,because the algorithm is based on the "recognition" to mark the atoms,so it has a good compatibility for images with dislocations or grain boundaries.