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Cabral et al. Microstructures 2023;3:2023040 https://dx.doi.org/10.20517/microstructures.2023.39 Page 9 of 17

additional orthogonal images can be included in the correction. By applying such programs, STEM images
free of artifacts resulting from sample drift or scanning distortions can be obtained for further
quantification.

Identifying positions of atomic columns
Material properties often result from complex relationships between chemical distribution and structural
distortions that occur at the atomic scale. To gain a better understanding of how these phenomena emerge
at the macroscale, it is crucial to comprehend the connection between atomic structure and material
properties. STEM imaging offers a valuable means of investigating both structure and chemistry at the
atomic scale with accuracy and precision. Thanks to advancements in instrumentation and the elimination
of artifacts in atomic resolution images, it is now possible to directly make accurate and reproducible
crystallographic measurements in real space . In the following sections, we will introduce several tools that
[75]
are available to extract and quantify useful information from atomic resolution images.

Before the widespread availability of aberration-corrected microscopes, advanced image analysis was mainly
conducted by specialized electron microscopy research groups. Manual identification of thousands of
atomic columns in atomic resolution images was a cumbersome and impractical process. As the technique
became more popular, efforts focused on developing tools for rapid analysis of multiple images. Various
[76]
approaches have been identified, including principal component analysis (PCA) and template
matching . These techniques are particularly effective for detailed analysis of materials at length scales
[77]
unattainable with other characterization methods. For example, in the case of a multiferroic BiFeO thin
3
film, initial guesses, followed by COM calculations, can determine the positions of cations and oxygen with
[76]
PCA, which can then be applied to extract information on atomic column shape . Combining this data
with STEM image simulations [78-80] reveals octahedral tilting at domain walls, providing parameters
applicable to theory. Such analyses are especially valuable for researchers investigating structure-property
relationships in material design.

Numerous tools now facilitate rapid quantitative analysis of atomic resolution images. These tools include
[81]
[82]
[83]
Atom Column Indexing (ACI) , Atomap , StatSTEM , CalAtom , and Oxygen octahedra picker .
[85]
[84]
Most of these programs offer freely available source code online and utilize popular engineering software,
such as MATLAB or Python. Additionally, software plugins such as DMPFIT can be installed on Digital
[86]
Micrograph for atom column fitting and analysis . These programs employ various algorithms to identify
and quantify atom column positions with sub-pixel precision. For example, ACI utilizes the image
processing toolbox of MATLAB for normalized cross-correlation, Gaussian template matching, and 2D
Gaussian fitting to determine column centers of mass, intensities, and shapes . ACI projects atom column
[81]
positions onto non-collinear reference vectors, assigning each column an (i, j) matrix index, facilitating
lattice analysis and quantitative calculations. In perovskite-structured oxides, matrix indices of atomic
columns allow direct comparison of nearest neighbor distances and intensities, providing insights into the
relationship between chemical distribution and structural distortion . Furthermore, direct analysis of
[87]
atom-atom distances enables strain mapping over large areas, replacing conventional methods such as
geometric phase analysis (GPA) or nanobeam electron diffraction [88-90] .

One of the best opportunities arising from recent developments in advanced electron microscope imaging
and analysis software is the detailed study of oxygen structure in piezoelectric materials with perovskite or
spinel structures. Many outstanding properties, such as antiferroelectricity, relaxor ferroelectricity, and
magnetoelectric properties, result from the interplay of polarization and chemical ordering, which are
evident in the tilting/distortion of oxygen octahedra [76,91-94] . While BF and ABF-STEM have been widely