Abstract text (incl. figure legends and references)

Differential phase contrast (DPC) in scanning transmission electron microscopy (STEM) allows the visualization and quantification of electric and magnetic fields. In combination with state-of-the-art C_s-correction, it is even possible to map the projected electric field distribution and the corresponding charge density with subatomic resolution [1]. The DPC method is based on the measurement of transferred momenta which are imposed on the incident electron beam by the Coulomb interaction with the electrostatic potentials of the specimen at each pixel of the scan. The transferred momentum is closely linked to phase differentials within the electron wave and measurable as a lateral change of the center of mass of the intensity distribution in the detector plane [1]. This change can be determined using a position sensitive detector, such as a segmented or pixelated detector. However, to obtain quantitative information, substantial and careful post-processing including precise calibration and removal of machine related image artefacts need to be conducted.

Here we report on the development of a software enabling microscopists to readily do a quantitative analysis of DPC measurements including removal of various image artefacts, reduction of image noises and precise determination of atomic column positions.

The software can be executed as a stand-alone version for post-processing and as an "in-line" tool during the specimen analysis, enabling the prompt correction of misalignments. All images (dark-field image, images of all detector segments, constructed (annular) bright-field images) are saved in a single project file, in which all calculated maps, the image information such as calibration and acceleration voltage, as well as a history of processing steps are stored. This allows for a simple handling of data and facilitates collaboration. To calculate quantitative maps, the toolbox uses dedicated calibration files which can be tailored for the microscope settings (camera length, accelerating voltage, etc.) used during the measurement. One of these optimizations performable with the DPC-Toolbox is the correction of rotation of the deflection direction. In addition, the calculation of the scattergram, which is a 2D histogram of the transferred momentum, and a subsequent correction of the beam centering is implemented. Especially the scattergram is an excellent tool to detect possible image artifacts arising from e.g. wrong centering of the beam, lens aberrations and dynamical diffraction effects ("in-line") during the analysis [2]. Furthermore, a background signal, which results from a scanning of the beam in the detector plane and is typically observed on microscopes without descanning coils, can be drastically reduced in post-processing. Further functions of the DPC-Toolbox include noise reductions using rigid and non-rigid image registration algorithms, determination of atomic column position by fitting Gaussian functions to the intensity of individual atomic columns in dark-field images, characterization of magnetic domain walls and determination of magnetic domain sizes. Moreover, the software includes a recipe function to correct and analyze a series of DPC images and thus facilitates a fast processing of DPC data. The software is made freely available by contacting the authors.

[1] K. Müller-Caspary et al., Ultramicroscopy 178 (2017): 62-80.

[2] J. Bürger et al., Ultramicroscopy 219 (2020): 113118.