  In this study we explore the possibility to use deep learning for the
reconstruction of phase images from 4D scanning transmission electron
microscopy (4D-STEM) data. The process can be divided into two main steps.
First, the complex electron wave function is recovered for a convergent beam
electron diffraction pattern (CBED) using a convolutional neural network (CNN).
Subsequently a corresponding patch of the phase object is recovered using the
phase object approximation (POA). Repeating this for each scan position in a
4D-STEM dataset and combining the patches by complex summation yields the full
phase object. Each patch is recovered from a kernel of 3x3 adjacent CBEDs only,
which eliminates common, large memory requirements and enables live processing
during an experiment. The machine learning pipeline, data generation and the
reconstruction algorithm are presented. We demonstrate that the CNN can
retrieve phase information beyond the aperture angle, enabling super-resolution
imaging. The image contrast formation is evaluated showing a dependence on
thickness and atomic column type. Columns containing light and heavy elements
can be imaged simultaneously and are distinguishable. The combination of
super-resolution, good noise robustness and intuitive image contrast
characteristics makes the approach unique among live imaging methods in
4D-STEM.
