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In this study we explore the possibility to use deep learning for thereconstruction of phase images from 4D scanning transmission electronmicroscopy (4D-STEM) data. The process can be divided into two main steps.First, the complex electron wave function is recovered for a convergent beamelectron diffraction pattern (CBED) using a convolutional neural network (CNN).Subsequently a corresponding patch of the phase object is recovered using thephase object approximation (POA). Repeating this for each scan position in a4D-STEM dataset and combining the patches by complex summation yields the fullphase object. Each patch is recovered from a kernel of 3x3 adjacent CBEDs only,which eliminates common, large memory requirements and enables live processingduring an experiment. The machine learning pipeline, data generation and thereconstruction algorithm are presented. We demonstrate that the CNN canretrieve phase information beyond the aperture angle, enabling super-resolutionimaging. The image contrast formation is evaluated showing a dependence onthickness and atomic column type. Columns containing light and heavy elementscan be imaged simultaneously and are distinguishable. The combination ofsuper-resolution, good noise robustness and intuitive image contrastcharacteristics makes the approach unique among live imaging methods in4D-STEM.

Phase Object Reconstruction for 4D-STEM using Deep Learning