# Phase Object Reconstruction for 4D-STEM using Deep Learning

arXiv: https://arxiv.org/abs/2202.12611 · HTML: https://mlsanity.com/paper/2202.12611/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Feb 2022.

## Built on by (most cited first, 3 of 3)

- [Improving Multislice Electron Ptychography with a Generative Prior](https://mlsanity.com/paper/2507.17800/) (2025)
- [Unsupervised Multi-Clustering and Decision-Making Strategies for 4D-STEM Orientation Mapping](https://mlsanity.com/paper/2503.06699/) (2025)
- [Zero-Shot Cross-Material Ptychographic Phase Reconstruction Using Deep Learning](https://mlsanity.com/paper/2609.13969/) (2026)

## Abstract (arXiv)

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.