# Disentangling multiple scattering with deep learning: application to strain mapping from electron diffraction patterns

arXiv: https://arxiv.org/abs/2202.00204 · HTML: https://mlsanity.com/paper/2202.00204/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 85 references that are in the map.
- First posted on arXiv 1 Feb 2022.

## Builds on (most cited first, 3 of 3)

- [Review: Deep Learning in Electron Microscopy](https://mlsanity.com/paper/2009.08328/) (2020)
- [Identification of Crystal Symmetry from Noisy Diffraction Patterns by A Shape Analysis and Deep Learning](https://mlsanity.com/paper/2005.12476/) (2020)
- [Manifold Learning of Four-dimensional Scanning Transmission Electron Microscopy](https://mlsanity.com/paper/1811.00080/) (2018)

## Built on by (most cited first, 7 of 7)

- [Leveraging generative adversarial networks to create realistic scanning transmission electron microscopy images](https://mlsanity.com/paper/2301.07743/) (2023)
- [A robust synthetic data generation framework for machine learning in High-Resolution Transmission Electron Microscopy (HRTEM)](https://mlsanity.com/paper/2309.06122/) (2023)
- [A dynamic Bayesian optimized active recommender system for curiosity-driven Human-in-the-loop automated experiments](https://mlsanity.com/paper/2304.02484/) (2023)
- [Contrast transfer functions help quantify neural network out-of-distribution generalization in HRTEM](https://mlsanity.com/paper/2512.09067/) (2025)
- [Physics Informed Generative AI Enabling Labour Free Segmentation For Microscopy Analysis](https://mlsanity.com/paper/2602.01710/) (2026)
- [Mapping Order in Semicrystalline Polymers using Machine Learning of Nanobeam Electron Diffraction](https://mlsanity.com/paper/2607.16570/) (2026)
- [4DMulti: automated multicomponent identification at complex material interfaces](https://mlsanity.com/paper/2609.14348/) (2026)

## Abstract (arXiv)

Implementation of a fast, robust, and fully-automated pipeline for crystal structure determination and underlying strain mapping for crystalline materials is important for many technological applications. Scanning electron nanodiffraction offers a procedure for identifying and collecting strain maps with good accuracy and high spatial resolutions. However, the application of this technique is limited, particularly in thick samples where the electron beam can undergo multiple scattering, which introduces signal nonlinearities. Deep learning methods have the potential to invert these complex signals, but previous implementations are often trained only on specific crystal systems or a small subset of the crystal structure and microscope parameter phase space. In this study, we implement a Fourier space, complex-valued deep neural network called FCU-Net, to invert highly nonlinear electron diffraction patterns into the corresponding quantitative structure factor images. We trained the FCU-Net using over 200,000 unique simulated dynamical diffraction patterns which include many different combinations of crystal structures, orientations, thicknesses, microscope parameters, and common experimental artifacts. We evaluated the trained FCU-Net model against simulated and experimental 4D-STEM diffraction datasets, where it substantially out-performs conventional analysis methods. Our simulated diffraction pattern library, implementation of FCU-Net, and trained model weights are freely available in open source repositories, and can be adapted to many different diffraction measurement problems.