FlowTIE: Flow-based Transport of Intensity Equation for Phase Gradient Estimation from 4D-STEM Data

TL;DR

FlowTIE is a neural network framework that combines physics-based TIE with flow-based phase gradient modeling to enhance phase reconstruction accuracy from 4D-STEM data, especially for thick specimens.

Contribution

FlowTIE introduces a novel integration of flow-based neural networks with the Transport of Intensity Equation for improved phase reconstruction in electron microscopy.

Findings

Improves phase reconstruction accuracy over classical methods.

Demonstrates robustness under dynamical scattering conditions.

Compatible with multislice thick specimen modeling.

Abstract

We introduce FlowTIE, a neural-network-based framework for phase reconstruction from 4D-Scanning Transmission Electron Microscopy (STEM) data, which integrates the Transport of Intensity Equation (TIE) with a flow-based representation of the phase gradient. This formulation allows the model to bridge data-driven learning with physics-based priors, improving robustness under dynamical scattering conditions for thick specimen. The validation on simulated datasets of crystalline materials, benchmarking to classical TIE and gradient-based optimization methods are presented. The results demonstrate that FlowTIE improves phase reconstruction accuracy, fast, and can be integrated with a thick specimen model, namely multislice method.