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

2025-11-10

AI Summary

To address the low accuracy and poor robustness of phase retrieval for thick specimens under dynamical scattering conditions in 4D-STEM, this paper proposes FlowTIE—a hybrid physics-informed and data-driven neural network framework. Its core innovation lies in a flow-based representation of phase gradients, wherein the Transport-of-Intensity Equation (TIE) is explicitly embedded into the network architecture to model nonlinear dynamical scattering effects; moreover, it seamlessly integrates with multislice propagation models. Evaluated on simulated crystallographic data, FlowTIE significantly outperforms conventional TIE-based and purely data-driven methods: it achieves ≥3.2 dB higher PSNR in phase reconstruction, accelerates computation by ≥5×, and exhibits superior adaptability to thick specimens. FlowTIE thus establishes a new paradigm for quantitative electron microscopy—delivering high robustness, physical interpretability, and quantitative phase recovery.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Intelligent Robots: Multimodal Perception & Sensor Fusion
• Computer Vision: Low Level & Physics-based Vision

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Search and Retrieval-Augmented AI: Retrieval-Augmented Generation (RAG) and multi-modal RAG
• Security and Privacy: Data transparency and provenance

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.

Problem

• Estimating phase gradients from 4D-STEM data
• Improving robustness under dynamical scattering conditions
• Integrating data-driven learning with physics-based priors

Innovation

• Neural network integrates Transport of Intensity Equation
• Flow-based representation models phase gradient
• Combines data-driven learning with physics priors