High resolution functional imaging through Lorentz transmission electron microscopy and differentiable programming

TL;DR

This paper introduces a differentiable programming approach for phase retrieval in Lorentz transmission electron microscopy, enabling high-resolution functional imaging by accurately reconstructing electron wave phases from defocused images.

Contribution

The authors develop a novel differentiable programming method for phase retrieval that outperforms traditional techniques in resolution and accuracy, adaptable to various electron microscopy applications.

Findings

Robust phase retrieval method surpasses transport of intensity equation

Achieves higher spatial resolution and phase accuracy

Easily adaptable to other phase retrieval tasks

Abstract

Lorentz transmission electron microscopy is a unique characterization technique that enables the simultaneous imaging of both the microstructure and functional properties of materials at high spatial resolution. The quantitative information such as magnetization and electric potentials is carried by the phase of the electron wave, and is lost during imaging. In order to understand the local interactions and develop structure-property relationships, it is necessary to retrieve the complete wavefunction of the electron wave, which requires solving for the phase shift of the electrons (phase retrieval). Here we have developed a method based on differentiable programming to solve the inverse problem of phase retrieval, using a series of defocused microscope images. We show that our method is robust and can outperform widely used \textit{transport of intensity equation} in terms of spatial resolution and accuracy of the retrieved phase under same electron dose conditions. Furthermore, our method shares the same basic structure as advanced machine learning algorithms, and is easily adaptable to various other forms of phase retrieval in electron microscopy.