Parallel mode differential phase contrast in transmission electron microscopy, I: Theory and analysis

TL;DR

This paper introduces the parallel mode differential phase contrast (TEM-DPC) technique in transmission electron microscopy, providing a theoretical framework, analysis methodology, and software tools, and compares it to the transport-of-intensity equation (TIE) method, highlighting its advantages for in-situ studies of samples with structural contrast.

Contribution

The paper presents a new TEM-DPC method, analysis tools, and a comparison to TIE, expanding capabilities for in-situ magnetic and electrostatic field studies in electron microscopy.

Findings

TEM-DPC effectively quantifies phase gradients in samples with structural contrast.

Compared to TIE, TEM-DPC offers advantages in in-situ studies with complex contrast.

Software tools facilitate analysis and comparison of phase contrast methods.

Abstract

In Part I of this diptych, we outline the parallel mode of differential phase contrast (TEM-DPC), which uses real-space distortion of Fresnel images arising from electrostatic or magnetostatic fields to quantify the phase gradient of samples with some degree of structural contrast. We present an analysis methodology and the associated software tools for the TEM-DPC method and, using them together with numerical simulations, compare the technique to the widely used method of phase recovery based on the transport-of-intensity equation (TIE), thereby highlighting the relative advantages and limitations of each. The TEM-DPC technique is particularly suitable for \textit{in-situ} studies of samples with significant structural contrast and, as such, complements the TIE method since structural contrast usually hinders the latter, but is an essential feature that enables the former. In Part II of this work, we apply the theory and methodology presented to the analysis of experimental data to gain insight into two-dimensional magnetic phase transitions.