Iterative Phase Retrieval Algorithms for Scanning Transmission Electron Microscopy

TL;DR

This paper reviews and compares three iterative phase retrieval algorithms for STEM imaging, highlighting their theoretical foundations, implementation, and performance on simulated and real data to improve dose efficiency and contrast for sensitive samples.

Contribution

It provides a comprehensive analysis of three phase retrieval methods in STEM, including theoretical background, implementation details, and experimental validation.

Findings

All three methods improve dose efficiency compared to traditional imaging.

Each method has distinct strengths and weaknesses in information transfer.

Experimental results demonstrate practical applicability of the algorithms.

Abstract

Scanning transmission electron microscopy (STEM) has been extensively used for imaging complex materials down to atomic resolution. The most commonly employed STEM modality, annular dark-field imaging, produces easily-interpretable contrast, but is dose-inefficient and produces little to no discernible contrast for light elements and weakly-scattering samples. An alternative is to use STEM phase retrieval imaging, enabled by high speed detectors able to record full images of a diffracted STEM probe over a grid of scan positions. Phase retrieval imaging in STEM is highly dose-efficient, enabling the measurement of the structure of beam-sensitive materials such as biological samples. Here, we comprehensively describe the theoretical background, algorithmic implementation details, and perform both simulated and experimental tests for three iterative phase retrieval STEM methods: focused-probe differential phase contrast, defocused-probe parallax imaging, and a generalized ptychographic gradient descent method implemented in two and three dimensions. We discuss the strengths and weaknesses of each of these approaches by comparing the transfer of information using analytical expressions and numerical results for a white-noise model. This presentation of STEM phase retrieval methods aims to make these methods more approachable, reproducible, and more readily adoptable for many classes of samples.