Iterative Phase Retrieval Algorithms for Scanning Transmission Electron Microscopy

Georgios Varnavides⁺, Stephanie M. Ribet,⁺ Steven E. Zeltmann, Yue Yu, Benjamin H. Savitzky, Vinayak P. Dravid, Mary C. Scott, Colin Ophus
Posted on Publisher's version


Scanning transmission electron microscopy (STEM) has been extensively used for imaging complex materials down to atomic resolution. The most commonly employed STEM imaging modality of annular dark field produces easily-interpretable contrast, but is dose-inefficient and produces little to no contrast for light elements and weakly-scattering samples. An alternative is to use phase contrast STEM imaging, enabled by high speed detectors able to record full images of a diffracted STEM probe over a grid of scan positions. Phase contrast imaging in STEM is highly dose-efficient, able to measure the structure of beam-sensitive materials and even 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 using a consistent framework to allow for easier comparison. This presentation of STEM phase retrieval methods will make these methods more approachable, reproducible and more readily adoptable for many classes of samples.