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.Comment: 25 pages, 11 figures, 1 tabl