Making the link between ADF and 4D STEM:Resolution,transfer and coherence

Steve Pennycook is a pioneer in the application of high-resolution scanning transmission electron microscopy(STEM)and in particular the use of annular dark-field(ADF)imaging.Here we show how a general framework for 4D STEM allows clear links to be made between ADF imaging and the emerging methods for reconstructing images from 4D STEM data sets.We show that both ADF imaging and ptychographical reconstruction can be thought of in terms of integrating over the overlap regions of diffracted discs in the detector plane.This approach allows the similarities in parts of their transfer functions to be understood,though we note that the transfer functions for ptychographic imaging cannot be used as a measure of information transfer.We also show that conditions of partial spatial and temporal coherence affect ADF imaging and ptychography similarly,showing that achromatic interference can always contribute to the image in both cases,leading to a robustness to partial temporal coherence that has enabled high-resolution imaging.