Information in 4D-STEM: Where it is, and How to Use it

Contrast transfer mechanisms for electron scattering have been extensively studied in transmission electron microscopy. Here we revisit H. Rose's generalized contrast formalism from scattering theory to understand where information is encoded in four-dimensional scanning transmission electron microscopy (4D-STEM) data, and consequently identify new imaging modes that can also serve as crude but fast approximations to iterative ptychography. We show that for a defocused probe tilt correction and summation of the symmetric and antisymmetric scattering components within the bright-field disk - corresponding to tilt-corrected bright field (tcBF) and tilt-corrected differential phase contrast (tcDPC) respectively - enables aberration-corrected, bright-field phase contrast imaging (acBF) that makes maximal use of the 4D-STEM information under the weak phase object approximation (WPOA), highlighting the value of operating out of focus. Beyond the WPOA, we identify the contrast transfer from the interference between inelastic/plural scattering electrons, which show up as quadratic terms, and show that under overfocus conditions, contrast can be further enhanced at selected frequencies, similar to phase-contrast TEM imaging. There is also usable parallax information encoded in the dark-field region, as in the bright field, which we demonstrate by constructing a tilt-corrected dark-field image (tcDF) that sums up the incoherent scattering components and holds promise for depth sectioning of strong scatterers without having to perform a through-focal series. This framework generalizes phase (and amplitude) contrast theory in conventional/scanning transmission electron microscopy to 4D-STEM and provides analytical models and insights into full-field iterative ptychography, which blindly exploits all above contrast mechanisms.