Analysis of HR-STEM theory for thin specimen

•A compact mathematical model of BF and DF HR-STEM for thin samples is derived.•This description is nonlinear due to the (well-known) nonlinearity of STEM imaging.•A STEM image is described by two terms, effectively imaging two different objects.•For the first time we combine BF and DF STEM in one formula without using the WPA.•Physical interpretation is obtained without simulation of the STEM scanning process.

A compact mathematical model of the STEM imaging process including bright field (BF) and dark field (DF) is derived. This description is valid for thin samples, does not rely on the weak phase approximation and does not require time-consuming simulation of the scanning process. It is well-known that STEM imaging is a nonlinear technique and therefore cannot be described in terms of a sample-independent linear contrast transfer function (CTF). In this work we derive a nonlinear description showing that a STEM image can in fact be described with two terms. Both terms are cross-correlations between a function that is independent of the sample and a function that depends only on the sample. The latter two can be seen as two different objects. These objects directly correspond to two specific cases: the weak phase approximation (WPA) and annular dark field (ADF) imaging, which are known from the literature. We clarify the need for recognizing and understanding what the object is of any particular STEM technique. The model was validated using simulated STEM images and an excellent agreement as well as a reduction in computation time of 3 orders of magnitude was found.