Linear imaging theory for differential phase contrast and other phase imaging modes in scanning transmission electron microscopy.

We propose a linear imaging theory for differential phase contrast under the weak-phase-weak-amplitude object approximation. Contrast transfer functions are defined for thin and thick weak objects, and they successfully describe several imaging characteristics of differential phase contrast. We discuss the defocus dependence of the contrast for several examples: atomic resolution, a p-n junction, a heterointerface, and grain boundaries. Understanding the imaging characteristics helps in adjusting aberrations in DPC STEM.