Theoretical framework of statistical noise in scanning transmission electron microscopy

Statistical noise, or shot noise, dominates experimental image quality in scanning transmission electron microscopy because efficiencies of recent detectors are close to ideal. We establish a general framework for the statistical noise taking into account two random processes in the electron incidence and the electron scattering. Using this framework, in terms of signal-to-noise ratio, we evaluate several STEM coherent imaging techniques: annular bright field, enhanced annular bright field, differential phase contrast, and ptychography and show that ptychography is the most efficient imaging for weak phase objects. Moreover, we find that normalizing annular-bright-field image by total electron count in the bright field significantly suppress the noise.