Crystal structure retrieval by maximum entropy analysis of atomic resolution incoherent images

In this paper, we discuss the application of the maximum entropy method to atomic resolution Z-contrast images acquired in a scanning transmission electron microscope. Z-contrast is an incoherent imaging technique, and can be described as a convolution between an object function (the real-space map of the columnar scattering cross-section to high angles) and a point spread function (the effective electron probe). As such, we show that the technique is ideally suited to maximum entropy analysis which can, given an electron probe distribution, retrieve the 'most likely' Z-contrast object function. Using both simulated and experimentally acquired data, we explore the capabilities of maximum entropy analysis when applied to atomic resolution Z-contrast images, drawing conclusions on both the range of applicability of the technique and the nature of the retrieved crystal structures. Ultimately, we show the way in which the combination of Z-contrast imaging with maximum entropy analysis can be used to yield important information on unexpected atomic structures.