Testing the accuracy of the two-dimensional object model in HAADF STEM

In high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) the two-dimensional (2D) object-function approximation and image convolution model is often used to describe the recorded image data from on-axis crystalline samples. In this model the sample, represented by an object function with sharp peaks at the atomic column positions, is convolved with the 2D point spread function (PSF) of the focussed STEM illumination. In this work the validity of the assumption that the object can be considered as 2D is evaluated experimentally through the use of HAADF-STEM focal-series from MgO smoke cubes. The intensity of laterally resolved image-information is evaluated using Fourier transforms and is tracked with respect to defocus. The experimental results are compared with the expected depth resolution capabilities of simulated STEM probes to yield the normalised or 'apparent thickness' of the samples. The 2D object-function and image convolution models are found to hold for sample thicknesses of up to 250 nm. As the 2D object model holds true for each individual frame in a recorded focal series, we can hence express the focal-series as a whole as the convolution of a 2D object function with a 3D probe function with implications for both the diagnosis of remnant aberrations and also image reconstruction.