Using convergence and spread-of-focus parameters to model spatial and temporal coherence in HRTEM image simulations

Abstract

In all HRTEM images, the incident electron beam suffers from the effects of limited spatial and temporal coherence. These effects produce a smearing of the image, and provide the ultimate limits as to how high a spatial frequency can be transferred to the image (i.e. resolution). The effect of partial temporal coherence is manifested as a spread of focus, and that of partial spatial coherence as incident beam convergence. The effects of partial coherence can be included in HRTEM image simulations by summing images in real space, or by applying an appropriate transmission cross-coefficient (TCC) when computing the image intensity spectrum in reciprocal space. Figure 1 shows a method of including the effects of incident beam convergence by real-space summation. The degree of convergence is estimated by measuring the spot size in the experimental diffraction pattern (a). Each spot in the diffraction pattern is sub-sampled (b), and a series of images is computed at incident beam angles appropriately sampling the convergence cone.