A comparison of the column approximation and the Howie-Basinski approach in simulations of TEM images under weak-beam diffraction conditions

The usual formulation of the dynamical theory of electron diffraction developed by Howie and Whelan [ 1] makes use of the so-called column approximation (CA). This approximation may fail in weak-beam diffraction contrast imaging if the thickness of the foil is relatively large and we are interested in reproducing fine details of the observed experimental images [2, 3]. The approach of Howie and Basinski [4] avoids the CA. In this paper we describe a new numerical algorithm for solving the Howie-Basinski (HB) equations. WB images of small dislocation loops have been simulated using a code based on this algorithm, enabling comparison of predictions made with and without the column approximation.