a slice thickness that is too thin, consider a simple example. The Fresnel propagator describes the propagation of electron waves in the z direction (the direction of the incident beam) in a solid: Where is the reciprocal lattice coordinate, z is the depth in the sample, and lambda is the wavelength of the electron wave (related to the wave vector by the relation ). Figure [fig:SliceThickness] shows vector diagram of the wave-fronts being diffracted by the atomic planes in the sample. In the case of the small-angle approximation ( 100 mRad) we can approximate the phase shift as . For 100 mRad the error is on the order of 0.5% since . For small angles this approximation holds regardless of how many slices there are, although choosing a greater than the lattice parameter (or half the lattice parameter in the case of perovskites) for a multislice simulation would result in missing atoms that should be in the crystal potential. Additional practical concerns are how to effectively include effects such as inelastic and diffuse scattering, quantized excitations (e.g. plasmons, phonons, excitons), etc. There was one code that took these things into consideration through a coherence function approach called Yet Another Multislice (YAMS), but the code is no longer available either for download or purchase. Available software There are several software packages available to perform multislice simulations of images. Among these is NCEMSS, NUMIS, MacTempas, and Kirkland . Other programs exist but unfortunately many have not been maintained (e.g. SHRLI81 by Mike O’Keefe of Lawrence Berkeley National Lab and Cerius2 of Accerlys). A brief chronology of multislice codes is given in Table 2, although this is by no means exhaustive. ACEM/JCSTEM This software is developed by Professor Earl Kirkland of Cornell University. This code is freely available as an interactive Java applet and as standalone code written in C/C++. The Java applet is ideal for a quick introduction and simulations under a basic incoherent linear imaging approximation. The ACEM code accompanies an excellent text of the same name by Kirkland which describes the background theory and computational techniques for simulating electron micrographs (including multislice) in detail. The main C/C++ routines use a command line interface (CLI) for automated batching of many simulation. The ACEM package also includes a graphical user interface that is more appropriate for beginners. The atomic scattering factors in ACEM are accurately characterized by a 12-parameter fit of Gaussians