Multislice - Background

Background

The mapping from a crystal structure to its image or diffraction pattern has been relatively well understood and documented. However, the reverse mapping from electron micrograph images to the crystal structure is generally more complicated. The fact that the images are two dimensional projections of three dimensional crystal structurse it makes it tedious to compare these projections to all plausible crystal structures. Hence, the use of numerical techniques in simulating results for different crystal structure is integral to the field of electron microscopy and crystallography. Several software packages exist to simulate electron micrographs.

There are two widely used simulation techniques that exist in literature: the Bloch wave method and the multislice method. In this paper, we will primarily focus on the multislice method. Furthermore, most of the packages that exist implement the multislice algorithm along with genetic algorithm to determine the image as well as address quantitatively aspects such as phase contract and diffraction contrast. The aim of these software packages is to solve the crystal potential. Once the crystal potential is known, the mapping to the images and diffraction pattern becomes a straightforward exercise.

The first description of what is now known as the multislice method was given in the classic paper by Cowley and Moodie . In this work, the authors describe scattering of electrons using a physical optics approach without invoking quantum mechanical arguments. We will present another derivation shortly that does treat electrons quantum mechanically but invokes several simplifying approximations.