Image Simulation

To understand the contrast of experimental HRTEM images, to test whether the resolution of the TEM in used is sufficient to solve determine a structural problem or to determine the experimental conditions under which an image was recorded are typical questions that are tackled by image simulation. Although all kinds of TEM images and electron diffraction pattern can be calculated, image simulation is especially important for interpreting HRTEM images. The direct interpretation of the image contrast is difficult because of strong electron-matter interaction (dynamical behaviour), the dependence on thickness of the crystal and on the CTF of the TEM (defocus) and the imperfect imaging system (aberrations like C_s, C_c).

In general, the simulation of HRTEM images involves the following steps:
1. modeling the crystal or defect structure
2. calculation of the propagation of the incident electron wave through the crystal
3. calculation of the transfer of the scattered wave by the optical system of the TEM
4. comparison with the experimental micrographs

Multislice Method
The most versatile approach is the multislice method developed by Cowley and Moodie already in 1957. It applicable to both perfect and defective crystals of large unit cell parameters. Such a calculation is done as follows (cf. scheme):
1. the crystal potential is devided in slices and then projected on a plane perpendicular to the direction of observation
2. incoming plane electron wave interacts with the first plane; calculation of beams
3. propagation of the (scattered) beams through vacuum
4. interaction of the beams with the next plane

For finding a good agreement between experimental HRTEM image and the simulation (e.g. Nb₄W₁₃O₄₇), reasonable values for thickness, as determined by the number of slices, and defocus are calculated to get so-called focus-thickness maps. Here, P. Stadelmann's versatile EMS program has been used for image simulation.