Comparison of Two Simulation Methods in Electron Crystallography: BW Method and a Modified Direct Product Method of Scattering Matrix

In this paper, a modified direct product method of scattering matrix (DPSM) was presented and the calculation formula was derived as follows: ϕ(z)=∑n1n!(Mz)nϕ(0) and ϕ(z+εj)=∑n1n!(Mεj)nϕ(z), where M is the scattering matrix of which the dimension can be reduced by 'Bethe potential method' drastically and therefore the calculation speed can be increased tremendously without losing accuracy very much. The results calculated with the DPSM method are in almost exact agreement with those calculated with BW method. However, the calculation speed for the modified DPSM method is approximately three times faster than that for the BW method. Furthermore, the DPSM is suitable for computing all types of matrices without requiring symmetry or conjugate symmetry.