Multiple scattering in low-energy electron holography

Abstract

The theory of the low-energy electron point source (LEEPS) microscope is reformulated in matrix form to readily account for multiple scattering. An algorithm is developed for the storage of the structure matrix and an iterative method is used to solve the matrix equation for the structure factor. Examples of small and large clusters of atoms are given to compare single and multiple scattering. A Kirchho 2Helmholtz transform is used for the reconstruction. We ®nd that in some cases the multiple scattering is too strong and reconstruction is not possible. We give examples which show that, even when multiple scattering is important, one can still obtain reconstructions that reveal the atomic structure both along and lateral to the optical axis. We also compare our results with those found in LEED. #

Multiple vs. single scattering in low energy electron holography

“…We examined, in ref. 13, the convergence properties of this equation for a large number of examples. We found, in general, that the series converges, and to the correct solution (see below) for "large" clusters only if L = 0.…”

“…If the cluster of atoms has some spatial symmetries then M will assume block form. We investigated this symmetry in our previous work [13]. We gave a simple example showing the symmetry and we developed an algorithm for storing only the distinct elements of the matrix M. By exploiting the symmetry and storing only the distinct elements of the matrix, it was our intention to find a quick method of solving for F .…”

“…(For details, see ref. 13.) In most cases of interest, it turned out that the iterative method was actually faster than using an alternative method wherein only distinct elements were stored (see ref.…”

“…In most cases of interest, it turned out that the iterative method was actually faster than using an alternative method wherein only distinct elements were stored (see ref. 13). This proves to be the case again in this work; the straightforward iteration procedure produces sufficient convergence.…”

“…In a recent work [13], we investigated the implications of multiple scattering. In particular, we compared the quality of the reconstructed images for multiple scattering vs. the approximation of single scattering.…”