Multiple vs. single scattering in low energy electron holography

The theory of the low energy electron point source (LEEPS) microscope is presented in matrix form to account for multiple scattering. An iterative method is used to solve the matrix equation for the structure factor. An algorithm is developed for the storage and use of only the dominant elements of the structure matrix; this allows for the study of considerably large clusters. Examples of large clusters of atoms are studied to compare single scattering (SS) and multiple scattering (MS). A Kirchhoff-Helmholtz transform is used for the reconstruction. We report results where SS and MS give essentially the same reconstructions, and other results where SS and MS reconstructions are in severe disagreement. We find, for example, that SS and MS give virtually the same reconstruction along the optical axis for clusters that are "short" lateral to, but "long" in the direction of, the optical axis. In contrast, we also find that SS and MS give vastly different reconstructions lateral to the optical axis for clusters that are "wide" lateral to, and "thin" in the direction of, the optical axis. Some other results are also reported. Implications for further theoretical work, and for experimental LEEPS microscopy, are discussed.