Abstract Calculated electron in-line holograms, for the low-energy electron point source (LEEPS) microscope and based on scattering theory, give reconstructions that exhibit atomic resolution perpendicular to the optical axis. The depth resolution is not as sharp, and spurious peaks also result. We investigate the possibility of obtaining overall atomic resolution in the reconstruction of LEEPS in-line holograms by using a tomographic approach. We examine a few object positions with displacements lateral to the optical axis. We inquire as to whether or not the reconstructions obtained from a small number of lateral tomographic holograms can be combined in a manner such that all spurious peaks are eliminated and only atomic peaks result. The experimental consequences of these inquiries are discussed.