Abstract: A type of tomography is described, wherein occupancy of lattice sites in a microscopic sample of crystalline material is predicted. An electron beam is projected through the sample, at a specific angle, causing discernible spots in a detector, such as photographic film. Each spot corresponds to a row of atoms. The intensity of each spot indicates the number of atoms in the row, and the number is called a "line count." Projecting the electron beam at specific additional angles produces additional line counts. From all the line counts, a set of equations is derived. Each variable in the equations corresponds to a lattice site in the material. A solution to the equations is found by linear programming techniques, thus assigning a value to each variable. Each value indicates the probability of occupancy of a respective lattice site.