The present paper is motivated by the demand from material sciences to reconstruct crystalline structures given through their images under high resolution transmission electron microscopy (HRTEM) in a certain limited number of directions. In particular, [31] and [22] show how a quantitative analysis of images from high resolution transmission electron microscopy can be used to determine the number of atoms on atomic columns in certain directions; see Sects. 2 and 3. Mathematically, this leads to the problem of reconstructing finite lattice sets from certain of their marginal sums; see Sect. 4.     «

The present paper is motivated by the demand from material sciences to reconstruct crystalline structures given through their images under high resolution transmission electron microscopy (HRTEM) in a certain limited number of directions. In particular, [31] and [22] show how a quantitative analysis of images from high resolution transmission electron microscopy can be used to determine the number of atoms on atomic columns in certain directions; see Sects. 2 and 3. Mathematically, this leads t...     »