Methods for characterizing an inspected object on the basis of attenuation determined from pair-wise illuminated voxels. A beam of penetrating radiation characterized by a propagation direction and an energy distribution is scanned across an object, while scatter detectors with collimated fields-of-view detect radiation scattered by each voxel of the inspected object that is intercepted by the incident beam of penetrating radiation. By calculating the attenuation of penetrating radiation between pairs of voxels of incidence of the incident beam, a tomographic image is obtained characterizing the three-dimensional distribution of attenuation in the object of one or more energies of penetrating radiation, and thus of various material characteristics.