A system and methods for characterizing an inspected object on the basis of attenuation between identified regions of scattering and a plurality of detectors. An incident beam of substantially monochromatic penetrating radiation is generated by a source, which may be a radioactive source. The incident beam is characterized by a propagation axis and a source energy. Radiation scattered by the object is detected by means of a plurality of detector elements disposed about the beam of penetrating radiation, each detector element generating a detector signal characterizing a detected energy of scattered radiation. The detector signal provides for determining a displacement for each scattering point of the object relative to a fiducial position on the propagation axis of the incident beam, based upon the detected energy of the scattered radiation. By calculating the attenuation of penetrating radiation between pairs of scattering voxels, 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 material characteristics.