In an instrument for reconstructing computerized tomograms utilizing penetrating radiation, typically X or gamma radiation, an apparatus and technique are disclosed for removing spectral artifacts and utilizing spectral effects to create output pictures which represent facsimilies of the distribution of molecules according to atomic number and electron density within the object being pictured. Combinations of these pictorial representations are also obtained. Reconstruction errors caused by panchromaticity in the radiation source are avoided. Attenuation within the object by means of photoelectric absorption, Compton scattering and Rayleigh scattering are isolated and analyzed separately. Techniques are disclosed for treating source beams which are arbitrarily thin or of a finite thickness. Measurements at two source spectra are performed either by means of different peak energy settings of the source, the use of a source input filter, or the utilization of detectors of different efficiencies or different response ranges, or a combination of any of the above. A statistical error analysis of the output picture is provided as a function of the statistical error in each of the two sets of measurements. A computerized fit using the least squares technique is made to establish parameters yielding analytical expressions for the various attenuation cross-sections. A calibration technique is disclosed which utilizes empirical measurements. A method for optimizing the measurement technique is disclosed. Finally, an analysis of the error in the waterbag technique is provided.