Abstract: In CSCT, by using a fan-shaped primary beam, combined with a 2D detector, single-slice transmission tomography and scatter tomography can be measured simultaneously. In such a System blurred scatter functions are measured unless a monochromatic source of radiation is used. According to the present invention, an energy resolving 1D or 2D detector System is proposed, which, in combination with a tomographic reconstruction, provides a good spectral resolution, even with a polychromatic primary beam. Furthermore, according to an aspect of the present invention, only one energy resolving detector-line is required to achieve the fall spectrum. Advantageous applications of the system and method according to the present invention are in medical imaging and material analysis, such as baggage inspection.