3D reconstructions can be calculated from grayscale X-ray images taken at different angular positions of an X-ray source and detector rotatable about a common axis. In the present case, X-ray radiation is applied to the object to be imaged such that one half of the X-ray detector receives radiation which differs in one characteristic from the radiation received by the second half of the detector via the object. A kind of dual-energy imaging can then be carried out in a single pass through the angular positions, enabling two 3D reconstructions to be generated simultaneously and then merged.