With the aid of discriminators on a picture element of an X-ray detector, digital outputs are generated that indicate energy intervals to which X-ray quanta are allocated. If this occurs for adjacent picture elements, a distinction may be made between true coincidences, in which k-fluorescence photons play a part, and random coincidences in which two primary quanta randomly strike adjacent picture elements. The energy of the primary quantum may also be at least roughly reconstructed in the case of true coincidences. An energy-triggering measurement may thereby be provided to the extent that different materials of a picture object should be distinguished.