Abstract: In an exemplary embodiment, several sources of radiation, arranged with their focuses angularly offset by angles of equal size, having a radiation measuring arrangement with a number of radiation receivers equal to the number of radiation sources for determining the radiation intensity behind the object, having a drive device which drives a rotating frame for producing rotational movements of the radiation sources and the radiation receivers, and also having a measured value converter for transforming the signals supplied by the radiation receivers into layer images. The radiation receivers are arranged opposite the radiation sources and are also displaced by equal angles. At least one of the measuring units each comprising a radiation source and a radiation receiver is arranged offset in the direction of the rotational axis so that the measuring units simultaneously scan a plurality of layers. This distance may be adjustable.