In an arrangement having an X-ray detector or a gamma detector with detector elements arranged in a matrix in row and column directions that form a detector surface with detection regions that are sensitive to X-rays or gamma radiation and insensitive intermediate regions, and a stray radiation grid or collimator of absorbent structure elements that is arranged over the detector surface, the absorbent structure elements proceed over the intermediate regions and are fashioned such that their detector-side center-to-center spacing in the row direction and/or column direction is greater by a whole-numbered factor than the center-to-center spacing of the detector elements in the same direction, and/or sections of the absorbent structure elements that proceed in one direction exhibit a lower height than sections that proceed in the respectively other direction. Moiré effects can be avoided in the image exposure and, at the same time, a reduced primary radiation absorption by the stray radiation grid or collimator is achieved even given a moving radiation source.