When an X-ray area detector based on a single-crystalline material, for instance a state-of-the-art hybrid pixel detector, is illuminated from a point source by monochromatic radiation, a pattern of lines appears which overlays the detected image. These lines are easily seen in scattering experiments with smooth patterns, such as small-angle X-ray scattering. The origin of this effect is Bragg reflection within the sensor layer of the detector. Experimental images are presented over a photon energy range from 3.4 to 10 keV, together with a theoretical analysis. The intensity of the detected signal is decreased by up to 20% on this pattern, which can affect the evaluation of scattering and diffraction experiments. The patterns can be exploited to check the alignment of the detector surface with the direct beam, and the alignment of individual detector modules with each other in the case of modular detectors, as well as for energy calibration of the radiation.