A focus-detector arrangement includes a radiation source with a focus, arranged on a first side of the subject, for generating a fan-shaped or conical beam of rays; at least one X-ray optical grating arranged in the beam path, with at least one phase grating arranged on the opposite second side of the subject in the beam path generating an interference pattern of the X-radiation preferably, in a particular energy range; and an analysis-detector system which detects at least the interference pattern generated by the phase grating in respect of its phase shift with position resolution. According to at least one embodiment of the invention, at least one X-ray optical grating including bars which are free from overhangs form shadows in the beam path of the fan-shaped or conical beam of rays.