An x-ray CT system that generates tomographic phase contrast or dark field exposures, has at least one grating interferometer with three grating structures arranged in series in the radiation direction, with a modular design of the second and third grating structures. The distance between the first grating structure of the x-ray source and the second grating structure (fashioned as a phase grating) of the respective grating/detector modules is adapted, depending on the fan angle, corresponding to a period of the grating structure of the x-ray source projected onto the grating detector module at a respective fan angle (φi).