The present invention relates to an interferometer for x-rays, in particular hard x-rays, for obtaining quantitative x-ray images from an object, comprising: a) an x-ray source, preferably a standard polychromatic x-ray source, b) a diffractive beam splitter grating other than a Bragg crystal, preferably in transmission geometry, c) a position-sensitive detector with spatially modulated detection sensitivity having a number of individual pixels; d) means for recording the images of the detector in a phase-stepping approach; and e) means for evaluating the intensities for each pixel in a series of images in order to identify the characteristic of the object for each individual pixel as an absorption dominated pixel and/or an differential phase contrast dominated pixel and/or an x-ray scattering dominated pixel.