several millimeters perpendicular to the optical axis y axis moreover it is preferred that carbon nanotubes cnt are used for the corresponding cathodes as this allows tube designs with fast switching and large anodes a grating g 0 is disposed in front of the x ray sources 11 11 u2032 to subdivide the emission in lines each of which is spatially coherent in transverse z direction more details about this approach can be found in literature e g pfeiffer et al above for purposes of clarity only one cylindrical wave propagating in y direction beyond one slit of the grating g 0 is illustrated in fig1 the cylindrical wave passes through an object 1 for example the body of a patient that is located in a center region around the origin of the x y z coordinate system and that shall be imaged by the device 100 the material of the object 1 induces a phase shift in the x ray wave resulting in an altered disturbed wave front behind the object 1 for each position z perpendicular to the optical y axis a phase shift u03c6 z is thus associated to the wave front that is characteristic of the material properties along the corresponding x ray path the complete function u03c6 is a phase contrast projection image of the object 1 one is interested in in order to determine the phase shift function u03c6 a diffractive optical element doe is disposed behind the object 1 in the shown example this doe is realized by a beam splitter phase grating g 1.