Far-field x-ray phase contrast imaging has no detailed information on the object

We show that x-ray phase contrast images of some objects with a small cross-section diameter d satisfy a condition for a far-field approximation d << r(1) where r(1) = (lambda z)(1/2), lambda is the x-ray wavelength, z is the distance from the object to the detector. In this case the size of the image does not match the size of the object contrary to the edge detection technique. Moreover, the structure of the central fringes of the image is universal, i.e. it is independent of the object cross-section structure. Therefore, these images have no detailed information on the object.