The effects of the imaging system on the validity limits of the ray-optical approach to phase contrast imaging

A theoretical analysis of the x-ray phase contrast imaging and its validation via synchrotron radiation imaging is here presented. Two different mathematical models have been followed: the simpler ray-optical approach and the more rigorous Fresnel-Kirchoff diffraction theory. Subsequently, the conditions upon which the x-ray optical approximation can be used to describe the image formation mechanism have been analyzed, taking into account also the effects due to the finite source size and detector resolution. It is possible to demonstrate that the ray-optics results can also be obtained by opportunely developing the diffraction formalism only with some restrictions on the spatial frequencies present in the final image, without any limitation on the maximum phase shift. The conditions allowing the use of the simplified ray-optical approach to describe the phase contrast images have been here defined and their validation has been proved by means of computer simulations and phantom experiments.