  In this paper, we develop a novel phase retrieval approach to reconstruct
x-ray differential phase shift induced by an object. A primary advantage of our
approach is a higher-order accuracy over that with the conventional linear
approximation models, relaxing the current restriction of weak absorption and
slow phase variation scenario. The optimal utilization of the diffraction
images at different distance in Fresnel diffraction region eliminates the
nonlinear terms in phase and attenuation, and simplifies the reconstruction to
a linear inverse problem. Numerical studies are also described to demonstrate
the accuracy and stability of our approach.
