  Recently, the dual-phase grating based X-ray differential phase contrast
imaging technique has shown better radiation dose efficiency performance than
the Talbot-Lau system. In this paper, we provide a theoretical analyses
framework derived from wave optics to ease the design of such interferometer
systems, including the inter-grating distances, the diffraction fringe period,
the phase grating periods, and especially the source grating period if a
medical grade X-ray tube with large focal spot is utilized. In addition, a
geometrical explanation of the dual-phase grating system similar to the
standard thin lens imaging theory is derived with an optical symmetry
assumption for the first time. Finally, both numerical and experimental studies
have been performed to validate the theory.
