A phase retrieval method for X-ray microscopy based on a π∕2-biased X-ray zone-plate pair

A method for X-ray imaging and phase retrieval of a sample is proposed, wherein a zone-plate pair with a bias of π∕2 is used to take only twice differential-interference-contrast images of the sample via reverse projection. The images of the sample and its reverse projection have the same absorption but opposite differential phase shift signals, which are post-processed to quantitatively retrieve the phase shift and the absorption of the sample. Theoretical analysis and numerical simulations indicate that the spatial resolution of the retrieved results could attain the Rayleigh limit of a single zone plate in the zone-plate pair.