X-ray computed tomography reconstruction algorithm for refractive index gradient

he?aim of this research?is to reconstruct the 3D X-ray refractive index gradient maps?by?the proposed vector Radon transform and its inverse, assuming that the small-angle deviation condition is met. Theoretical analyses?show?that the X-ray beam can be modeled as a streamline with continuous change of direction in a row?when measured in one grating period, which allows?the extraction of the refraction angle signals.?Experimental results show that?all the 2D refraction signals of different directions can be acquired by a standard circular scanning procedure, which is typically used in the X-ray differential phase-contrast computed tomography. Furthermore, the 3D refractive index gradient maps that contain the directional density changes, can also be accurately reconstructed.