Physico-Mathematical Considerations on X-Ray Computed Tomography Based on Diffraction Enhanced Imaging

We consider x-ray computed tomography (CT) technique based on refractive effects, which has advantages for delineating biological weakly-absorbing soft-tissues over the conventional absorption-contrast CT (computed tomography) because of the use of phase sensitive detection. The refraction-based CT described here detects the angular deviation of the beam, refracted by a sample, from the incident beam in a cross-sectional plane of interest, based on the diffraction enhanced imaging (DEI) method using the Bragg-case analyzing crystal, which is arranged behind the sample on a positioning device for collecting projection data from various directions. The set of angular deviation data from various directions, which corresponds to the projection data in the conventional absorption-contrast CT, are used for reconstruction of the refractive-index gradient vector field. So far, some groups have proposed the distinct DEI-based CT protocols. We theoretically summarize and compare the algorithms from the viewpoint of geometrical optics.