Mathematical foundations of phase-contrast computed tomography

Gabor´s idea of in-line holography, which was proposed in 1948, has recently found application in phase-contrast imaging with X-rays. In particular, third generation synchrotron radiation sources make it possible to detect weak perturbations of X-ray wavefronts arising due to variations of the index of refraction in the investigated medium. This enables one to visualize the differences in refraction properties of materials, rather than the differences absorption as was done in the entire history of X-ray imaging. Also, as has recently been reported, phase-contrast imaging can be implemented with a more conventional polychromatic X-ray microfocus source