Reconstruction formulas in phase-contrast tomography

An inverse problem of three-dimensional reconstruction of the index of refr action of a phase object from phase-contrast intensity measurements obtaine d with the use of a synchrotron X-ray source is considered. A linear closed -form solution to the problem is presented. Two reconstruction formulas are derived using an original relation established between the three-dimension al Radon transform of the object function and the two-dimensional Radon tra nsform of the phase-contrast intensity data. The application of the formula s requires tomographic acquisition of two-dimensional intensity distributio ns in a single plane of the near field. The reconstruction algorithms can b e implemented by using the fast Fourier transform. (C) 1999 Elsevier Scienc e B.V. All rights reserved.