title: Theory of quantitative phase-contrast computed tomography.
abstract: Phase-contrast x-ray computed tomography (CT) is an emerging imaging technique that can be implemented at third-generation synchrotron radiation sources or by using a microfocus x-ray source. Promising results have recently been obtained in materials science and medicine. At the same time, the lack of a mathematical theory comparable with that of conventional CT limits the progress in this field. Such a theory is now suggested, establishing a fundamental relation between the three-dimensional Radon transform of the object function and the two-dimensional Radon transform of the phase-contrast projection. A reconstruction algorithm is derived in the form of a filtered backprojection. The filter function is given in the space and spatial-frequency domains. The theory suggested enables one to quantitatively determine the refractive index of a weakly absorbing medium from x-ray intensity data measured in the near-field region. The results of computer simulations are discussed.
authors.affiliation: KEMA, Arnhem, The Netherlands. andrei@kema.nl
authors.forename: Andrei V
authors.initials: AV
authors.lastname: Bronnikov
mesh_terms: D000818:Animals; D005583:Fourier Analysis; D006801:Humans; D007091:Image Processing, Computer-Assisted; D008858:Microscopy, Phase-Contrast; D008962:Models, Theoretical; D019047:Phantoms, Imaging; D014057:Tomography, X-Ray Computed