Blurring in Tomograms Made with X-Ray Beams of Finite Width

Abstract

Tomographic reconstruction has ordinarily assumed that the measurement data can be regarded as line integrals, but the finite width of the X-ray beam invalidates this assumption. The data can be expressed in the form of integrals over a strip rather than a line. The strip integral kernel is calculated allowing for extended source and detector, as well as for nonuniform photon emission and detector sensitivity. Strip eccentricity, which occurs in practice, is also taken into account. Even if the measurement data were to cover all scanning angles, there would be imperfect reconstruction expressible as a space-variant point spread function deducible from the strip integral kernel. To deal with this it is convenient to introduce the concepts of generalized projection and generalized Ra transform. Point-spread functions are given for cases involving piecewide-uniform symmetrical source distributions and uniform detectors.