Effects of arbitrary focal spot intensity distribution, detector width, and scanning eccentricity in X-ray computed tomography

Recent developments in X-ray computed tomography have shown that the focal spot intensity distribution, the detector width, and the scanning eccentricity all combine to degrade the reconstructed images in a way precisely describable by a complicated space-variant point-spread function (PSF). Following a brief review of the underlying problem of image reconstruction from strip integrals, a new route leading to an elegant expression for this PSF is presented. Whereas this and related formulas generally involve a double integral requiring numerical evaluation, the form of the new expression readily singles out a class of focal spot intensity distributions for which one of the integrations can be performed analytically. It is shown that this simplification occurs if the Hilbert transform of the function used to describe the focal spot can be computed analytically. The paper concludes with the application of the theory to various focal spot models proposed in the literature.