Analytical evaluation of the signal and noise propagation in x-ray differential phase-contrast computed tomography

We analyze the signal and noise propagation of differential phase-contrast computed tomography (PCT) compared with conventional attenuation-based computed tomography (CT) from a theoretical point of view. This work focuses on grating-based differential phase-contrast imaging. A mathematical framework is derived that is able to analytically predict the relative performance of both imaging techniques in the sense of the relative contrast-to-noise ratio for the contrast of any two materials. Two fundamentally different properties of PCT compared with CT are identified. First, the noise power spectra show qualitatively different characteristics implying a resolution-dependent performance ratio. The break-even point is derived analytically as a function of system parameters such as geometry and visibility. A superior performance of PCT compared with CT can only be achieved at a sufficiently high spatial resolution. Second, due to periodicity of phase information which is non-ambiguous only in a bounded interval statistical phase wrapping can occur. This effect causes a collapse of information propagation for low signals which limits the applicability of phase-contrast imaging at low dose.