Scaling law for noise variance and spatial resolution in differential phase contrast computed tomography.

PURPOSE The noise variance versus spatial resolution relationship in differential phase contrast (DPC) projection imaging and computed tomography (CT) are derived and compared to conventional absorption-based x-ray projection imaging and CT. METHODS The scaling law for DPC-CT is theoretically derived and subsequently validated with phantom results from an experimental Talbot-Lau interferometer system. RESULTS For the DPC imaging method, the noise variance in the differential projection images follows the same inverse-square law with spatial resolution as in conventional absorption-based x-ray imaging projections. However, both in theory and experimental results, in DPC-CT the noise variance scales with spatial resolution following an inverse linear relationship with fixed slice thickness. CONCLUSIONS The scaling law in DPC-CT implies a lesser noise, and therefore dose, penalty for moving to higher spatial resolutions when compared to conventional absorption-based CT in order to maintain the same contrast-to-noise ratio.