a theoretical framework for comparing noise characteristics of spectral differential phasecontrast and spectral differential phasecontrast xray imaging spectral and gratingbased differential phasecontrast dpc xray imaging are two emerging technologies that offer additional information compared with conventional attenuationbased xray imaging in the case of spectral imaging energyresolved measurements allow the generation of materialspecific images by exploiting differences in the energydependent attenuation dpc imaging uses the phase shift that an xray wave exhibits when traversing an object as contrast generation mechanism recently we have investigated the combination of these two imaging techniques spectral dpc imaging and demonstrated potential advantages compared with spectral imaging in this work we present a noise analysis framework that allows the prediction of co variances and noise power spectra for all three imaging methods moreover the optimum acquisition parameters for a particular imaging task can be determined we use this framework for a performance comparison of all three imaging methods the comparison is focused on projected electron density images since they can be calculated with all three imaging methods our study shows that spectral dpc imaging enables the calculation of electron density images with strongly reduced noise levels compared with the other two imaging methods for a large range of clinically relevant pixel sizes in contrast to conventional dpc imaging there are no longrange noise correlations for spectral dpc imaging this means that excessive low frequency noise can be avoided we confirm the analytical predictions by numerical simulations