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A quantitative theory for the contrast-to-noise ratio (CNR) in differential phase contrast imaging (DPCI) is proposed and compared to that of images derived from classical absorption contrast imaging (ACI). Most prominently, the CNR for DPCI contains the reciprocal of thespatial wavelength to be imaged, the fringe visibility, and a tunable factor dependent on the system geometry. DPCI is thus potentiallybeneficial especially for the imaging of small object structures. We demonstrate CNR calculations for mammography, finding optimal imaging energies between 15 and 22 keV for ACI, and between 20 and 40 keV for DPCI.