  In conventional absorption based x-ray computed tomography (CT), the noise
variance in reconstructed CT images scales with spatial resolution following an
inverse cubic relationship. Without reconstruction, in x-ray absorption
radiography, the noise variance scales as an inverse square with spatial
resolution. In this letter we report that while the inverse square relationship
holds for differential phase contrast projection imaging, there exists an
anomalous scaling law in differential phase contrast CT, where the noise
variance scales with spatial resolution following an inverse linear
relationship. The anomalous scaling law is theoretically derived and
subsequently validated with phantom results from an experimental Talbot-Lau
interferometer system.
