Anomalous scaling law for noise variance and spatial resolution in differential phase contrast computed tomography

TL;DR

This paper reveals an anomalous linear scaling law for noise variance in differential phase contrast CT, differing from traditional absorption CT, supported by theoretical derivation and experimental validation.

Contribution

It introduces and validates a new linear scaling law for noise variance in differential phase contrast CT, contrasting with known relationships in absorption CT.

Findings

Noise variance in differential phase contrast CT scales inversely with spatial resolution.

The linear scaling law is derived theoretically and confirmed experimentally.

Differential phase contrast CT exhibits unique noise-resolution behavior compared to absorption CT.

Abstract

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.