Signal estimation bias in x-ray dark-field imaging using dual phase grating interferometer

In x-ray dark-field imaging using dual phase grating interferometer, multi-contrast signals are extracted from a set of acquired phase-stepping data by using the least-squares fitting algorithm. The extracted mean intensity, amplitude and visibility signals may be intrinsically biased. However, it is still unclear how large these biases are and how the data acquisition parameters influence the biases in the extracted signals. This work set out to address these questions. Analytical expressions of the biases of the extracted signals were theoretically derived by using a second-order Taylor series expansion.Extensive numerical simulations were performed to validate the theoretical results. It is illustrated that while the estimated mean intensity signal is always unbiased, the estimated amplitude and visibility signals are both positively biased. While the biases of the estimated amplitude signals are proportional to the inverse of the total number of phase steps, the biases of the estimated visibility signals are inversely proportional to the product of the total number of phase steps and the mean number of photons counted per phase step. Meanwhile, it is demonstrated that the dependence of the biases on the mean visibility is quite different from that of Talbot–Lau interferometer due to the difference in the intensity model. We expect that these results can be useful for data acquisition optimizations and interpretation of x-ray dark-field images.