  Purpose: Grating-based imaging (GBI) and edge-illumination (EI) are two
promising types of XPCI as the conventional x-ray sources can be directly
utilized. For GBI and EI systems, the phase-stepping acquisition with multiple
exposures at a constant fluence is usually adopted in the literature. This
work, however, attempts to challenge such a constant fluence concept during the
phase-stepping process and proposes a fluence adaptation mechanism for dose
reduction. Method: Recently, analytic multi-order moment analysis has been
proposed to improve the computing efficiency. In these algorithms, multiple
contrasts can be calculated by summing together the weighted phase-stepping
curves (PSCs) with some kernel functions, which suggests us that the raw data
at different steps have different contributions for the noise in retrieved
contrasts. Based on analytic retrieval formulas and the Gaussian noise model
for detected signals, we derived an optimal adaptive fluence distribution,
which is proportional to the absolute weighting kernel functions and the root
of original sample PSCs acquired under the constant fluence. Results: To
validate our analyses, simulations and experiments are conducted for GBI and EI
systems. Simulated results demonstrate that the dose reduction ratio between
our proposed fluence distributions and the typical constant one can be about
20% for the phase contrast, which is consistent with our theoretical
predictions. Although the experimental noise reduction ratios are a little
smaller than the theoretical ones, synthetic and real experiments both observe
better noise performance by our proposed method. Our simulated results also
give out the effective ranges of the parameters of the PSCs, such as the
visibility in GBI, the standard deviation and the mean value in EI, providing a
guidance for the use of our proposed approach in practice.
