Phase-contrast x-ray computed tomography (PCCT) is currently investigated and developed as a potentially very interesting extension of conventional CT, because it promises to provide high soft-tissue contrast for weakly absorbing samples. For data acquisition several images at different grating positions are combined to obtain a phase-contrast projection. For short exposure times, which are necessary for lower radiation dose, the photon counts in a single stepping position are very low. In this case, the currently used phase-retrieval does not provide reliable results for some pixels. This uncertainty results in statistical phase wrapping, which leads to a higher standard deviation in the phase-contrast projections than theoretically expected. For even lower statistics, the phase retrieval breaks down completely and the phase information is lost. New measurement procedures rely on a linear approximation of the sinusoidal phase stepping curve around the zero crossings. In this case only two images are acquired to obtain the phase-contrast projection. The approximation is only valid for small phase values. However, typically nearly all pixels are within this regime due to the differential nature of the signal. We examine the statistical properties of a linear approximation method and illustrate by simulation and experiment that the lower statistical limit can be redefined using this method. That means that the phase signal can be retrieved even with very low photon counts and statistical phase wrapping can be avoided. This is an important step towards enhanced image quality in PCCT with very low photon counts.
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