Analysis and correction of bias induced by phase stepping jitter in grating-based X-ray phase-contrast imaging

Grating-based X-ray phase-contrast (gbPC) is an X-ray phase-contrast imaging method involving optical gratings that typically employs the Talbot self-imaging effect. X-ray phase contrast is known to provide significant benefits for biomedical imaging. To investigate these benefits for gbPC, a high-sensitivity gbPC micro-CT setup for small biological samples has been constructed. A gbPC projection measurement simultaneously retrieves the transmittance, differential-phase and dark-field modalities of a sample. Phase stepping, the most common gbPC acquisition technique, involves several acquisitions at different lateral positions of one of the gratings. The three modalities can then be retrieved by least-squares- or FFT-based methods. Unfortunately, increasing differential-phase sensitivity also leads to an increased magnitude of artifacts introduced during retrieval of the modalities from the phase-stepping data, which limits image quality. Most importantly, processing of phase-stepping data with incorrect stepping positions (i.e., spatial sampling jitter) can introduce artifacts to the modalities. Using data from the high-sensitivity gbPC setup, as well as simulations, we show that an artifact is introduced by the jitter which is correlated with the phase of the stepping curve. We present a theoretical explanation for this correlation by introducing small deviations to an equidistant sampling of a stepping curve and approximating the effect on the calculation of the three gbPC modalities with a first-order Taylor approximation. Finally, we present an algorithm for the detection and removal of these artifacts that exploits these correlations. We show that this algorithm is able to eliminate these artifacts without degrading true image information.