The fractional Talbot effect in differential x-ray phase-contrast imaging for extended and polychromatic x-ray sources

Grating-based x-ray differential phase contrast imaging with twin peaks in phase-stepping curves-phase retrieval and dewrapping

PURPOSE

X-ray differential phase contrast CT implemented with Talbot interferometry employs phase-stepping to extract information of x-ray attenuation, phase shift, and small-angle scattering. Since inaccuracy may exist in the absorption grating G2 due to an imperfect fabrication, the effective period of G2 can be as large as twice the nominal period, leading to a phenomenon of twin peaks that differ remarkably in their heights. In this work, the authors investigate how to retrieve and dewrap the phase signal from the phase-stepping curve (PSC) with the feature of twin peaks for x-ray phase contrast imaging.

METHODS

Based on the paraxial Fresnel-Kirchhoff theory, the analytical formulae to characterize the phenomenon of twin peaks in the PSC are derived. Then an approach to dewrap the retrieved phase signal by jointly using the phases of the first- and second-order Fourier components is proposed. Through an experimental investigation using a prototype x-ray phase contrast imaging system implemented with Talbot interferometry, the authors evaluate and verify the derived analytic formulae and the proposed approach for phase retrieval and dewrapping.

RESULTS

According to theoretical analysis, the twin-peak phenomenon in PSC is a consequence of combined effects, including the inaccuracy in absorption grating G2, mismatch between phase grating and x-ray source spectrum, and finite size of x-ray tube's focal spot. The proposed approach is experimentally evaluated by scanning a phantom consisting of organic materials and a lab mouse. The preliminary data show that compared to scanning G2 over only one single nominal period and correcting the measured phase signal with an intuitive phase dewrapping method that is being used in the field, stepping G2 over twice its nominal period and dewrapping the measured phase signal with the proposed approach can significantly improve the quality of x-ray differential phase contrast imaging in both radiograph and CT.

CONCLUSIONS

Using the phase retrieval and dewrapping methods proposed to deal with the phenomenon of twin peaks in PSCs and phase wrapping, the performance of grating-based x-ray differential phase contrast radiography and CT can be significantly improved.