Moir\'e Artifact Reduction in Grating Interferometry Using Multiple Harmonics and Total Variation Regularization

X-ray interferometry is an emerging imaging modality with a wide variety of potential clinical applications, including lung imaging. A grating interferometer uses a diffraction grating to produce a periodic interference pattern and measures how a patient or sample perturbs the pattern, producing three unique images that highlight X-ray absorption, refraction, and small angle scattering, known as the attenuation, differential-phase, and dark-field images, respectively. Inaccuracies in grating position and multi-harmonic fringes produce Moir\'e artifacts when assuming the fringe pattern is perfectly sinusoidal and the phase steps are evenly spaced. We have developed an image recovery algorithm that estimates the true phase stepping positions using multiple harmonics and total variation regularization, removing the Moir\'e artifacts present in the attenuation, differential-phase, and dark-field images. We demonstrate the algorithm's utility for the Talbot-Lau and Modulated Phase Grating Interferometers by imaging multiple samples, including PMMA microspheres and a euthanized mouse.