Theoretical analysis on x-ray cylindrical grating interferometer

Grating interferometer is a state of art x-ray imaging approach, which can simultaneously acquire information of x-ray attenuation, phase shift, and small angle scattering. This approach is very sensitive to micro-structural variation and offers superior contrast resolution for biological soft tissues. The present grating interferometer often uses flat gratings, with serious limitations in the field of view and the flux of photons. The use of curved gratings allows perpendicular incidence of x-rays on the gratings, and gives higher visibility over a larger field of view than a conventional interferometer with flat gratings. In the study, we present a rigorous theoretical analysis of the self-imaging of curved transmission gratings based on Rayleigh-Sommerfeld diffraction. Numerical simulations have demonstrated the self-imaging phenomenon of cylindrical grating interferometer. The theoretical results are in agreement with the results of numerical simulations.