  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.
