Large-scale optical interferometry in general spacetimes

We introduce a convenient formalism to evaluate the phase of a light signal propagating on a general curved background. It allows us to obtain a transparent relation between the frequency-shift and the phase difference in large-scale optical interferometry for a general relativistic setting, as well as to derive compact expressions generalizing the Doppler effect in one-way and two-way schemes. Our recipe is easily applicable to stationary spacetimes, and in particular to the near-Earth experiments where the geometry is described in the parametrized post-Newtonian approximation. As an example, we use it to evaluate the phase difference arising in the optical version of the Colella-Overhauser-Werner experiment.