Light rays in the Solar system experiments: phases and displacements

Abstract: Geometric optics approximation is sufficient to describe the effects in the near-Earth environment. In this framework Faraday rotation is purely a reference frame (gauge) effect. However, it cannot be simply dismissed. Establishing local reference frame with respect to some distant stars leads to the Faraday phase error between the ground station and the spacecraft of the order of $10^{-10}$ in the leading post-Newtonian expansion of the Earth's gravitational field. While the Wigner phase of special relativity is of the order $10^{-4}$--$10^{-5}$. Both types of errors can be simultaneously mitigated by simple encoding procedures. We also present briefly the covariant formulation of geometric optic correction up to the subleading order approximation, which is necessary for the propagation of electromagnetic/ gravitational waves of large but finite frequencies. We use this formalism to obtain a closed form of the polarization dependent correction of the light ray trajectory in the leading order in a weak spherically symmetric gravitational field.