Atmospheric refraction path integrals of ground-based interferometry

One basic effect of the Earth's atmospheric refraction on telescope operation is the reduction of the true zenith angle to the apparent zenith angle, associated with prismatic aberrations due to the dispersion in air. Coherent superposition of star images in ground-based interferometry depends in addition on the optical path length associated with the refracted rays. In a precolumbian model of a flat Earth, the translational symmetry of the setup means no net effect on the optical path difference remains. This work evaluates these interferometric path integrals in the more realistic arrangement of two telescopes on the surface of a common Earth sphere, which point through a layered atmosphere of the same spherical symmetry. Focus is Out on working out series expansions in the small ratio of the baseline over the Earth radius, which bypasses some numerics which otherwise is challenged by strong cancellation effects in building the optical path difference.