Relativistic modeling of atmospheric occultations with time transfer functions

Context. Occultation experiments represent unique opportunities to remotely probe the physical properties of atmospheres. The data processing involved in modeling time and frequency transfers an electromagnetic signal requires that refractivity be properly accounted for. On theoretical grounds, little work has been done concerning elaboration a covariant approach for occultation data. Aims. We present original method allowing fully analytical expressions derived up appropriate order description during atmospheric experiment. Methods. make use two independent powerful relativistic tools, namely optical metric transfer functions formalism. former allows us consider as spacetime curvature while latter is used determine occurring curved spacetime. Results. provide integral form function any post-Minkowskian order. discussion focuses on stationary describing by steadily rotating spherically symmetric atmosphere. Explicit are provided at first their accuracy assessed comparing them results numerical integration equations rays. Conclusions. accurately describes vertical temperature gradients accounts light-dragging effect due motion medium. It can pushed further derive explicit higher beyond spherical symmetry assumption.