Radio wave back-propagating in polar coordinates: A linear filter in the time-frequency angle-frequency domain

The Comet Nucleus Sounding Experiment by Radio Wave Transmission (CONSERT) is a tomography of a comet nucleus for the ROSETTA mission, which consists of the transmission of electromagnetic waves between a lander on the comet nucleus surface and an orbiter through the nucleus to study its internal structure. The data inversion requires back-propagating the electric field from the orbit to the nucleus surface. In order to take into account the circular geometry of the boundary conditions, we propose a back-propagation in the angle-frequency time-frequency domain. This new method is described in this paper. We analyze similarities and differences with classical methods in Cartesian coordinates in terms of dispersion equations and evanescent waves; and we used this study to stabilize our back-propagating filter. This method is then tested on CONSERT synthetic data.