Spatial Coherence Constraints on Passive Radar Sounding With Radio-Astronomical Sources

Recent work has highlighted the simulated performance of passive synthetic aperture radar (SAR) using Jupiter's radio emissions to probe the icy moons of Jupiter. Terrestrially, passive radar sounding using the Sun as a source for echo detection, ranging, imaging, and measuring ice thickness has also been recently demonstrated for the first time. With increasing advancements in passive radar sounders that use extended, incoherent radio-astronomical sources for echo detection, we revisit a potential limitation of the technique in terms of the sources' spatial coherence properties. While previous work has considered the spatial coherence effects of extended sources for passive sounding in terms of pulse broadening, there has been little work to date that has examined the spatial coherence constraints for passive sounding imposed by source size, wavelength, incidence angle, and altitude-all of which govern the potential performance of passive SAR focusing. Starting from antenna theory, the Van Cittert-Zernike (VCZ) theorem, and the coherence function for passive sounding, we derive additional bounds set by these parameters and the expected source extent to estimate the maximum orbital altitudes when using radio-astronomical sources; in particular, we analyze the scenarios for a spacecraft using the Sun and Jovian bursts as sources for passive sounding of the Earth, Mars, and Europa. While the results of our analysis and simulations show that the coherence requirements (in terms of both pulse broadening and spatial radius of coherence) are met for terrestrial ground-based experiments up to large incidence angles, the limited spatial coherence at these greater altitudes creates an upper bound for orbital passive radar sounding. Our results therefore provide a richer understanding of the passive sounding technique, its viability, and a critical design constraint when planning future planetary and terrestrial passive sounding experiments.