Investigation of Wavelength-induced Uncertainties in Full-Wave Radar Tomography of High Contrast Domain: An Application to Small Solar System Bodies

Abstract: This paper aims to reconstruct the internal structure of a two-dimensional test object via numerically simulated full-wave time domain radar tomography with the presence of wavelength-induced (WI) uncertainties, following from a complex domain structure, and domain diameters 21 or 64 times the wavelength of the signal propagating inside the target. In particular, we consider an application in planetary scientific studies of reconstructing the interior structure of an arbitrary high contrast small Solar System Body (SSSB), i.e., an asteroid, with a probing signal wavelength limited by the instrument and mission payload requirements. Our uncertainty reduction model finds the reconstruction via averaging multiple inverse solutions assuming that the WI deviations in the solutions correspond to random deviations, which we assume to be independent and identically distributed (IID). It incorporates error marginalisation via a randomised signal configuration, spatial-averaging of candidate solutions, frequency-based error marginalisation, and the truncated singular value decomposition (TSVD) filtering technique, based on our assumptions of the phase discrepancy of the signal, domain parameters, and the full-wave forward model. The numerical experiments are performed for 20 and 60 MHz centre frequencies proposed for CubeSat-based radars, the latter being the centre frequency of the Juventas Radar which will be aboard Hera mission to investigate the interior structure of asteroid Dimorphos. A benchmark reconstruction of the target was obtained with the spatial averaging, sparse point density and frequency randomised configuration for both 20 and 60 MHz frequency systems.