Angular and radial sampling criteria for monostatic and bistatic radar tomography of solar system small bodies

Abstract

Low-frequency radar tomography is an important subsurface imaging method for future planetary missions to solar system small bodies. We derive angular and radial sampling criteria for monostatic and bistatic radar tomography algorithms that are based on monochromatic free-space backprojection and spherical apertures. We use the vector Born approximation to highlight the degeneracy of monochromatic bistatic source/receiver direction pair measurements in k-space. Analytical expressions are then derived for the scalar point target response of different spherical sampling geometries. We also derive the angular sampling step and total number of sampling points required to fully reconstruct the point target response for monostatic, bistatic, and non-degenerate k-space spherical apertures. These are evaluated for object sizes and radar operating frequencies expected in small body tomography. We also analyze and derive expressions for the coherence loss of spherical apertures due to random errors in a sensor’s radial position, which provides requirements on the a posteriori ephemeris knowledge. Finally, we derive a vector backprojection algorithm suitable for focusing quad-pol scattering matrix (S-matrix) data that is tested using full-wave S-matrix simulations of dielectric point targets. This work is intended to aid radar instrument performance analysis and inform the design and architecture of future instruments and missions.