The Phase Response of a Rough Rectangular Facet for Radar Sounder Simulations of Both Coherent and Incoherent Scattering

• Published in: Radio science Vol. 58; no. 6
• Main Authors: Gerekos, C., Haynes, M. S., Schroeder, D. M., Blankenship, D. D.
• Format: Journal Article
• Language: English
• Published: Washington Blackwell Publishing Ltd 01.06.2023
• Subjects: Approximation; Backscattering; Clutter; Coherent scattering; Correlation; Digital Elevation Models; facets; Incoherent scatter radar; Linear phase; Mathematical analysis; Polynomials; Radar; Roughness; Scattering angle; Simulation; Simulators; Stratton‐Chu
• ISSN: 0048-6604; 1944-799X; 1944-799X
• DOI: 10.1029/2022RS007594

With radar sounders, coherent backscattering simulations from global planetary digital elevation models (DEMs) typically display a deficit in diffuse clutter, which is mainly due to the implicit assumption that roughness at scales below the resolution of the DEM is absent. Indeed, while polynomial approximations of the phase evolution across the facet allow for fast and mathematically rigorous simulators, the coarse resolution of these planetary DEMs leads to a potentially significant portion of the backscattering response being neglected. In this paper, we derive the analytical phase response of a rough rectangular facet characterized by Gaussian roughness and a Gaussian isotropic correlation function under the linear phase approximation. Formulae for the coherent and incoherent power scattered by such an object are obtained for arbitrary bistatic scattering angles. Validation is done both in isolation and after inclusion in different Stratton‐Chu simulators. In order to illustrate the different uses of such a formulation, we reproduce two lunar radargrams acquired by the Lunar Radar Sounder instrument with a Stratton‐Chu simulator incorporating the proposed rough facet phase integral, and we show that the original radargrams are significantly better‐reproduced than with state‐of‐the‐art methods, at a similar computational cost. We also show how the rough facet integral formulation can be used in isolation to better characterize subglacial water bodies on Earth. Key Points Planetary digital elevation models are often of coarse resolution and depict a surface that is smooth at scales below that resolution Polynomial phase approximations can be used to simulate radar scattering rigorously but they overestimate the coherence of reflected signals We analytically derive the linear phase approximation formula on a rough rectangular facet, leading to much better clutter simulations