Support: US Air Force Office of Scientific Research (AFOSR)

Period of Performance: July 1st, 2017 — March 31st, 2021

Budget: $983,000

Summary: In our previous work on synthetic aperture radar (SAR) which is supported by AFOSR, we have shown that the commonly used models for radar targets appear inconsistent from the standpoint of physics. Specifically, the key assumption of weak scattering that facilitates the first Born approximation and subsequent linear inversion is not compatible with the assumption that the scattering occurs only at the surface of the target and the target itself is impenetrable. Moreover, interpreting the SAR observable as a variation of the local refractive index does not allow for any backscattering in the most basic case of a uniform target. Yet backscattering is always assumed present as it enables the monostatic SAR imaging. We have also constructed a new type of models for SAR targets that keep the scattering linear yet not necessarily weak. It involves a dielectric half-space with the permittivity that varies in the horizontal direction; and it interprets the SAR observable as the amplitude of the Bragg harmonic in the local spectrum of the dielectric permittivity. This type of models allow one to avoid the foregoing inconsistencies. In the course of the proposed effort, we plan to address a number of important issues that still require attention. In particular, we will extend the analysis to the full vector case of electromagnetic scattering. We will account for the possible anisotropy and electric conductivity of the target material. We will also consider the non-flat surface topographies. We will include both the short scale variations of material properties, as well as those of surface elevation (i.e., surface roughness) as sources of backscattering (more generally, sources of non-specular reflection). We will incorporate the new target models into the SAR ambiguity theory, which, in particular, will require accounting for the scattering anisotropy. We will analyze dispersive targets. We will compare the number of degrees of freedom provided by a given model against the number of independent quantities that a given SAR sensor can reconstruct. Overall, our effort will help bring the correct physics into the SAR ambiguity theory at the rigorous rather than heuristic level.