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A mathematical model for SAR imaging beyond the first Born approximation. (English) Zbl 1334.78027

The paper generalizes the conventional synthetic aperture radar (SAR) ambiguity theory in view of removing inconsistencies presented in the conventional theory. The authors propose a new model for radar targets that exploits a horizontally inhomogeneous dielectric half-space. In the framework of this model, one can consider the linearized scattering without assuming that it is weak (as in the conventional theory). The physical observable is a slowly varying amplitude of the Bragg resonant harmonic in the spectrum of electric permittivity computed on a resolution size window. The model represents the scattered field as a surface (rather than volumetric) retarded potential. Moreover, the linearization can be performed against various background solutions rather than only the unobstructed incident field in free space. It is also shown that in the case of weak scattering, the results following from the new model are equivalent to those from the classical theory.

MSC:

78A45 Diffraction, scattering
35B20 Perturbations in context of PDEs
35R30 Inverse problems for PDEs
45Q05 Inverse problems for integral equations
78A46 Inverse problems (including inverse scattering) in optics and electromagnetic theory
78A55 Technical applications of optics and electromagnetic theory
78M34 Model reduction in optics and electromagnetic theory
78M35 Asymptotic analysis in optics and electromagnetic theory
86A22 Inverse problems in geophysics
94A08 Image processing (compression, reconstruction, etc.) in information and communication theory
94A12 Signal theory (characterization, reconstruction, filtering, etc.)
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