Analytical Modeling of Rough Surface SAR Images Under Small Perturbation Approximation

In high-resolution synthetic aperture radar (SAR) images, the spatial pattern of a homogenous region conveys rich information regarding the specific scatterers being imaged. Analytical modelings of both scattering and imaging processes are critical to better interpret a specific scatterer's appearances in SAR imagery and thereafter quantitatively retrieve its physical parameters. Small-scale rough surface scattering represents one of the mostly common scattering mechanisms and yet its SAR image characteristics have not been well studied. This becomes more critical in millimeter-wave/terahertz regime as smooth surfaces would become slightly rough under millimeter/submillimeter wavelengths. In this paper, we recast the small perturbation method (SPM) approximation of rough surface scattering under the deterministic finite-length surface condition. By ignoring evanescent waves, a simplified SPM solution for rough facet is derived as well as the analytical form of its SAR image under the conventional setup. Then, we reformulate the scattering imaging process of rough facet as a signal processing chain that further reveals the underlying mechanism of rough surface as imaged by radar. The proposed method is extensively validated against the method of moments in terms of both scattering coefficients and imaging patterns. It is found that under the conventional SPM validity condition, the error of scattering coefficients is less than 1.5 dB, while the correlation between SPM-calculated and MoM-calcualted SAR images is larger than 0.9. The proposed model of rough facet SAR image could serve as the theoretical basis for parameter inversion and surface reconstruction. Preliminary cases of the inversion of rough surface spectrum using both simulated and real SAR image patches are presented.