Radar images of rough surface scattering: comparison of numerical and analytical models

Rough surface scattering theories are investigated through analysis of radar images. Backscatter results from 10 GHz to 14 GHz under tapered wave illumination are considered for one-dimension (1D) random rough surface realizations which satisfy an impedance boundary condition. Back-projection tomography is applied to form two-dimensional (2D) synthetic aperture radar images from deterministic surface scattered field data at multiple incidence angles and frequencies. Numerical predictions of surface backscattered fields are obtained from an accelerated forward-backward (FB) method and the resulting images are compared with those obtained from approximate scattering theories such as the physical optics (PO) approximation, the small slope approximation (SSA), and the nonlocal SSA (NLSSA). The resulting radar images illustrate scattering sources associated with single and multiple scattering on the boundary, and a ray tracing analysis confirms the locations of time-delayed image points due to double reflections. For single scattering effects, the images demonstrate excellent agreement between analytical and numerical methods in both horizontal and vertical polarizations. For surfaces with RMS height 2.0 cm and correlation length 7.5 cm at normal incidence, multiple-scattering effects are observed and successfully captured when the lowest-order NLSSA is employed.