Polarimetric Simulations of SAR at L-Band Over Bare Soil Using Scattering Matrices of Random Rough Surfaces From Numerical Three-Dimensional Solutions of Maxwell Equations

Abstract

We have performed simulations of random rough surface scattering using 3-D numerical solution of Maxwell equations (NMM3D) using surface size up to 32 × 32 squared wavelengths. The rough surfaces are characterized by exponential correlation functions. The simulation results of crossand copolarization backscattering coefficients were in good agreement with experimental measurements of bare soils at L-band. Because in numerical solutions of Maxwell equations the electric fields of the scattered wave are calculated for each realization, scattering matrices can be simulated by NMM3D, and such simulations are performed in this paper. For a given RMS height, correlation length, soil permittivity, and incident angle, we calculated the radar scattering matrix up to 958 independent realizations. For each realization, the components of the scattering matrix, namely, S <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">HH</sub> , S <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">VV</sub> , S <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">HV</sub> , and S <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">VH</sub> , are calculated. Using the simulated scattering matrices, we calculate the polarimetric speckle statistics (amplitude and phase difference), followed by a comparison with theoretical distributions. For fully developed speckle from the homogeneous rough surface, the results are examined and validated to ensure the simulated data quality as far as polarimetric properties are concerned. By taking ensemble averages, we calculate the coherency matrix from which the eigenvalues, entropy, anisotropy, and alpha angle in coherent target decomposition are then calculated. In particular, characterization of polarimetric descriptors for rough surface is presented. Issues of scattering symmetry characteristics are also discussed.