Simulation model and eigen-analysis for polarimetric scattering in SAR imaging

In this paper, to simulate fully polarimetric scattering from tree canopies applicable to SAR imaging at C band, the scattering amplitude functions of randomly oriented, non-spherical particles (e.g. leaves with thin thickness, branches with small radius) are derived in the generalized Rayleigh-Gans (GRG) approximation. Numerical results show the difference between the GRG and conventional Rayleigh approximations. These functions averaged over randomly spatial orientation are employed to construct the non-diagonal extinction matrix and the Mueller matrix solution. Four Stokes parameters of scattered fields are coupled. It is different from the conventional iterative solution of isotropic scattering media. Further, to physically identify polarimetric scattering of the Mueller matrix solution, the coherency matrix and its eigen-analysis are discussed. Information of the eigenvalues and entropy from the Mueller matrix measurement is related with polarimetric scattering process and medium randomness, and can be used to investigate directly the influence of different scattering mechanisms in complex scenarios on observable parameters. As an application, the eigenvalues and entropy derived from the Mueller matrix measurement of an AirSAR image are demonstrated.