Scattering From Multilayer Rough Surfaces Based on the Extended Boundary Condition Method and Truncated Singular Value Decomposition

Electromagnetic scattering from rough surfaces has been investigated extensively for the past decades. There exist analytical solutions to rough surface scattering such as small perturbation method (SPM) or Kirchhoff approximation (KA). These solutions, however, are limited to either small or large roughness regimes. Recent efforts have been put forth to study electromagnetic scattering of multilayer rough surface in the application of deep soil moisture and ice property estimation. In this paper, multilayer rough surface scattering is analyzed based on the extended boundary condition method (EBCM) and truncated singular value decomposition. The method of extended boundary condition can accurately handle scattering from a slightly rough surface. For mild and large roughness regime, ill-conditioned matrices can arise from EBCM. In this paper, we present a regularization scheme to mitigate this ill-conditioning effect via truncated singular value decomposition (TSVD).The truncation parameters are set to enforce power conservation relations across all rough interfaces. Bistatic scattering coefficients are then obtained by incoherently averaging the power computed from the resulting Floquet modes in the scattering directions. Therefore, the electromagnetic wave interactions in multilayer rough surfaces are analyzed in a systematic way. Finally, the results are validated against the analytical SPM solution to two-rough-interface rough surface scattering. In addition, the formulation is extended to solve scattering from three-rough-interface rough surfaces. Several results are reported