Decomposition-Reconstruction Theory in Conjugation With Extended Boundary Condition Method for Scattering From Rough Surfaces: Derivation and Application

The challenge of computing electromagnetic (EM) scattering from rough surfaces is a notably complex yet crucial issue in the field of microwave remote sensing. The decomposition-reconstruction theory (DRT) has been previously introduced with the objective of reducing the computational complexity of scattering from rough surfaces. The central idea of DRT is to replace the scattering from rough surfaces with that from sinusoidal or other simpler, basic surfaces. The EM scattering from these simpler surfaces can be calculated more easily. The total scattering from the original rough surface is then reconstructed with the scattering from all the basic surfaces. This article introduces the decomposition reconstruction theory-based extended boundary condition method (DRT-EBCM), a novel method that combines the DRT and the extended boundary condition method (EBCM) to handle scattering from rough surfaces. The DRT-EBCM method decomposes the system integrals within the Dirichlet/Neumann matrices (system matrices) of the rough surface and represents them with the basic system integrals from complex sinusoidal surfaces (basic surfaces). This process leads to the derivation of new DRT-EBCM formulations. These new formulations not only establish a quantitative relationship between EM scattering from rough surfaces and basic surfaces, but they also significantly enhance computational efficiency due to the reduced complexity of the basic system integrals. Moreover, a new Fourier-Bessel (FB) function is introduced, which plays a crucial role in the scattering from basic surfaces. This function possesses a series of excellent properties that simplify the DRT-EBCM formulations and can potentially be applied in other scattering calculation methods. Simulation experiments were conducted to validate the proposed DRT-EBCM, confirming its correctness and validity. Furthermore, the application of DRT-EBCM in fast scattering calculation for rough surfaces was demonstrated. The results showed that DRT-EBCM significantly improves computational efficiency compared to the classical EBCM.