Electromagnetic Forward And Inverse Scattering Of 3D Inhomogeneous Anisotropic Objects Embedded In Uniaxial Anisotropic Media

In this work,we study the electromagnetic scattering of 3D inhomogeneous biaxial anisotropic objects embedded in uniaxial anisotropic media,and present complete solu?tions of the Green's functions,forward and inversion problems.Thus,the main contribu-tions of this work include three parts.Firstly,an effective method for solving the dyadic Green's functions of the magnetic vector potential for a homogeneous uniaxial medium is presented.Then we investigate the electromagnetic forward scattering of anisotropic objects embedded in uniaxial anisotropic homogeneous and layered media,respective-ly.Finally,based on the forward model,we study the multiparametric reconstruction of 3D inhomogeneous biaxial anisotropic objects embedded in layered uniaxial background media.This work starts with solving dyadic Green's functions of the magnetic vector potential A(DGFA)for a homogeneous uniaxial anisotropic magnetodielectric medium.The equa-tion of the DGFA is directly derived from the Maxwell's equations.Through the Fourier transform and the inverse Fourier transform,the triple integral form of the DGFA in the spatial domain is obtained.And it is finally simplified to Sommerfeld integrals to get the numerical solution.The singularity subtraction technique is used to reduce the oscillation amplitude of Sommerfeld integrands and expedite decaying to accelerate the numerical calculation of DGFA.At the same time,the singularity in the z axis is discussed and the weak form of DGFA is given.Electromagnetic inversion is using the method of computational electromagnetism to in?fer the structures and electromagnetic properties of the unknown objects.Its purpose is to provide reference for practical engineering applications.The electromagnetic forward simulation is very important for electromagnetic inversion.Therefore,the second task of this work is to study the efficient algorithms for electromagnetic forward in the uniaxial background media.The stabilized biconjugate gradient fast Fourier transform(BCGS-FFT)method has been successfully used to solve the forward electromagnetic scattering of 3D inhomogeneous biaxial anisotropic magnetodielectric objects embedded in uniax?ial anisotropic homogeneous medium and the forward electromagnetic scattering of 3D inhomogeneous biaxial anisotropic dielectric objects embedded in uniaxial anisotropic layered media,respectively.For the magnetodielectric objects,the weak forms of coupled field volume integral equations are formulated by using the mixed-order basis functions to expand the flux densities(D,B)and the vector potentials(A,F).For the dielectric ob-jects,The electric field integral equation(EFIE)is formulated by using the first-order 3D volumetric rooftop basis function to expand electric flux density D and magnetic vector potential A.In both cases,the situation that the optical axis of the background media not aligned with the optical axis of the scatterer medium is also considered.Finally,multiparametric reconstruction of 3D inhomogeneous biaxial anisotropic objects embedded in layered uniaxial media is developed.The optical axes of both the scatterers and the background media are perpendicular to the layer interface.Meanwhile,the scat-terers and the background medium are non-magnetic and lossy.In the forward model,BCGS-FFT is used to solve the electric field integral equation.In order to simultaneously invert permittivity and conductivity,we formulate the variational inversion real data e-quation based on multifrequency scattering field data in the inversion model.Proper range constraints for the multiparametric unknowns are used to avoid non-physical values.There are six parameters to be reconstructed for both the permittivity and conductivity.Noting that these six parameters usually share the same geometry structure,we develop a struc-ture consistency constraint(SCC)algorithm based on the Monte Carlo method to reduce the reconstruction region as well as the unknowns in the nonlinear inversion iterations.Fi-nally,VBIM with SCC is employed to minimize the cost function subject to the inversion data equation.All the theory and solutions in this thesis have been verified by corresponding numerical examples.The results show that the forward and inversion of anisotropic electromagnetic scattering in uniaxial anisotropic background media are feasible and effective.The pro-posed VBIM with SCC shows significant advantages over the traditional VBIM method.