Three-dimensional reconstructing of objects buried in spherically multilayered medium using Born Iterative Methods

摘要

In this paper, we applied the Born Iterative Method (BIM) to reconstruct three-dimensional inhomogeneous objects buried in spherically multilayered media. The nonlinear inverse problem is linearized by Born approximations and solved iteratively via the conjugate-gradient approach (CG). The forward scattering problem in the spherically multilayered media is solved by stabilized biconjugate-gradient fast Fourier transform method (BCGS-FFT). The dyadic Greens' functions for spherically multilayered media are constructed using the method of scattering superposition and the recurrence equation system of coefficient matrix. Numerical results showed that these methods are capable of solving the EM scattering problem and inverse problems for inhomogeneous objects of arbitrary shape buried in spherically multilayered media. Figure 1 illustrates the comparison of the electric fields inside the scatter between the simulation results from the commercial software Wavenology and our solutions in spherically three-layered media with the scatter entirely embedded in the second layer. As illustrated in Figure 1(a), an inhomogeneous cuboid is embedded entirely in the second layer in a spherically three-layered medium where r1 = 20m and r2 = 10 m. The three-layered medium is characterized by ∈r1 = 1, σ1 = 0, ∈r2 = 2, σ2 = 0.001 S/m, ∈r3 = 4, σ3 = 0.001 S/m and μr = 1 for all three layers. The electrical parameters of the scatter are ∈rs = 6, σrs = 0.001 S/m and μrs = 1. The center of the scatter is located at (7.25, 7.25.7.25)m and the dimension of the cube is 0.5 × 0.5 × 0.5 m. The electric dipole source is distributed at (15, 15, 15) m. We use Nx = Ny = Nz = 10 for discretization and choose 50MHz to do the calculation. The total electric field of Ez inside the scatter caused by the electric dipole is compared with Wavenology, as is shown in Figures 1(b) and (c).