Time-Domain Microwave Imaging of Inhomogeneous Debye Dispersive Scatterers

A time-domain inverse scattering method for the reconstruction of inhomogeneous dispersive media described by the Debye model is presented. The method aims to the simultaneous reconstruction of the spatial distributions of the optical and static permittivity as well as of the relaxation time. The reconstruction of the scatterer is based on the minimization of a cost functional, which describes the difference between measured and estimated values of the electric field. The fulfillment of the Maxwell's curl equations is set as constraint by means of Lagrange multipliers in an augmented functional. The Fréchet derivatives with respect to the scatterer properties are derived analytically and can be utilized by any gradient-based optimization technique. The proposed reconstruction technique is based on the Polak-Ribière nonlinear conjugate-gradient algorithm, while the finite-difference time-domain (FDTD) method is employed for the solution of the direct and the adjoint electromagnetic problem. Numerical results for the reconstruction of one-dimensional layered scatterers illustrate the performance of the proposed method.