Inverse scattering in the time domain: an iterative method using an FDTD sensitivity analysis scheme

A scatterer reconstruction technique, which is based on the inversion of electromagnetic total-field measurements in the time domain, is presented. The spatial distributions of the permittivity, permeability, and conductivity inside the domain of study are estimated, simultaneously, by applying the Polak-Ribiere conjugate-gradient optimization algorithm. This algorithm minimizes a functional, which represents the difference between the measured and the calculated values of the total field. The latter are computed, under the current estimate of the scatterer profile, by using the finite-difference time-domain method. In addition, the Maxwell's equations satisfied by the calculated field are introduced to the functional as constraints. The gradients of the augmented functional, which are needed for the application of the Polak-Ribiere algorithm, are given by the calculus of variations. Furthermore, the possibility of utilizing an adjoint-state-vector methodology is illustrated. In numerical results, the presented technique is applied successfully to the reconstruction of multiple two-dimensional scatterers.