Analytic continuation methods for reconstructing electromagnetic data

Analytic continuation methods for reconstructing electromagnetic data are investigated with focus on two areas of application: the analytic continuation of constitutive material data and the analytic continuation of scattering data.;The second area of interest is the phase retrieval problem because there are several electromagnetic measurement applications where the wave phase is lost or impractical to measure. The case of far field electromagnetic scattering where only amplitude data is available is addressed specifically. A new derivation of the conditions under which the phase reconstruction is unique is given. Then, the Spectral Iteration Technique (SIT) is described that enforces the uniqueness condition as it automatically reconstructs the missing phase information. Numerical experiments are used to prove the fidelity of the algorithm, with the reconstructed phase differing from the original data by less than 0.1 percent regardless of the initial guess. The application of the algorithm to the defect detection problem is demonstrated.;Because all dielectrics are dispersive, the frequency dependence of the material properties must be modeled in a well-defined way whenever microwave structures are expected to operate over broad bands of frequency. The well known analytic properties of the permittivity can be used to generate such models by fitting them to experimental data using non-linear optimizers. However, in that approach the questions of convergence to the true global solution and the sensitivity to experimental noise remain open. Here, it is shown that an automated deterministic approach to generate such a model for the important case of multi-Debye relaxation materials can be implemented. The method is compared to a recently proposed alternate approach: hybrid particle swarm-least squares optimization method (PSO/LS) that was demonstrated on data sets of idealized pure multi-Debye materials assuming the availability of bandwidths in excess of 10,000:1. As with most optimizers, that method requires an initial guess and the ad-hoc adjustment of the iteration parameters. In this study, no arbitrary parameters need be set to guarantee convergence. The case of materials with DC conductivity (imaginary permittivity growing to infinity at DC) is as easily dealt with as the conventional pure multi-Debye case. Physically realizable results are generated even when the bandwidth of data spans a frequency range as small as 18:1.