Gap detection with electromagnetic terahertz signals

We apply an inverse problem formulation to determine characteristics of a defect from a perturbed electromagnetic interrogating signal. A defect (gap) inside of a dielectric material causes a disruption, via reflections and refractions at the material interfaces, of the windowed interrogating signal. We model the electromagnetic waves inside the material with Maxwell's equations. This leads to a non-standard, nonlinear optimization problem for the dimensions and location of the defect. Using simulations as forward solves, we employ a Newton-based, iterative optimization scheme to a novel modified least-squares objective function. Numerical results are given in tables and plots, standard errors are calculated, and computational issues are addressed.