Time-Domain Inverse Electromagnetic Scattering using FDTD and Gradient-based Minimization

The thesis addresses time-domain inverse electromagnetic scattering for determining unknown characteristics of an object from observations of the scattered field. Applications include non-destructive characterization of media and optimization of material properties, for example the design of radar absorbing materials. Another interesting application is the parameter optimization of subcell models to avoid detailed modeling of complex geometries. The inverse problem is formulated as an optimal control problem where the cost function to be minimized is the difference between the estimated and observed fields, and the control parameters are the unknown object characteristics. The problem is solved in a deterministic gradient-based optimization algorithm using a parallel 2D FDTD scheme for the direct problem. This approach is computationally intensive since the direct problem needs to be solved in every optimization iteration in order to compute an estimated field. Highly accurate analytical gradients are computed from the adjoint formulation. In addition to giving better accuracy than finite differences, the analytical gradients also have the advantage of only requiring one direct and one adjoint problem to be solved regardless of the number of parameters. When absorbing boundary conditions are used to truncate the computational domain, the equations are non-reversible and the entire time-history of the direct solution needs to be stored for the gradient computation. However, using an additional direct simulation and a restart procedure it is possible to keep the storage at an acceptable level. The inverse method has been successfully applied to a wide range of industrial problems within the European project, IMPACT (Inverse Methods for Wave Propagation Applications in Time-Domain). The results presented here include characterization of layered dispersive media, determination of parameters in subcell models for thin sheets and narrow slots and optimization problems where the observed field is given by design objectives. ISBN 91-7283-800-0 • TRITA-NA-0414 • ISSN 0348-2952 • ISRN KTH/NA/R-04/14-SE