Inverse electromagnetic scattering for a locally perturbed perfectly conducting plate

•The linear sampling method is applied to reconstruct the shape of a local perturbation of a perfectly conducting plate from far-field measurements of time harmonic electromagnetic fields.•The linear sampling method with near-field data is also discussed.•Numerical examples in case of far-field data, limited aperture data and near-field data are included to illustrate the feasibility of this method.

We consider a simple but fully three-dimensional inverse problem to determine the shape of a local perturbation of a perfectly conducting plate from far-field measurements of time harmonic electromagnetic fields. For this purpose we reformulate the model problem as an exterior Maxwell problem for a symmetric domain, and prove an equivalence between the model problem and its reformulation. Then, linear sampling method is applied to solve the reformulated problem. We illustrate the feasibility of this method by some numerical examples.