Fast shape reconstruction of perfectly conducting cracks by using a multi-frequency topological derivative strategy

This paper concerns a fast, one-step iterative technique of imaging extended perfectly conducting cracks with Dirichlet boundary condition. In order to reconstruct the shape of cracks from scattered field data measured at the boundary, we introduce a topological derivative-based electromagnetic imaging function operated at several nonzero frequencies. The properties of the imaging function are carefully analyzed for the configurations of both symmetric and non-symmetric incident field directions. This analysis explains why the application of incident fields with symmetric direction operated at multiple frequencies guarantees a successful reconstruction. Various numerical simulations with noise-corrupted data are conducted to assess the performance, effectiveness, robustness, and limitations of the proposed technique.Comment: 17 pages, 27 figure

Multi-frequency imaging of perfectly conducting cracks via boundary measurements

Imaging of perfectly conducting crack(s) in a 2-D homogeneous medium using boundary data is studied. Based on the singular structure of the Multi-Static Response (MSR) matrix whose elements are normalized by an adequate test function at several frequencies, an imaging functional is introduced and analyzed. A non-iterative imaging procedure is proposed. Numerical experiments from noisy synthetic data show that acceptable images of single and multiple cracks are obtained.Comment: 4 pages, 3 figure