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We consider a topological derivative based imaging technique for non-iterative imaging of small and extended perfectly conducting cracks with Dirichlet boundary condition. For this purpose, we introduce topological derivative imaging function based on the asymptotic formula in the existence of narrow crack. We then mathematically analyze its structure in order to investigate why it yields the shape of crack(s). Analyzed structure gives us an optimal condition to get a better image of them. Various numerical experiments support our analysis.

ANALYSIS OF TOPOLOGICAL DERIVATIVE FUNCTION FOR A FAST ELECTROMAGNETIC IMAGING OF PERFECTLY CONDUCING CRACKS