Topological Derivative for Imaging of Thin Electromagnetic Inhomogeneity: Least Condition of Incident Directions

Abstract EN

It is well-known that using topological derivative is an effective noniterative technique for imaging of crack-like electromagnetic inhomogeneity with small thickness when small number of incident directions are applied.

However, there is no theoretical investigation about the configuration of the range of incident directions.

In this paper, we carefully explore the mathematical structure of topological derivative imaging functional by establishing a relationship with an infinite series of Bessel functions of integer order of the first kind.

Based on this, we identify the condition of the range of incident directions and it is highly depending on the shape of unknown defect.

Results of numerical simulations with noisy data support our identification.