Reconstruction of thickness variation of a dielectric coating through the generalized impedance boundary conditions

Abstract

We deal with an inverse scattering problem whose aim is to determine the thickness variation of a dielectric thin coating located on a conducting structure of unknown shape. The inverse scattering problem is solved through the application of the Generalized Impedance Boundary Conditions (GIBCs) which contain the thickness, curvature as well as material properties of the coating and they have been obtained in the previous work [B. Aslanyürek, H. Haddar and H. Şahintürk, Wave Motion 48 (2011) 681-700] up to the third order with respect to the thickness. After proving uniqueness results for the inverse problem, the required total field as well as its higher order derivatives appearing in the GIBCs are obtained by the analytical continuation of the measured data to the coating surface through the single layer potential representation. The resulting system of non-linear differential equations for the unknown coating thickness is solved iteratively via the Newton−Raphson method after expanding the thickness function in a series of exponentials. Through the simulations it has been shown that the approach is effective under the validity conditions of the GIBCs.

Reconstruction of generalized impedance functions for 3D acoustic scattering

“…The inverse problem we are interested in is to determine the surface impedance functions for a given obstacle from the knowledge of the far field pattern for a few incident plane waves. This problem appears in practical application such as NDT for detecting porosity, reconstruction of surface roughness or coating thickness, [3], for modeling related to stealth technology or antennas, [4]. Additionally, it is motivated by the need to minimize the wave reflected by the obstacle in some directions what can be achieved by introducing a coating on the surface of the obstacle.…”