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.