Hilbert-Riemann problems in recovering parameters of a plane layered dielectric on conducting substrate

An inverse scattering problem for electromagnetic wave normal incidence on a plane layered structure with perfect conducting substrate is considered in the paper. The initial data is a frequency dependence of the reflection coefficient, phase characteristic of which provides information to extract optical depth of the structure and formulate two Hilbert-Riemann problems. Successive solutions of these problems allow reduction of the inverse problem to a trivial one, where both thickness and permittivity of layers are recovered from scattering coefficients in form of finite trigonometric series. Determination of electrical parameters and thickness of layered coatings that are used for electrical isolation and protection from corrosion of metal surfaces, is one of the most important problems of nondestructive evaluation. This problem is considered in the paper as an inverse scattering problem (ISP) for interaction of a plane electromagnetic wave with a plane layered dielectric on perfect conducting surface. Unlike the ISP for pure dielectrics, less attention is paid to the considered problem, although similar ISPs occur in many different applications [1, 2]. One of approaches is a treatment of the problem in time domain [3], where pulse response of the structure is considered only within period of wave propagation time until the pulse fully reflects from a perfect conducting substrate. Another idea of rigorous derivation of ISP solution is developed in the paper to represent the inverse problem as one for a pure dielectric medium with a piecewise-constant function of permittivity.