ONE-DIMENSIONAL INVERSE PROBLEMS OF ELECTROMAGNETIC PROBING STRATIFIED DIELECTRIC MEDIA

The problem of permittivity profile reconstruction from reflection coefficient data for a stratified dielectric medium illuminated with a probing plane electromagnetic wave at a finite set of frequencies is considered to deal with a topical problem in the context of the development of state-of-the-art nondestructive methods of testing. The initial problem is reduced to the search of an optimal control (permittivity profile) of the Cauchy problem for the Riccati equation. The optimal control is treated in the class of polynomial functions and is based on the minimization of a relevant functional. A criterion is suggested for choosing polynomial approximations to the permittivity profile, which separates input data sets between training and test sequences of probing frequencies. Error analysis made for the reconstruction of the permittivity imaginary part in a stratified medium shows that the relative error of the reconstruction does not exceed 10 % when the permittivity imaginary part is small (Ime ~ 10^–4) and it is under 1 % when the permittivity imaginary part is large (Ime ³ 0.1). The developed algorithms can reconstruct the complex permittivity in a stratified medium to accuracy appropriate for practical applications.