ABSTRACT

The problem of recovering the permittivity profile of stratified dielectric media from the reflection factor values measured for probe electromagnetic plane waves at a finite set of frequencies is of topical importance one for the development of novel methods of nondestructive inspection. To solve the problem, the initial ones are reduced to the search of an optimal control (permittivity profile) of the Cauchy problem for the Riccati equation. The procedure of construction of the optimal control is based on minimizing the appropriate functional. A criterion is suggested for the selection of polynomial approximations of the permittivity profile, which uses separation of the input data into the learning and checking sequences of the sounding frequencies. The error of recovering the imaginary part of the stratified medium permittivity is analyzed. It is shown that the relative restoration error in the cases of rather small (Im_ε ~ 10^-4) and great (Im_ε ≥ 0.1) values of the imaginary part of the dielectric constant does not exceed 10 % and is less than 1 %, respectively. The developed algorithms make it possible to recover the complex permittivity of stratified media to an accuracy which is acceptable for practical applications.