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Telecommunications and Radio Engineering

ISSN Print: 0040-2508
ISSN Online: 1943-6009

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Telecommunications and Radio Engineering

DOI: 10.1615/TelecomRadEng.v75.i6.10
pages 477-487

ONE-DIMENSIONAL INVERSE PROBLEMS OF ELECTROMAGNETIC SOUNDING OF STRATIFIED DIELECTRIC MEDIA

A. V. Brovenko
A. Usikov Institute of Radio Physics and Electronics, National Academy of Sciences of Ukraine, 12, Academician Proskura St., Kharkiv 61085, Ukraine
Alexey A. Vertiy
L.N. Gumilyov Eurasian National University, 2, Mirzoyana St., Astana 010000, Republic of Kazakhstan
N. P. Melezhik
A.Ya. Usikov Institute for Radiophysics and Electronics of the National Academy of Sciences of Ukraine 12, Academician Proskura St., Kharkiv 61085, Ukraine
P. N. Melezhik
A. Usikov Institute of Radio Physics and Electronics, National Academy of Sciences of Ukraine 12, Academician Proskura St., Kharkov 61085, Ukraine
A. Ye. Poyedinchuk
A. Usikov Institute of Radio Physics and Electronics, National Academy of Sciences of Ukraine, 12, Academician Proskura St., Kharkov 61085, Ukraine

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 (Imε ~ 10-4) and great (Imε ≥ 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.