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A NUMERICAL ANALYTICAL METHOD FOR SOLVING REVERSE PROBLEMS OF WAVE DIFFRACTION BY LAYERED INHOMOGENEOUS MEDIA

Brovenko, AV, Vertiy, AA, Melezhik, NP, Melezhik, PN, A. Poyedinchuk, Y
Organization: 

O. Ya. Usikov Institute for Radiophysics and Electronics of the National Academy of Sciences of Ukraine
12, Proskura st., Kharkov, 61085, Ukraine

L. N. Gumilyov Eurasian National University
Astana, 2 Mirzoyan st., Astana, 010000, Republic of Kazakhstan

E-mail: melezhik@ire.rharkov.ua

https://doi.org/10.15407/rej2015.01.013
Language: Russian
Abstract: 

A numerical analytical method of the reverse problem solution is suggested for the relative permittivity profile of layered inhomogeneous media to be obtained from the frequency dependence of the reflection coefficient of a monochromatic plane electromagnetic wave. The idea of the method is to reduce the initial reverse problem to the optimal control problem of the Riccati equation. The solution scheme employs a numerical analytical method for the direct problem solution of monochromatic plane wave diffraction by layered inhomogeneous media and takes advantage of some algorithm developed for smoothing the gradient of the residual functional. With the algorithms elaborated for solving the direct and reverse problems of wave diffraction by layered structures, a series of numerical experiments has been performed, the efficiency of the suggested approach in not a direct determination of layered structure parameters is demonstrated.

Keywords: reflection coefficient, regularization technique, residual functional, reverse problem

Manuscript submitted 12.12.2014
PACS 02.30.Zz; 02.60.Cb; 42.25.Fx
Radiofiz. elektron. 2015, 20(1): 13-25
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References: 
  1. Shanda, E., 1990. Physical fundamentals of remote sensing. Moscow: Nedra Publ. (in Russian).
  2. Pike, R. and Sabatier, P., 2002. Scattering and inverse scattering in pure and applied science. San Diego: Academic Press.
  3. Lavrentiev, M. M., Reznitskaya, K. G., and Yakhno, V. G., 1982. One-dimensional inverse problems of the mathematical physics. Novosibirsk: Nauka Publ. (in Russian).
  4. Khruslov, E. Y., 1982. An inverse problem of the theory of electromagnetic sounding. Uspekhi matematicheskih nauk. 37(4), pp. 107–108 (in Russian).
  5. Marchenko, V. A., 1976. Sturm-Liouville operators and their applications. Kiev: Naukova dumka Publ. (in Russian).
  6. Gelfand, I. M. and Levitan, B. M., 1951. Definition of differential equations from their spectral function. Izv. Akad. Nauk SSSR. Ser. Matematika. 15(4), pp. 309–360 (in Russian).
  7. Khruslov, E. Y., 1985. One-dimensional inverse problems of electrodynamics. Zh. vychislitelnoy matematiki i matematicheskoy fiziki. 25(4), pp. 548–561 (in Russian).
  8. Kovensky, S. Y. and Tikhonravov, A. V., 1988. Synthesis of absorbing stratified media. Zh. vychislitelnoy matematiki i matematicheskoy fiziki. 28(6), pp. 887–900 (in Russian).
  9. Drobakhin, O. O. and Alexin, S. G., 2012. Solution of inverse problems for multi-layer dielectric structures. Dnipropetrovsk: DNU Publ. (in Ukrainian).
  10. Tijhuis, A. J. and Van der Worn, C., 1984. Iterative approach to the frequency-domain solution of the inverse scattering problem for an inhomogeneous lossless dielectric slab. IEEE Trans. Antennas Propag. 32(7), pp. 711–716.DOI: https://doi.org/10.1109/TAP.1984.1143410
  11. Yung Chen, 1979. An iterative procedure for solving inverse problem arising from active remote sensing. In: Proc. Conf. Held at Catholic University Washington. Mathematical Methods and Applications of Scattering Theory. Washington, USA, 21–25 May 1979.
  12. Batrakov, D. O. and Tarasov, M. M., 1999. An algorithm for solving inverse problems of scattering on the basis of the Pontrjagin maximum principle. Radiotekhnika i elektronika. 44(2), pp. 137–142 (in Russian).
  13. Batrakov, D. O. and Simachev, A. A., 2009. Dielectric permittivity profile reconstruction by frequency probing problem for a plane-layered media with regard to dispersion. Vestnik KhNU. Ser. Radiophysics and Electronics. 15(883), pp. 45–49 (in Russian).
  14. Tikhonov, A. N. and Arsenin, V. Y., 1986. Methods of solving ill-posed problems. Moscow: Nauka Publ. (in Russian).
  15. Dmitriev, V. I., 1986. Inverse problems of electromagnetic methods in geophysics. Moscow: Moscow State University Publ. (in Russian).
  16. Brovenko, A. V., Melezhik, P. N., Panin, S. B., and Poyedinchuk, A. E., 2013. A semi-analytical method for solving problems of wave diffraction by inhomogeneous layer structures. Physical bases of instrumentation. 2(1), pp. 34–47 (in Russian).
  17. Chandezon, J., Granet, G., Melezhik, P. N., Poyedinchuk, A. Ye., Sirenko, Yu. K. ed., Sjöberg, D., Ström, S. ed., Tuchkin, Yu. A., Yashina, N. P., 2010. Modern Theory of gratings. Resonant scattering: analysis techniques and phenomena. N. Y.-Dordrecht-Heidelberg-L.: Springer-Verlag.
  18. Vasiliev, F. P., 1973. Numerical methods of solving extremal problems. Moscow: Nauka Publ. (in Russian).
  19. Brekhovskih, L. M., 1973. Waves in the layered media. Moscow: Nauka Publ. (in Russian).