Estimation of the accuracy of reconstruction of electrophysical and geometric parameters by the polarimetric method of multilayer dielectric medium

The development of methods for quantitative interpretation of the results of monitoring the electrophysical and geometric parameters of a multilayer medium is one of the most important problems in assessing its state, both practical and theoretical significance. The paper presents the results of a study of the potential informativeness of the method for remote identification of the state of snow-ice cover by the ratio of Fresnel reflection coefficients, using an ultra-wideband linear-frequency-modulated signal in the reconstruction of electrophysical and geometric parameters of multilayer dielectric medium. An estimation of the accuracy of reconstruction of electrophysical and geometric parameters of multilayer dielectric medium is presented, taking into account the values of electrophysical and geometric parameters of the medium layers, the noise level in the measurement data and the measurement bandwidth. The results of simulation modeling of the reconstruction of the relative permittivity and thickness of a multilayer medium in the form of snow-ice cover at different values of the mean square deviation of the noise level in the polarization relations of the measured reflection coefficients of the electromagnetic wave are presented. It is established that the accuracy of reconstruction of the electrophysical parameters of the layers of snow-ice cover decreases with increasing noise level, as well as with decreasing permittivity and layer thickness. The results of experimental studies confirm the adequacy of the developed simulation model. The presented model allows us to quantify the potential accuracy of reconstruction of the electrophysical parameters of multilayer dielectric medium for a specific measuring complex that implements the multi-frequency method of electromagnetic waves. Experimental studies and simulation results of a multi-layer dielectric medium in the form of snow-ice cover have demonstrated the theoretical possibilities of obtaining the relative permittivity and thick-ness of individual layers with a relative error of no more than 10 %, with a measurement band of 6 GHz and an RMS of the noise level of 3.8–4.8.

1. Finkelstein M.I., Lazarev E.I., Chizhov A.N. Radar aeroledomeric surveys of rivers, lakes, reservoirs; ed. by Finkelstein M.I. Leningrad: Gidrometeoizdat. 1984. (In Russ)

2. Order of the Ministry of Transport of the Russian Federation no. 128 of July 31, 2009 "On Approval of the Federal Aviation Regulations" Preparation and Execution of flights in Civil Aviation of the Russian Federation". Available at: https://base.garant.ru/196235/ (accessed 11.03.2021). (In Russ)

3. Grinev A.Yu., Temchenko V.S., Bagno D.V. Radars of subsurface sounding. Monitoring and diagnostics among the features of the Monograph. M.: Radio Engineering. 2013. (In Russ)

4. Pennock S.R., Redfern M.A. Optimising Multihead Configurations for Depth Determination in Ground Penetrating Radar. Proc. of the Euro-pean Conference on Antennas and Propagation. 06–10 Nov. 2006, Eu-CAP, Nice, France. 2006 .

5. Kazmin A.I., Fedyunin P.A. Evaluation of the accuracy of reconstruction of electrophysical and geometric parameters of multilayer dielectric coatings by the multi-frequency radio-wave method of surface slow electromagnetic waves. Measuring equipment. 2020;8:51–58. Available at: https://izmt.ru/kurilka/admin/izmt/2020/8/19550188055f6b45e294ec9.pdf. DOI: 10.32446/0368-1025it.2020-8-51-58 (In Russ) DOI: 10.32446/0368-1025it.2020-8-51-58 (accessed 11.03.2021).

6. Mikhnev V.A., Nyfors E., Vainkainen P., IEEE Transactions on Antennas and Propagation. 1997;45(9):1405–1410. DOI:10.1109/8.623130

7. Mohamed Abou-Khousa, Zoughi R., IEEE Transactions on instrumentation and measurement. 2007;56(4):1107–1113. DOI:10.1098/rspa.2009.0664

8. Borulko V.F., Drobakhin O.O., Slavin I.V. Multi-frequency microwave non-destructive methods for measuring parameters of layered dielectrics. Dnepropetrovsk: DSU Publishing House. 1982. (In Russ)

9. Andreev M.V., Borulko V.F., Drobakhin O.O. Application of the quasi-solution concept for determining the parameters of layered dielectric structures based on measurements of reflection characteristics at many frequencies. Part I. Flaw detection. 1995;12:41–50. (In Russ)

10. Akhmetshin A.M., Slavin V.I., Tikhy V.G., Platonov E.D. Identification of layered dielectric structures by parametric optimization in multi-frequency microwave introscopy. Flaw detection. 1983;12:57–65. (In Russ)

11. Mashkov V.G. Method of remote identification of the state of the snow-ice cover by the relations of the Fresnel reflection coefficients. Izv. vuzov Rossii. Radio electronics. 2020;23(5):46-56. Available at: https://re.eltech.ru/jour/article/view/467. DOI:10.32603/1993-8985-2020-23-5-46-56 (In Russ) DOI:10.32603/1993-8985-2020-23-5-46-56 (accessed 11.03.2021).

12. Brovchenko A.V., Vertiy A.A., Melezhik N.P., Melezhik P.N., Duelchuk A.E. One-dimensional inverse problems of electromagnetic sounding of layered dielectric media. Applied Radiophysics. 2015;6(20)(4):92–97. (In Russ)

13. Denisova N.A., Rezvov A.V. The inverse problem of reflection of electromagnetic waves for a layered-inhomogeneous half-space with a real permittivity without dispersion. Izvestiya vuzov. Radiophysics. 2012;LV(5):369–379. Available at: https://radiophysics.unn.ru/sites/default/files/papers/2012_5_369.pdf (accessed 11.03.2021). (In Russ)

14. Avdochenko B.I., Zadorin A.S., Zabotinsky V.A., Ilyin A.A., Kruglov R.S., Litvinov R.V., Sialkot A.A. Restoring the dielectric permittivity of the layered medium in the frequency dependence of the reflection coefficient by minimizing the regularizing functional: the collection of reports of TUSUR. Voronezh, June 2007 Voronezh: TUSUR. 2007:5–9. (In Russ)

15. Batrakov D.O., Simachev A.A. Restoration of the profile of the dielectric permittivity of a planar-layered medium taking into account the dispersion in frequency sounding. Bulletin of the V.N. Karazin Kharkiv National University. Radiophysics and Electronics Series. 2009;883:45–49. (In Russ)

16. Coen S. Inverse scattering of a layered and dispersionless dielectric half-space, IEEE Trans. Antennas Propagat. 1981;29:726–732.

17. Balanis G.N. Inverse scattering: Determination of inhomogeneites in sound speed, J. Math. Phys. 1982;23:2562–2568.

18. Denisova N.A., Stepanova S.A. The inverse problem of restoring the dielectric constant with a discontinuous profile. ZHVMMF. 1999;39(7):1180-1187. (In Russ)

19. Avdochenko B.I., Zadorin A.S., Zamotrinsky V.A., Ilinykh A.A., etc. Restoration of the dielectric permittivity of a layered medium from the frequency dependence of the reflection coefficient by minimizing the regularizing functional. Reports of TUSUR. 2007;1:5–8. (In Russ)

20. Rezvov A.V., Denisova N.A. On the reconstruction of the profile of the refractive index of a layered-inhomogeneous dielectric medium by the amplitude and energy reflection coefficients. Available at: http://www.mivlgu.ru/conf/ormand 2012/pdf/S3_19.pdf (accessed 18.02.2021). (In Russ)

21. Kazmin A.I., Fedyunin P.A. Restoration of the structure of electrophysical parameters of multilayer dielectric materials and coatings according to the frequency dependence of the attenuation coefficient of the field of a surface electromagnetic wave. Measuring equipment. 2019;9:39–45. Available at: https://izmt.ru/kurilka/admin/izmt/2019/9/21123204785da0565c919c8.pdf. DOI:10.32446/0368-1025it.2019-9-39-45 (In Russ) DOI:10.32446/0368-1025it.2019-9-39-45 (accessed 18.02.2021).

22. Fedyunin P.A., Kazmin A.I., Manin V.A. SHF-method of flaw detection of radio-absorbing coatings and a device for its implementation. Diagnostics. 2017;11:32–39. Available at: http://www.td-j.ru/index.php/current-issue-rus/1526-032-039. DOI:10.14489/td. 2017.11. pp.032-039 (In Russ) DOI:10.14489/td. 2017.11. pp.032–039 (accessed 18.02.2021).

23. Brekhovskikh L.M. Waves in layered medum. M.: Nauka. 1973. (In Russ)

24. Karpov I.G. Approximation of experimental distributions of radar signals using modernized Pearson distributions. Radiotekhnika. 2003;5:56–61. (In Russ)

25. Pozdnyak S.I., Melititsky V.A. Introduction to the statistical theory of radio wave polarization. Moscow: Sov. radio. 1974. (In Russ)

26. Certificate of official registration of the computer program no. 2020618468 Russian Federation. Identification of snow-ice cover layers by the polarization relations of Fresnel reflection coefficients. Mashkov V.G., (RU); copyright holder Mashkov V.G. no. 2020615405; declared on 26.05.2020; registered in the Register of Computer Programs on 29.07.2020. (In Russ)

27. Alexandrov P.N. Theoretical foundations of the georadar method: Monograph. Moscow: FIZMATLIT, 2017. (In Russ)

28. Guido Valerio, David R. Jackson, Alessandro Galli. Proceedings of the Royal Society. 2010;466:2447–2469. DOI:10.1098/rspa.2009. 0664

29. Shostak A.S., Zagoskin V.V., Lukyanov S.P., Karaush A.S. On the possibility of determining the dielectric permittivity of the upper layers of underlying media from the measured reflection coefficients during oblique sounding by plane waves of vertical and horizontal polarization in the microwave range. Journal of Radioelectronics. 1999. (In Russ)

30. RF Patent no. 2613810, IPC G01R 27/00 (2006.01). Method for measuring the relative complex permittivity of a material with losses in the microwave range. Valeev G.G.; applicant and patent holder Valeev G.G. Application no. 2015142390 of 06.10.2015. Published on 21.03.2017. Byul. no. 9. (In Russ)

31. RF patent no 2623668, IPC G01N 27/06 (2006.01) G01R 27/26 (2006.01). Method for determination of the relative dielectric constant of the medium under the edge of the atmosphere-ocean. Zapevalov A.S.; applicant and patentee of MGI wounds. Application no. 2015156757 dated 28.12.2015. Published on 28.06.2017. Byul. no. 19. (In Russ)

32. Pinchuk A.N. Influence of the polarization of the sounding radio signal on the efficiency of the selection of the response of a surface target. Nauka i obrazovanie. Bauman Moscow State Technical University. 2015;3:140–152. Available at: http://engineering-science.ru/doc/760670.html. DOI:10.7463/0315.0760670 (In Russ) (accessed 18.02.2021).