volume | PIER Journals

Abstract

The goal of the present paper is on retrieving the electrical and geometrical parameters of a stratified medium with two rough interfaces. The inversion problem is formulated as a cost function optimization problem, and it is solved using the simulated annealing algorithm. The cost function consists in the integrated squared deviation between the co-polarized incoherent intensities obtained from the Small Slope Approximation and those obtained from the Small Perturbation Method. The inversion scheme is applied to the electrical and geometrical parameters involved into the analytical expressions of the incoherent intensities given by the SPM. We study the influence of the shape of the autocorrelation function and the isotropy factor upon the estimation of parameters. We test the sensitivity of the inversion scheme to noisy synthetic data. The study is applied to snow-covered soils in L-band. For the configurations under study, we show that the inverse method is efficient for eight-parameter or ten-parameter predicting problems.

1. Tabatabaeenejad, A. and M. Moghaddam, "Study of validity region of small perturbation method for two-layer rough surfaces," IEEE Geosci. Remote Sens. Lett., Vol. 7, No. 2, 319-323, Apr. 2010.
doi:10.1109/LGRS.2009.2034543 Google Scholar

2. Imperatore, P., A. Iodice, M. Pastorino, and N. Pinel, "Modelling scattering of electromagnetic waves in layered media: An up-to-date perspective," Int. J. Antennas Propag., Vol. 2017, 1-14, 2017.
doi:10.1155/2017/7513239 Google Scholar

3. Amra, C., M. Lequime, and M. Zerrad, Electromagnetic Optics of Thin-film Coatings: Light Scattering, Giant Field Enhancement, and Planar Microcavities, Cambridge University Press, 2021.

4. El-Shenawee, M., "Polarimetric scattering from two-layered two dimensional random rough surfaces with and without buried objects," IEEE Trans. Geosci. Remote Sens., Vol. 42, No. 1, 67-76, Jan. 2001.
doi:10.1109/TGRS.2003.815675 Google Scholar

5. Dechamps, N., N. de Beaucoudrey, C. Bourlier, and S. Toutain, "Fast numerical method for electromagnetic scattering by rough layered interfaces: Propagation-inside-layer expansion method," J. Opt. Soc. Amer. A, Vol. 23, No. 2, 359, Feb. 2006.
doi:10.1364/JOSAA.23.000359 Google Scholar

6. Dechamps, N. and C. Bourlier, "Electromagnetic scattering from a rough layer: Propagation-inside-layer expansion method combined to the forward-backward novel spectral acceleration," IEEE Trans. Antennas Propag., Vol. 55, No. 12, 3576-3586, Dec. 2007.
doi:10.1109/TAP.2007.910360 Google Scholar

7. Zamani, H., A. Tavakoli, and M. Dehmollaian, "Scattering from layered rough surfaces: Analytical and numerical investigations," IEEE Trans. Geosci. Rem. Sens., Vol. 54, No. 6, 3685-3696, Jun. 2016.
doi:10.1109/TGRS.2016.2524639 Google Scholar

8. Yang, Y. and K.-S. Chen, "Full-polarization bistatic scattering from an inhomogeneous rough surface," IEEE Trans. Geosci. Remote Sens., Vol. 57, No. 9, 6434-6446, Sep. 2019.
doi:10.1109/TGRS.2019.2906079 Google Scholar

9. Jonard, F., F. Ande, N. Pinel, C. Warren, H. Vereecken, and S. Lambot, "Modeling of multilayered media Green's functions with rough interfaces," IEEE Trans. Geosci. Remote Sens., Vol. 57, No. 10, 7671-7681, Oct. 2019.
doi:10.1109/TGRS.2019.2915676 Google Scholar

10. Tijhuis, A. G., Electromagnetic Inverse Profiling: Theory and Numerical Implementation, VNU, 1987.

11. Ghosh Roy, D. N. and L. S. Couchman, Inverse Problems and Inverse Scattering of Plane Waves, Academic Press, 1996.

12. Afifi, S. and M. Diaf, "Scattering by random rough surfaces: Study of direct and inverse problem," Optics Comm., Vol. 265, 11-17, 2006.
doi:10.1016/j.optcom.2006.02.044 Google Scholar

13. Tabatabaeenejad, A. and M. Moghaddam, "Inversion of subsurface properties of layered dielectric structures with random slightly rough interfaces using the method of simulated annealing," IEEE Trans. Geosci. Remote Sensing, Vol. 47, No. 7, 2035-2046, Jul. 2009.
doi:10.1109/TGRS.2008.2011982 Google Scholar

14. Elson, J. M., "Infrared light scattering from surfaces covered with multiple dielectric overlayers," Appl. Opt., Vol. 16, No. 11, 2873-2881, Nov. 1977. Google Scholar

15. Elson, J. M., J. P. Rahn, and J. M. Bennett, "Relationship of the total integrated scattering from multilayer-coated optics to angle of incidence, polarization, correlation length, and roughness cross-correlation properties," Appl. Opt., Vol. 22, No. 20, 3207-3219, Oct. 1983.
doi:10.1364/AO.22.003207 Google Scholar

16. Fuks, I. M., "Wave diffraction by a rough boundary of an arbitrary plane-layered medium," IEEE Trans. Antennas Propag., Vol. 49, No. 4, 630-639, Apr. 2001.
doi:10.1109/8.923325 Google Scholar

17. Tabatabaeenejad, A. and M. Moghaddam, "Bistatic scattering from three-dimensional layered rough surfaces," IEEE Trans. Geosci. Remote Sens., Vol. 44, No. 8, 2102-2114, Aug. 2006.
doi:10.1109/TGRS.2006.872140 Google Scholar

18. Imperatore, P., A. Iodiceand, and D. Riccio, "Electromagnetic wave scattering from layered structures with an arbitrary number of rough interfaces," IEEE Trans. Geosci. Remote Sens., Vol. 47, No. 4, 1056-1072, Apr. 2009.
doi:10.1109/TGRS.2008.2007804 Google Scholar

19. Afifi, S., R. Duseaux, and R. de Oliveira, "Statistical distribution of the field scattered by rough layered interfaces: Formulae derived from the small perturbation method," Waves Random Complex Media, Vol. 20, No. 1, 1-22, Feb. 2010.
doi:10.1080/17455030903329374 Google Scholar

20. Afifi, S. and R. Dusseaux, "Scattering by anisotropic rough layered 2D interfaces," IEEE Trans. Antenna Propagat., Vol. 60, No. 11, 5315-5328, Nov. 2012.
doi:10.1109/TAP.2012.2207671 Google Scholar

21. Zamani, H., A. Tavakoli, and M. Dehmollaian, "Scattering from two rough surfaces with inhomogeneous dielectric profiles," IEEE Trans. Antenna. Propag., Vol. 63, No. 12, 5753-5766, Dec. 2015.
doi:10.1109/TAP.2015.2490668 Google Scholar

22. Van Laarhoven, P. J. M. and E. H. L. Aarts, Simulated Annealing: Theory and Applications, Reidel, 1987.
doi:10.1007/978-94-015-7744-1

23. Kirkpatrick, S., C. D. Gelatt, and M. P. Vecchi, "Optimization by simulated annealing," Science, Vol. 220, No. 4598, 671-680, May 1983.
doi:10.1126/science.220.4598.671 Google Scholar

24. Kirkpatrick, S., "Optimization by simulated annealing: Quantitative studies," J. Stat. Phys., Vol. 34, No. 5/6, 975-986, Mar. 1984.
doi:10.1007/BF01009452 Google Scholar

25. Corana, A., M. Marchesi, C. Martini, and S. Ridella, "Minimizing multimodal functions of continuous variables with the "simulated annealin" algorithm," ACM Trans. Math. Soft., Vol. 13, No. 3, 262-280, Sep. 1987.
doi:10.1145/29380.29864 Google Scholar

26. Lee, K.-C., "Frequency-domain analyses of non-linearly loaded antenna arrays using simulated annealing algorithms," Progress In Electromagnetics Research, Vol. 53, 271-281, 2005.
doi:10.2528/PIER04101501 Google Scholar

27. Voronovich, G., Wave Scattering from Rough Surfaces, Springer, 1994.
doi:10.1007/978-3-642-97544-8

28. Voronovich, G., "Small-slope approximation for electromagnetic wave scattering at a rough interface of two dielectric half-spaces," Wave Random Media, Vol. 4, 337-367, 1994.
doi:10.1088/0959-7174/4/3/008 Google Scholar

29. Berrouk, A., R. Duseaux, and S. Afifi, "Electromagnetic wave scattering from rough layered interfaces: Analysis with the small perturbation method and the small slope approximation," Progress In Electromagnetics Research B, Vol. 57, 177-190, 2014.
doi:10.2528/PIERB13101802 Google Scholar

30. Afifi, S., R. Dusseaux, and A. Berrouk, "Electromagnetic scattering from 3D layered structures with randomly rough interfaces: Analysis with the small perturbation method and the small slope approximation," IEEE Trans. Ant. Prop., Vol. 62, No. 10, 5200-5208, Oct. 2014.
doi:10.1109/TAP.2014.2341704 Google Scholar

31. Duseaux, R., S. Afifi, and M. Dechambre, "Scattering properties of a stratified air/snow/sea ice medium. Small slope approximation," Comptes Rendus Physique, Vol. 17, No. 9, 995-1002, Elsevier Masson, 2016.
doi:10.1016/j.crhy.2016.07.017 Google Scholar

32. Jackson, D. R. and D. R. Olson, "The small-slope approximation for layered, fluid seafloors," J. Acoust. Soc. Am., Vol. 147, 56-73, 2020.
doi:10.1121/10.0000470 Google Scholar

33. Beckmann, P. and A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces, Pergamon Press, 1963.

34. Chen, Q., D. Won, and D. M. Akos, "Snow depth estimation accuracy using a dual-interface GPS-IR model with experimental results," GPS Solut., Vol. 21, 211-223, 2017.
doi:10.1007/s10291-016-0517-1 Google Scholar

35. Lemmetyinen, J., M. Schwank, K. Rautiainen, A. Kontu, T. Parkkinen, C. Matzler, A. Wiesmann, U. Weguller, C. Derksen, and P. Toose, "Snow density and ground permittivity retrieved from L-band radiometry: Application to experimental data," Remote Sensing of Environment, Vol. 180, 377-391, 2016.
doi:10.1016/j.rse.2016.02.002 Google Scholar

36. Frolov, A. D. and Y. Y. Macheret, "On dielectric properties of dry and wet snow," Hydrol. Process., Vol. 13, 1755-1760, 1999.
doi:10.1002/(SICI)1099-1085(199909)13:12/13<1755::AID-HYP854>3.0.CO;2-T Google Scholar

37. Kennedy, J. and R. Eberhart, "Particle swarm optimization," Proc. IEEE of International Conference on Neural Networks, 1942-1948, 1995.
doi:10.1109/ICNN.1995.488968 Google Scholar

38. Holland, J. H., Adaptation in Natural and Artificial Systems, University of Michigan Press, 1975.

39. Tso, B. C. K. and P. M. Mather, "Classification of multisource remote sensing imagery using a genetic algorithm and Markov random fields," IEEE Trans. Geosci. Remote Sens., Vol. 37, No. 3, 1255-1260, May 1999.
doi:10.1109/36.763284 Google Scholar

Dr. Nada Djedouani

Prof. Saddek Afifi

Professor Richard Dusséaux