volume | PIER Journals

Abstract

This paper is aimed at analyzing the electromagnetic (EM) scattering from the two-dimensional (2-D) Gaussian rough surfaces characterized by textures. Visual appearances of the stripe texture can be generated through the angle rotating in Fourier transform when the ratio of the correlation lengths in two directions is large enough. The scattering field is derived in Cartesian coordinate system through the small-slope approximation (SSA) method with plane incident wave. The normalized co-polarized radar cross section (NRCS) from 2-D Gaussian rough surface characterized by textures are calculated. In particular, several numerical results show the influences of incident angle, texture angle, correlation length, and root-mean-square height on the scattering from the textured rough surface. Finally, the validity of the SSA method is verified by comparisons of theoretical value and measured data.

1. Tsang, L. and J. A. Kong, Scattering of Electromagnetic Waves, Advanced Topics, Wiley Series in Remote Sensing, Wiley Interscience, 2001.
doi:10.1002/0471224278

2. Zhao, Y. W., M. Zhang, X. Geng, and P. Zhou, "A comprehensive facet model for bistatic SAR imagery of dynamic ocean scene," Progress In Electromagnetics Research, Vol. 123, 427-445, 2012.
doi:10.2528/PIER11100910 Google Scholar

3. Mcdaniel, S. T., "An extension of the small-slope approximation for rough surface scattering," Waves in Random Media, Vol. 5, No. 2, 201-214, 1995.
doi:10.1088/0959-7174/5/2/004 Google Scholar

4. Sun, R. Q., G. Luo, M. Zhang, and C. Wang, "Electromagnetic scattering model of the Kelvin wake and turbulent wake by a moving ship," Waves in Random Media, Vol. 21, No. 3, 501-504, 2011.
doi:10.1080/17455030.2011.591446 Google Scholar

5. Chen, H., M. Zhang, and H.-C. Yin, "Facet-based treatment on microwave bistatic scattering of three-dimensional sea surface with electrically large ship," Progress In Electromagnetics Research, Vol. 123, 385-405, 2012.
doi:10.2528/PIER11101108 Google Scholar

6. Warnick, K. F. and W. C. Chew, "Numerical simulation methods for rough surface scattering," Waves in Random Media, Vol. 11, No. 1, R1-R30, 2001.
doi:10.1088/0959-7174/11/1/201 Google Scholar

7. Thorsos, E. I., "The validity of the Kirchhoff approximation for rough surface scattering using a Gaussian roughness spectrum," J. Acoust. Soc. Am., Vol. 83, No. 1, 78-92, 1988.
doi:10.1121/1.396188 Google Scholar

8. Guo, L.-X., Y. Liang, J. Li, and Z.-S. Wu, "A high order integral SPM for the conducting rough surface scattering with the tapered wave incidence --- TE case ," Progress In Electromagnetics Research, Vol. 114, 333-352, 2011.
doi:10.2528/PIER11011605 Google Scholar

9. Lee, P. H. Y., et al. "Wind-speed dependence of small-grazing-angle microwave backscatter from sea surfaces," IEEE Trans. Antennas Propagat., Vol. 44, No. 3, 333-340, 1996.
doi:10.1109/8.486302 Google Scholar

10. Sajjad, N., A. Khenchaf, et al. "An improved two-scale model for the ocean surface bistatic scattering," Proc. Of International Geoscience and Remote Sensing Symposium, Vol. 1, 387-390, 2008. Google Scholar

11. Vaitilingom, L. and A. Khenchaf, "Radar cross sections of sea and ground clutter estimated by two scale model and small slope approximation in Hf-VHF bands," Progress In Electromagnetics Research B, Vol. 29, 311-338, 2011.
doi:10.2528/PIERB11021607 Google Scholar

12. Voronovich, A. G., "Small-slope approximation in wave scattering by rough surfaces," Sov. Phys.-JETP, Vol. 62, 65-70, 1985. Google Scholar

13. Berginc, G. and C. Bourrely, "The small-slope approximation method applied to a three-dimensional slab with rough boundaries," Progress In Electromagnetics Research, Vol. 73, 131-211, 2007.
doi:10.2528/PIER07030806 Google Scholar

14. Toporkov, J. V. and G. S. Brown, "Numerical study of the extended Kirchhoff approach and the lowest order small slope approximation for scattering from ocean-like surfaces: Doppler analysis," IEEE Trans. Antennas Propagat., Vol. 50, No. 4, 417-425, 2002.
doi:10.1109/TAP.2002.1003376 Google Scholar

15. Chevalier, B. and G. Berginc, "Small-slope approximation method: scattering of a vector wave from 2-D dielectric and metallic surfaces with Gaussian and non-Gaussian statistics," Proceedings of SPIE, Vol. 4100, 22-32, 2000.
doi:10.1117/12.401662 Google Scholar

16. Johnson, J. T. and K. F. Warnick, "On the geometrical optics (Hagfors' law) and physical optics approximations for scattering from exponentially correlated surfaces," IEEE Trans. Geosci. Remote Sens., Vol. 45, No. 8, 2619-2629, 2007.
doi:10.1109/TGRS.2007.900682 Google Scholar

17. Hu, S. Z., et al. "Comparison of various approximation theories for randomly rough surface scattering," Wave Motion, Vol. 46, No. 5, 281-292, 2009.
doi:10.1016/j.wavemoti.2009.03.001 Google Scholar

18. Li, X. F. and X. J. Xu, "Scattering and doppler spectral analysis for two-dimensional linear and nonlinear sea surfaces," IEEE Trans. Geosci. Remote Sens., Vol. 49, No. 2, 603-611, 2011.
doi:10.1109/TGRS.2010.2060204 Google Scholar

19. Cao, G. Z., P. Hou, Y. Q. Jin, et al. "Image fusion of SAR remote sensing with Laplacian Pyramid transformation fusion algorithm based on local conditional information of image," Remote Sensing Technology and Application, Vol. 22, No. 5, 628-632, 2007. Google Scholar

20. Wei, P. B., M. Zhang, R. Q. Sun, and X. F. Yuan, "Scattering studies for two-dimensional exponential correlation textured rough surfaces using small-slope approximation method," IEEE Trans. Geosci. Remote Sens., Vol. 52, No. 9, 5364-5373, 2014.
doi:10.1109/TGRS.2013.2288278 Google Scholar

21. Prakash, R., D. Singh, and N. P. Pathak, "Microwave specular scattering response of soil texture at X-band," Advances in Space Research, Vol. 44, No. 7, 801-814, 2009.
doi:10.1016/j.asr.2009.05.016 Google Scholar

22. Hu, Y. Z. and K. Tonder, "Simulation of 3-D random rough surface by 2-D digital filter and Fourier analysis," Int. J. Mach. Tools Manufact., Vol. 32, No. 12, 83-90, 1992.
doi:10.1016/0890-6955(92)90064-N Google Scholar

23. Zhang, M., H. Chen, and H. C. Yin, "Facet-based investigation on EM scattering from electrically large sea surface with two-scale profiles: Theoretical model," IEEE Trans. Geosci. Remote Sens., Vol. 49, No. 6, 1967-1975, 2011.
doi:10.1109/TGRS.2010.2099662 Google Scholar

24. Tsang, L., J. A. Kong, K. H. Ding, and C. A. Ao, Scattering of Electromagnetic Waves, Numerical Simulations, 124-134, Wiley Series in Remote Sensing, Wiley Interscience, 2001.
doi:10.1002/0471224308

25. Tatarskii, V. I. and V. V. Tatarskii, "Statistical non-Gaussian model of sea surface with anisotropic spectrum for wave scattering theory. Part I," Progress In Electromagnetics Research, Vol. 22, 259-291, 1999. Google Scholar

26. Voronovich, A. G. and V. U. Zavorotny, "Theoretical model for scattering of radar signals in Ku- and C-bands from a rough sea surface with breaking waves," Waves in Random Media, Vol. 11, No. 3, 247-269, 2001. Google Scholar

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

28. Chevalier, B. and G. Berginc, "Small-slope approximation method: scattering of a vector wave from 2-D dielectric and metallic surfaces with Gaussian and non-Gaussian statistics," Proceedings of SPIE, Vol. 4100, 22-32, 2000.
doi:10.1117/12.401662 Google Scholar

29. Bourlier, C., N. Déchamps, and G. Berginc, "Comparison of asymptotic backscattering models (SSA,WCA, and LCA) from one-dimensional Gaussian ocean-like surfaces," IEEE Trans. Antennas Propagat., Vol. 53, No. 5, 1640-1652, 2005.
doi:10.1109/TAP.2005.846800 Google Scholar

30. Stogryn, A., "Equations for calculating the dielectric constant of saline water," IEEE Trans. Micro. Theory Tech., Vol. 19, No. 8, 733-736, 1971.
doi:10.1109/TMTT.1971.1127617 Google Scholar

31. Ulaby, F. T., R. K. Moore, and A. K. Fung, Microwave Remote Sensing: Active and Passive --- From Theory to Applications, Artech House, 1986.

Dr. Rong-Qing Sun

Dr. Jing Xie

Dr. Yang-Wei Zhang