In this study, the physical optics approximation (POA) algorithm is described for predicting the electromagnetic (EM) scattering of three dimensional (3D) two-layer rough surfaces. The POA is initially used to calculate the composite scattering of an object and single layer rough surface for two dimensional (2D) situations. We extend this method to the case of a rough layer with two rough interfaces. The multiple coupling interactions between the upper and lower layer are considered based on an iterative strategy. Because the coupling effect is considered, the 3D model is quite time-consuming. In order to obtain numerical results rapidly, a parallel technique based on the OpenMP is adopted to accelerate the coupling iterative calculation. The model is applicable for moderate to large surface roughness. However, the rough surface should have small to moderate slopes so as to meet the conditions of POA. In numerical results, the normalized radar cross section of two-layer rough surfaces model under different polarizations is calculated, and the model is validated by comparison with a numerical reference method based on the method of moment. In addition, the influence of roughness on the scattering model is analyzed and discussed.
1. Garcia, N. and E. Stoll, "Monte Carlo calculation for electromagnetic-wave scattering from random rough surfaces," Physical Review Letters, Vol. 52, No. 20, 1798, 1984. doi:10.1103/PhysRevLett.52.1798
2. Kuga, Y. and P. Phu, "Experimental studies of millimeter-wave scattering in discrete random media and from rough surfaces," Progress In Electromagnetics Research, Vol. 14, 37-88, 1996.
3. Ogilvy, J. A., Theory of Wave Scattering from Random Rough Surfaces, Adam Hilger, Philadelphia, 1991.
4. Nieto-Vesperinas, M. and N. Garcıa, "A detailed study of the scattering of scalar waves from random rough surfaces," Journal of Modern Optics, Vol. 28, No. 12, 1651-1672, 1981.
5. Garcıa, N. and A. A. Maradudin, "Exact calculations of the diffraction of S-polarized electromagnetic radiation from large-amplitude dielectric gratings," Optics Communications, Vol. 45, No. 5, 301-306, 1983. doi:10.1016/0030-4018(83)90253-5
6. Nieto-Vesperinas, M. and J. M. Soto-Crespo, "Light-diffracted intensities from very deep gratings," Physical Review B: Condensed Matter, Vol. 38, No. 11, 7250, 1988. doi:10.1103/PhysRevB.38.7250
7. Maystre, D. and M. Saillard, "Scattering from metallic and dielectric rough surfaces," Journal of the Optical Society of America A, Vol. 7, No. 6, 982-990, 1990. doi:10.1364/JOSAA.7.000982
8. Beckmann, P. and A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces, Pergamon Press, 1963.
9. Thorsos, E. I., "The validity of the Kirchhoff approximation for rough surface scattering using a Gaussian roughness spectrum," Journal of the Acoustical Society of America, Vol. 83, No. 1, 78-92, 1988. doi:10.1121/1.396188
10. Pak, K., J. Johnson, L. Tsang, and C. H. Chan, "Backscattering enhancement of electromagnetic waves from two-dimensional perfectly conducting random rough surfaces based on Monte Carlo simulations," Journal of the Optical Society of America A — Optics Image Science & Vision, Vol. 12, No. 11, 2491-2499, 1995. doi:10.1364/JOSAA.12.002491
11. Li, Z. and Y. Q. Jin, "Bistatic scattering and transmitting through a fractal rough surface with high permittivity using the physics-based two-grid method in conjunction with the forward-backward method and spectrum acceleration algorithm," IEEE Transactions on Antennas & Propagation, Vol. 50, No. 9, 1323-1327, 2002. doi:10.1109/TAP.2002.802166
12. Ishimaru and J. S. Chen, "Scattering from very rough surfaces based on the modified second-order Kirchhoff approximation with angular and propagation shadowing," J. Acoust. Soc. Am., Vol. 88, No. 4, 1877-1883, 1990. doi:10.1121/1.400210
13. Chen, J. S. and A. Ishimaru, "Numerical simulation of the second-order Kirchhoff approximation from very rough surfaces and a study of backscattering enhancement," J. Acoust. Soc. Am., Vol. 88, No. 4, 1846-1850, 1990. doi:10.1121/1.400207
14. Bruce, N. C. and J. C. Dainty, "Multiple scattering from rough dielectric and metal surfaces using the Kirchhoff approximation," Optica Acta International Journal of Optics, Vol. 38, No. 8, 1471-1481, 1991.
15. Bruce, N. C., A. J. Sant, and J. C. Dainty, "The Mueller matrix for rough surface scattering using the Kirchhoff approximation," Optics Communications, Vol. 88, No. 4–6, 471-484, 1992. doi:10.1016/0030-4018(92)90076-4
16. Bruce, N. C., "Double scatter vector-wave Kirchhoff scattering from perfectly conducting surfaces with infinite slopes," Journal of Optics, Vol. 12, No. 8, 526-526, 2010. doi:10.1088/2040-8978/12/8/085701
17. Bruce, N. C., "Multiple scatter of vector electromagnetic waves from rough metal surfaces with infinite slopes using the Kirchhoff approximation," Waves in Random & Complex Media, Vol. 21, No. 2, 362-377, 2011. doi:10.1080/17455030.2011.563803
18. Yang, W., C. Y. Kee, and C. F. Wang, "Novel extension of SBR-PO method for solving electrically large and complex electromagnetic scattering problemshould be a spacein half-space," IEEE Transactions on Geoscience & Remote Sensing, Vol. 55, No. 99, 1-10, 2017.
19. Ye, H. and Y. Q. Jin, "A hybrid KA-MoM algorithm for computation of scattering from a 3-D PEC target above a dielectric rough surface," Radio Science, Vol. 43, No. 3, 2008. doi:10.1029/2007RS003702
20. Duan, X. and M. Moghaddam, "3-D vector electromagnetic scattering from arbitrary random rough surfaces using stabilized extended boundary condition method for remote sensing of soil moisture," IEEE Transactions on Geoscience & Remote Sensing, Vol. 50, No. 1, 87-103, 2012. doi:10.1109/TGRS.2011.2160549
21. Gutierrez-Meana, J., J. A. Marti Nez-Lorenzo, and F. Las-Heras, "High frequency techniques: The physical optics approximation and the modified equivalent current approximation (MECA)," Electromagnetic Waves Propagation in Complex Matter, 2011.
22. Qi, C. H. and Z. Q. Zhao, "Electromagnetic scattering and statistic analysis of clutter from oil contaminated sea surface," Radioengineering, Vol. 24, No. 1, 87-92, 2015. doi:10.13164/re.2015.0087
23. Tabatabaeenejad, A., X. Duan, and M. Moghaddam, "Coherent scattering of electromagnetic waves from two-layer rough surfaces within the Kirchhoff regime," IEEE Transactions on Geoscience & Remote Sensing, Vol. 51, No. 7, 3943-3953, 2013. doi:10.1109/TGRS.2012.2229391
24. El-Shenawee, M., "Polarimetric scattering from two-layered two-dimensional random rough surfaces with and without buried objects," IEEE Transactions on Geoscience & Remote Sensing, Vol. 42, No. 1, 67-76, 2004. doi:10.1109/TGRS.2003.815675
25. Pinel, N., J. T. Johnson, and C. Bourlier, "A geometrical optics model of three dimensional scattering from a rough layer with two rough surfaces," IEEE Transactions on Antennas & Propagation, Vol. 57, No. 2, 546-554, 2009. doi:10.1109/TAP.2008.2011252
26. Pinel, N., J. T. Johnson, and C. Bourlier, "A geometrical optics model of three dimensional scattering from a rough surface over a planar surface," IEEE Transactions on Antennas & Propagation, Vol. 57, No. 2, 546-554, 2009. doi:10.1109/TAP.2008.2011252
27. Li, J., L. Guo, and S. Chai, "Composite electromagnetic scattering from an object situated above rough surface," Applied Optics, Vol. 53, No. 35, 8189, 2014. doi:10.1364/AO.53.008189
28. Li, J., L. X. Guo, S. R. Chai, and Y. C. Jiao, "Electromagnetic scattering from a PEC object above a dielectric rough sea surface by a hybrid PO-PO method," Waves in Random & Complex Media, Vol. 25, No. 1, 60-74, 2015. doi:10.1080/17455030.2014.961587
29. Ji, W.-J. and C.-M. Tong, "The E-Pile+Smcg for scattering from an object below 2D soil rough surface," Progress In Electromagnetics Research B, Vol. 33, 317-337, 2011. doi:10.2528/PIERB11061004
30. Ulaby, F. T., et al., Microwave Remote Sensing: Active and Passive, Volume II: Radar Remote Sensing and Surface Scattering and Emission Theory, Addison-Wesley Pub. Co., 1982.
31. Kouali, M., G. Kubicke, and C. Bourlier, "Electromagnetic interactions analysis between two 3-D scatterers using the E-PILE method combined with the PO approximation," Progress in Electromagnetics Research B, Vol. 58, 123-138, 2014. doi:10.2528/PIERB14011204
32. Tsang, L. and J. A. Kong, Scattering of Electromagnetic Waves, Advanced Topics, Wiley Interscience, New York, 2001. doi:10.1002/0471224278
33. Chandra, R., L. Dagum, D. Kohr, D. Maydan, J. Mcdonald, and R. Menon, Parallel Programming in OpenMP, Morgan Kaufmann Publishers, 2001.