Abstract

A hybrid method, combining analytic Kirchhoff approximation (KA) and numerical method of moment (MoM), is developed to solve the 2D scattering problem of a dielectric target with arbitrary cross section above a moderate perfect electric conductor (PEC) rough surface under TM-polarized tapered wave incidence. Consider the target as the MoM region and the rough surface as the KA region, the induced current on the rough surface is obtained through the KA method, which depends on the incident tapered wave and the field illuminating by current distribution on the target, leaving only unknowns on the target region. In order to reduce the computational costs further, the rough surface is truncated to speed up computation of the scattering contribution from the rough surface to the target. Compared with the conventional MoM, the hybrid method is very efficient to solve the composite scattering problem of target above rough surface, especially for long underlying rough surface. Simulation results validate the effectiveness and accuracy of the hybrid method.

© 2013 Optical Society of America

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References

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  1. J. T. Johnson, “A study of the four-path model for scattering from an object above a half space,” Microw. Opt. Technol. Lett. 30, 130–134 (2001).
    [CrossRef]
  2. L. X. Guo and Z. Wu, “Application of the extended boundary condition method to electromagnetic scattering from rough dielectric fractal sea surface,” J. Electromagn. Waves Appl. 18, 1219–1234 (2004).
    [CrossRef]
  3. X. Wang, C. F. Wang, and Y. B. Gan, “Electromagnetic scattering from a circular target above or below rough surface,” Prog. Electromagn. Res. 40, 207–227 (2003).
    [CrossRef]
  4. Z. Li and Y. Q. Jin, “Bistatic scattering from a fractal dynamic rough sea surface with a ship presence at low grazing-angle incidence using the GFBM/SAA,” Microw. Opt. Technol. Lett. 31, 146–151 (2001).
    [CrossRef]
  5. Z. X. Li 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 Trans. Antennas Propag. 50, 1323–1327 (2002).
    [CrossRef]
  6. P. Liu and Y. Q. Jin, “The finite-element method with domain decomposition for electromagnetic bistatic scattering from the comprehensive model of a ship on and a target above a large scale rough sea surface,” IEEE Trans. Geosci. Remote Sens. 42, 950–956 (2004).
    [CrossRef]
  7. Z. J. Liu, R. J. Adams, and L. Carin, “Well-conditioned MLFMA formulation for closed PEC targets in the vicinity of a half space,” IEEE Trans. Antennas Propag. 51, 2822–2829 (2003).
    [CrossRef]
  8. L. Li, J. Q. He, Z. J. Liu, X. L. Dong, and L. Carin, “MLFMA analysis of scattering from multiple targets in the presence of a half-space,” IEEE Trans. Antennas Propag. 51, 810–819 (2003).
    [CrossRef]
  9. G. Kubicke, C. Bourlier, and J. Saillard, “Scattering by an object above a randomly rough surface from a fast numerical method: extended PILE method combined with FB-SA,” Waves Random Complex Media 18, 495–519 (2008).
    [CrossRef]
  10. L. X. Guo, Y. Liang, and Z. S. Wu, “A study of electromagnetic scattering from conducting targets above and below the dielectric rough surface,” Opt. Express 19, 5785–5801 (2011).
    [CrossRef]
  11. H. X. Ye and Y. Q. Jin, “Fast iterative approach to difference scattering from the target above a rough surface,” IEEE Trans. Geosci. Remote Sens. 44, 108–115 (2006).
    [CrossRef]
  12. H. X. Ye and Y. Q. Jin, “Fast iterative approach to the difference scattering from a dielectric target above a rough surface,” Sci. China: Phys., Mech. Astron. 48, 723–738 (2005).
  13. H. Chen and W. J. Ji, “Fast calculation of EM scattering from a dielectric target above the dielectric Gauss rough surface based on the cross coupling iterative approach,” 2011 Cross Strait Quad-Regional Radio Science and Wireless Technology Conference (2011), pp. 168–170.
  14. Y. Zhang, Y. E. Yang, H. Braunisch, and J. A. Kong, “Electromagnetic wave interaction of conducting object with rough surface by hybrid SPM/MOM technique,” Prog. Electromagn. Res. 22, 315–335 (1999).
    [CrossRef]
  15. S. Y. He and G. Q. Zhu, “A hybrid MM-PO method combing UV technique for scattering from two-dimensional target above a rough surface,” Microw. Opt. Technol. Lett. 49, 2957–2960 (2007).
    [CrossRef]
  16. H. X. Ye and Y. Q. Jin, “A hybrid analytic-numerical algorithm of scattering from an object above a rough surface,” IEEE Trans. Geosci. Remote Sens. 45, 1174–1180 (2007).
    [CrossRef]
  17. R. Wang, L. X. Guo, J. Ma, and Z. S. Wu, “Hybrid method for investigation of electromagnetic scattering from conducting target above the randomly rough surface,” Chin. Phys. B 18, 1503–1511 (2009).
    [CrossRef]
  18. L. Tsang, J. A. Kong, K. H. Ding, and C. O. Ao, Scattering of Electromagnetic Waves: Numerical Simulations (Wiley-Interscience, 2001).
  19. H. Ye and Y. Q. Jin, “Parameterization of the tapered incident wave for numerical simulation of electromagnetic scattering from rough surface,” IEEE Trans. Antennas Propag. 50, 1361–1367 (2005).
  20. A. F. Peterson, S. L. Ray, and R. Mittra, Computational Methods for Electromagnetics (Wiley-IEEE, 1997).
  21. F. Ticconi, L. Pulvirenti, and N. Pierdicca, “Models for scattering from rough surfaces,” in Electromagnetic Waves, V. Zhurbenko, ed. (InTech, 2011), pp. 203–226.
  22. E. I. Thorsos, “The validity of the Kirchhoff approximation for rough surface scattering using a Gaussian roughness spectrum,” J. Acoust. Soc. Am. 83, 78–92 (1988).
    [CrossRef]
  23. G. S. Brown, “The validity of shadowing corrections in rough surface scattering,” Radio Sci. 19, 1461–1468 (1984).
    [CrossRef]

2011 (1)

2009 (1)

R. Wang, L. X. Guo, J. Ma, and Z. S. Wu, “Hybrid method for investigation of electromagnetic scattering from conducting target above the randomly rough surface,” Chin. Phys. B 18, 1503–1511 (2009).
[CrossRef]

2008 (1)

G. Kubicke, C. Bourlier, and J. Saillard, “Scattering by an object above a randomly rough surface from a fast numerical method: extended PILE method combined with FB-SA,” Waves Random Complex Media 18, 495–519 (2008).
[CrossRef]

2007 (2)

S. Y. He and G. Q. Zhu, “A hybrid MM-PO method combing UV technique for scattering from two-dimensional target above a rough surface,” Microw. Opt. Technol. Lett. 49, 2957–2960 (2007).
[CrossRef]

H. X. Ye and Y. Q. Jin, “A hybrid analytic-numerical algorithm of scattering from an object above a rough surface,” IEEE Trans. Geosci. Remote Sens. 45, 1174–1180 (2007).
[CrossRef]

2006 (1)

H. X. Ye and Y. Q. Jin, “Fast iterative approach to difference scattering from the target above a rough surface,” IEEE Trans. Geosci. Remote Sens. 44, 108–115 (2006).
[CrossRef]

2005 (2)

H. X. Ye and Y. Q. Jin, “Fast iterative approach to the difference scattering from a dielectric target above a rough surface,” Sci. China: Phys., Mech. Astron. 48, 723–738 (2005).

H. Ye and Y. Q. Jin, “Parameterization of the tapered incident wave for numerical simulation of electromagnetic scattering from rough surface,” IEEE Trans. Antennas Propag. 50, 1361–1367 (2005).

2004 (2)

P. Liu and Y. Q. Jin, “The finite-element method with domain decomposition for electromagnetic bistatic scattering from the comprehensive model of a ship on and a target above a large scale rough sea surface,” IEEE Trans. Geosci. Remote Sens. 42, 950–956 (2004).
[CrossRef]

L. X. Guo and Z. Wu, “Application of the extended boundary condition method to electromagnetic scattering from rough dielectric fractal sea surface,” J. Electromagn. Waves Appl. 18, 1219–1234 (2004).
[CrossRef]

2003 (3)

X. Wang, C. F. Wang, and Y. B. Gan, “Electromagnetic scattering from a circular target above or below rough surface,” Prog. Electromagn. Res. 40, 207–227 (2003).
[CrossRef]

Z. J. Liu, R. J. Adams, and L. Carin, “Well-conditioned MLFMA formulation for closed PEC targets in the vicinity of a half space,” IEEE Trans. Antennas Propag. 51, 2822–2829 (2003).
[CrossRef]

L. Li, J. Q. He, Z. J. Liu, X. L. Dong, and L. Carin, “MLFMA analysis of scattering from multiple targets in the presence of a half-space,” IEEE Trans. Antennas Propag. 51, 810–819 (2003).
[CrossRef]

2002 (1)

Z. X. Li 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 Trans. Antennas Propag. 50, 1323–1327 (2002).
[CrossRef]

2001 (2)

J. T. Johnson, “A study of the four-path model for scattering from an object above a half space,” Microw. Opt. Technol. Lett. 30, 130–134 (2001).
[CrossRef]

Z. Li and Y. Q. Jin, “Bistatic scattering from a fractal dynamic rough sea surface with a ship presence at low grazing-angle incidence using the GFBM/SAA,” Microw. Opt. Technol. Lett. 31, 146–151 (2001).
[CrossRef]

1999 (1)

Y. Zhang, Y. E. Yang, H. Braunisch, and J. A. Kong, “Electromagnetic wave interaction of conducting object with rough surface by hybrid SPM/MOM technique,” Prog. Electromagn. Res. 22, 315–335 (1999).
[CrossRef]

1988 (1)

E. I. Thorsos, “The validity of the Kirchhoff approximation for rough surface scattering using a Gaussian roughness spectrum,” J. Acoust. Soc. Am. 83, 78–92 (1988).
[CrossRef]

1984 (1)

G. S. Brown, “The validity of shadowing corrections in rough surface scattering,” Radio Sci. 19, 1461–1468 (1984).
[CrossRef]

Adams, R. J.

Z. J. Liu, R. J. Adams, and L. Carin, “Well-conditioned MLFMA formulation for closed PEC targets in the vicinity of a half space,” IEEE Trans. Antennas Propag. 51, 2822–2829 (2003).
[CrossRef]

Ao, C. O.

L. Tsang, J. A. Kong, K. H. Ding, and C. O. Ao, Scattering of Electromagnetic Waves: Numerical Simulations (Wiley-Interscience, 2001).

Bourlier, C.

G. Kubicke, C. Bourlier, and J. Saillard, “Scattering by an object above a randomly rough surface from a fast numerical method: extended PILE method combined with FB-SA,” Waves Random Complex Media 18, 495–519 (2008).
[CrossRef]

Braunisch, H.

Y. Zhang, Y. E. Yang, H. Braunisch, and J. A. Kong, “Electromagnetic wave interaction of conducting object with rough surface by hybrid SPM/MOM technique,” Prog. Electromagn. Res. 22, 315–335 (1999).
[CrossRef]

Brown, G. S.

G. S. Brown, “The validity of shadowing corrections in rough surface scattering,” Radio Sci. 19, 1461–1468 (1984).
[CrossRef]

Carin, L.

L. Li, J. Q. He, Z. J. Liu, X. L. Dong, and L. Carin, “MLFMA analysis of scattering from multiple targets in the presence of a half-space,” IEEE Trans. Antennas Propag. 51, 810–819 (2003).
[CrossRef]

Z. J. Liu, R. J. Adams, and L. Carin, “Well-conditioned MLFMA formulation for closed PEC targets in the vicinity of a half space,” IEEE Trans. Antennas Propag. 51, 2822–2829 (2003).
[CrossRef]

Chen, H.

H. Chen and W. J. Ji, “Fast calculation of EM scattering from a dielectric target above the dielectric Gauss rough surface based on the cross coupling iterative approach,” 2011 Cross Strait Quad-Regional Radio Science and Wireless Technology Conference (2011), pp. 168–170.

Ding, K. H.

L. Tsang, J. A. Kong, K. H. Ding, and C. O. Ao, Scattering of Electromagnetic Waves: Numerical Simulations (Wiley-Interscience, 2001).

Dong, X. L.

L. Li, J. Q. He, Z. J. Liu, X. L. Dong, and L. Carin, “MLFMA analysis of scattering from multiple targets in the presence of a half-space,” IEEE Trans. Antennas Propag. 51, 810–819 (2003).
[CrossRef]

Gan, Y. B.

X. Wang, C. F. Wang, and Y. B. Gan, “Electromagnetic scattering from a circular target above or below rough surface,” Prog. Electromagn. Res. 40, 207–227 (2003).
[CrossRef]

Guo, L. X.

L. X. Guo, Y. Liang, and Z. S. Wu, “A study of electromagnetic scattering from conducting targets above and below the dielectric rough surface,” Opt. Express 19, 5785–5801 (2011).
[CrossRef]

R. Wang, L. X. Guo, J. Ma, and Z. S. Wu, “Hybrid method for investigation of electromagnetic scattering from conducting target above the randomly rough surface,” Chin. Phys. B 18, 1503–1511 (2009).
[CrossRef]

L. X. Guo and Z. Wu, “Application of the extended boundary condition method to electromagnetic scattering from rough dielectric fractal sea surface,” J. Electromagn. Waves Appl. 18, 1219–1234 (2004).
[CrossRef]

He, J. Q.

L. Li, J. Q. He, Z. J. Liu, X. L. Dong, and L. Carin, “MLFMA analysis of scattering from multiple targets in the presence of a half-space,” IEEE Trans. Antennas Propag. 51, 810–819 (2003).
[CrossRef]

He, S. Y.

S. Y. He and G. Q. Zhu, “A hybrid MM-PO method combing UV technique for scattering from two-dimensional target above a rough surface,” Microw. Opt. Technol. Lett. 49, 2957–2960 (2007).
[CrossRef]

Ji, W. J.

H. Chen and W. J. Ji, “Fast calculation of EM scattering from a dielectric target above the dielectric Gauss rough surface based on the cross coupling iterative approach,” 2011 Cross Strait Quad-Regional Radio Science and Wireless Technology Conference (2011), pp. 168–170.

Jin, Y. Q.

H. X. Ye and Y. Q. Jin, “A hybrid analytic-numerical algorithm of scattering from an object above a rough surface,” IEEE Trans. Geosci. Remote Sens. 45, 1174–1180 (2007).
[CrossRef]

H. X. Ye and Y. Q. Jin, “Fast iterative approach to difference scattering from the target above a rough surface,” IEEE Trans. Geosci. Remote Sens. 44, 108–115 (2006).
[CrossRef]

H. X. Ye and Y. Q. Jin, “Fast iterative approach to the difference scattering from a dielectric target above a rough surface,” Sci. China: Phys., Mech. Astron. 48, 723–738 (2005).

H. Ye and Y. Q. Jin, “Parameterization of the tapered incident wave for numerical simulation of electromagnetic scattering from rough surface,” IEEE Trans. Antennas Propag. 50, 1361–1367 (2005).

P. Liu and Y. Q. Jin, “The finite-element method with domain decomposition for electromagnetic bistatic scattering from the comprehensive model of a ship on and a target above a large scale rough sea surface,” IEEE Trans. Geosci. Remote Sens. 42, 950–956 (2004).
[CrossRef]

Z. X. Li 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 Trans. Antennas Propag. 50, 1323–1327 (2002).
[CrossRef]

Z. Li and Y. Q. Jin, “Bistatic scattering from a fractal dynamic rough sea surface with a ship presence at low grazing-angle incidence using the GFBM/SAA,” Microw. Opt. Technol. Lett. 31, 146–151 (2001).
[CrossRef]

Johnson, J. T.

J. T. Johnson, “A study of the four-path model for scattering from an object above a half space,” Microw. Opt. Technol. Lett. 30, 130–134 (2001).
[CrossRef]

Kong, J. A.

Y. Zhang, Y. E. Yang, H. Braunisch, and J. A. Kong, “Electromagnetic wave interaction of conducting object with rough surface by hybrid SPM/MOM technique,” Prog. Electromagn. Res. 22, 315–335 (1999).
[CrossRef]

L. Tsang, J. A. Kong, K. H. Ding, and C. O. Ao, Scattering of Electromagnetic Waves: Numerical Simulations (Wiley-Interscience, 2001).

Kubicke, G.

G. Kubicke, C. Bourlier, and J. Saillard, “Scattering by an object above a randomly rough surface from a fast numerical method: extended PILE method combined with FB-SA,” Waves Random Complex Media 18, 495–519 (2008).
[CrossRef]

Li, L.

L. Li, J. Q. He, Z. J. Liu, X. L. Dong, and L. Carin, “MLFMA analysis of scattering from multiple targets in the presence of a half-space,” IEEE Trans. Antennas Propag. 51, 810–819 (2003).
[CrossRef]

Li, Z.

Z. Li and Y. Q. Jin, “Bistatic scattering from a fractal dynamic rough sea surface with a ship presence at low grazing-angle incidence using the GFBM/SAA,” Microw. Opt. Technol. Lett. 31, 146–151 (2001).
[CrossRef]

Li, Z. X.

Z. X. Li 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 Trans. Antennas Propag. 50, 1323–1327 (2002).
[CrossRef]

Liang, Y.

Liu, P.

P. Liu and Y. Q. Jin, “The finite-element method with domain decomposition for electromagnetic bistatic scattering from the comprehensive model of a ship on and a target above a large scale rough sea surface,” IEEE Trans. Geosci. Remote Sens. 42, 950–956 (2004).
[CrossRef]

Liu, Z. J.

Z. J. Liu, R. J. Adams, and L. Carin, “Well-conditioned MLFMA formulation for closed PEC targets in the vicinity of a half space,” IEEE Trans. Antennas Propag. 51, 2822–2829 (2003).
[CrossRef]

L. Li, J. Q. He, Z. J. Liu, X. L. Dong, and L. Carin, “MLFMA analysis of scattering from multiple targets in the presence of a half-space,” IEEE Trans. Antennas Propag. 51, 810–819 (2003).
[CrossRef]

Ma, J.

R. Wang, L. X. Guo, J. Ma, and Z. S. Wu, “Hybrid method for investigation of electromagnetic scattering from conducting target above the randomly rough surface,” Chin. Phys. B 18, 1503–1511 (2009).
[CrossRef]

Mittra, R.

A. F. Peterson, S. L. Ray, and R. Mittra, Computational Methods for Electromagnetics (Wiley-IEEE, 1997).

Peterson, A. F.

A. F. Peterson, S. L. Ray, and R. Mittra, Computational Methods for Electromagnetics (Wiley-IEEE, 1997).

Pierdicca, N.

F. Ticconi, L. Pulvirenti, and N. Pierdicca, “Models for scattering from rough surfaces,” in Electromagnetic Waves, V. Zhurbenko, ed. (InTech, 2011), pp. 203–226.

Pulvirenti, L.

F. Ticconi, L. Pulvirenti, and N. Pierdicca, “Models for scattering from rough surfaces,” in Electromagnetic Waves, V. Zhurbenko, ed. (InTech, 2011), pp. 203–226.

Ray, S. L.

A. F. Peterson, S. L. Ray, and R. Mittra, Computational Methods for Electromagnetics (Wiley-IEEE, 1997).

Saillard, J.

G. Kubicke, C. Bourlier, and J. Saillard, “Scattering by an object above a randomly rough surface from a fast numerical method: extended PILE method combined with FB-SA,” Waves Random Complex Media 18, 495–519 (2008).
[CrossRef]

Thorsos, E. I.

E. I. Thorsos, “The validity of the Kirchhoff approximation for rough surface scattering using a Gaussian roughness spectrum,” J. Acoust. Soc. Am. 83, 78–92 (1988).
[CrossRef]

Ticconi, F.

F. Ticconi, L. Pulvirenti, and N. Pierdicca, “Models for scattering from rough surfaces,” in Electromagnetic Waves, V. Zhurbenko, ed. (InTech, 2011), pp. 203–226.

Tsang, L.

L. Tsang, J. A. Kong, K. H. Ding, and C. O. Ao, Scattering of Electromagnetic Waves: Numerical Simulations (Wiley-Interscience, 2001).

Wang, C. F.

X. Wang, C. F. Wang, and Y. B. Gan, “Electromagnetic scattering from a circular target above or below rough surface,” Prog. Electromagn. Res. 40, 207–227 (2003).
[CrossRef]

Wang, R.

R. Wang, L. X. Guo, J. Ma, and Z. S. Wu, “Hybrid method for investigation of electromagnetic scattering from conducting target above the randomly rough surface,” Chin. Phys. B 18, 1503–1511 (2009).
[CrossRef]

Wang, X.

X. Wang, C. F. Wang, and Y. B. Gan, “Electromagnetic scattering from a circular target above or below rough surface,” Prog. Electromagn. Res. 40, 207–227 (2003).
[CrossRef]

Wu, Z.

L. X. Guo and Z. Wu, “Application of the extended boundary condition method to electromagnetic scattering from rough dielectric fractal sea surface,” J. Electromagn. Waves Appl. 18, 1219–1234 (2004).
[CrossRef]

Wu, Z. S.

L. X. Guo, Y. Liang, and Z. S. Wu, “A study of electromagnetic scattering from conducting targets above and below the dielectric rough surface,” Opt. Express 19, 5785–5801 (2011).
[CrossRef]

R. Wang, L. X. Guo, J. Ma, and Z. S. Wu, “Hybrid method for investigation of electromagnetic scattering from conducting target above the randomly rough surface,” Chin. Phys. B 18, 1503–1511 (2009).
[CrossRef]

Yang, Y. E.

Y. Zhang, Y. E. Yang, H. Braunisch, and J. A. Kong, “Electromagnetic wave interaction of conducting object with rough surface by hybrid SPM/MOM technique,” Prog. Electromagn. Res. 22, 315–335 (1999).
[CrossRef]

Ye, H.

H. Ye and Y. Q. Jin, “Parameterization of the tapered incident wave for numerical simulation of electromagnetic scattering from rough surface,” IEEE Trans. Antennas Propag. 50, 1361–1367 (2005).

Ye, H. X.

H. X. Ye and Y. Q. Jin, “A hybrid analytic-numerical algorithm of scattering from an object above a rough surface,” IEEE Trans. Geosci. Remote Sens. 45, 1174–1180 (2007).
[CrossRef]

H. X. Ye and Y. Q. Jin, “Fast iterative approach to difference scattering from the target above a rough surface,” IEEE Trans. Geosci. Remote Sens. 44, 108–115 (2006).
[CrossRef]

H. X. Ye and Y. Q. Jin, “Fast iterative approach to the difference scattering from a dielectric target above a rough surface,” Sci. China: Phys., Mech. Astron. 48, 723–738 (2005).

Zhang, Y.

Y. Zhang, Y. E. Yang, H. Braunisch, and J. A. Kong, “Electromagnetic wave interaction of conducting object with rough surface by hybrid SPM/MOM technique,” Prog. Electromagn. Res. 22, 315–335 (1999).
[CrossRef]

Zhu, G. Q.

S. Y. He and G. Q. Zhu, “A hybrid MM-PO method combing UV technique for scattering from two-dimensional target above a rough surface,” Microw. Opt. Technol. Lett. 49, 2957–2960 (2007).
[CrossRef]

Chin. Phys. B (1)

R. Wang, L. X. Guo, J. Ma, and Z. S. Wu, “Hybrid method for investigation of electromagnetic scattering from conducting target above the randomly rough surface,” Chin. Phys. B 18, 1503–1511 (2009).
[CrossRef]

IEEE Trans. Antennas Propag. (4)

Z. X. Li 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 Trans. Antennas Propag. 50, 1323–1327 (2002).
[CrossRef]

Z. J. Liu, R. J. Adams, and L. Carin, “Well-conditioned MLFMA formulation for closed PEC targets in the vicinity of a half space,” IEEE Trans. Antennas Propag. 51, 2822–2829 (2003).
[CrossRef]

L. Li, J. Q. He, Z. J. Liu, X. L. Dong, and L. Carin, “MLFMA analysis of scattering from multiple targets in the presence of a half-space,” IEEE Trans. Antennas Propag. 51, 810–819 (2003).
[CrossRef]

H. Ye and Y. Q. Jin, “Parameterization of the tapered incident wave for numerical simulation of electromagnetic scattering from rough surface,” IEEE Trans. Antennas Propag. 50, 1361–1367 (2005).

IEEE Trans. Geosci. Remote Sens. (3)

P. Liu and Y. Q. Jin, “The finite-element method with domain decomposition for electromagnetic bistatic scattering from the comprehensive model of a ship on and a target above a large scale rough sea surface,” IEEE Trans. Geosci. Remote Sens. 42, 950–956 (2004).
[CrossRef]

H. X. Ye and Y. Q. Jin, “A hybrid analytic-numerical algorithm of scattering from an object above a rough surface,” IEEE Trans. Geosci. Remote Sens. 45, 1174–1180 (2007).
[CrossRef]

H. X. Ye and Y. Q. Jin, “Fast iterative approach to difference scattering from the target above a rough surface,” IEEE Trans. Geosci. Remote Sens. 44, 108–115 (2006).
[CrossRef]

J. Acoust. Soc. Am. (1)

E. I. Thorsos, “The validity of the Kirchhoff approximation for rough surface scattering using a Gaussian roughness spectrum,” J. Acoust. Soc. Am. 83, 78–92 (1988).
[CrossRef]

J. Electromagn. Waves Appl. (1)

L. X. Guo and Z. Wu, “Application of the extended boundary condition method to electromagnetic scattering from rough dielectric fractal sea surface,” J. Electromagn. Waves Appl. 18, 1219–1234 (2004).
[CrossRef]

Microw. Opt. Technol. Lett. (3)

J. T. Johnson, “A study of the four-path model for scattering from an object above a half space,” Microw. Opt. Technol. Lett. 30, 130–134 (2001).
[CrossRef]

Z. Li and Y. Q. Jin, “Bistatic scattering from a fractal dynamic rough sea surface with a ship presence at low grazing-angle incidence using the GFBM/SAA,” Microw. Opt. Technol. Lett. 31, 146–151 (2001).
[CrossRef]

S. Y. He and G. Q. Zhu, “A hybrid MM-PO method combing UV technique for scattering from two-dimensional target above a rough surface,” Microw. Opt. Technol. Lett. 49, 2957–2960 (2007).
[CrossRef]

Opt. Express (1)

Prog. Electromagn. Res. (2)

Y. Zhang, Y. E. Yang, H. Braunisch, and J. A. Kong, “Electromagnetic wave interaction of conducting object with rough surface by hybrid SPM/MOM technique,” Prog. Electromagn. Res. 22, 315–335 (1999).
[CrossRef]

X. Wang, C. F. Wang, and Y. B. Gan, “Electromagnetic scattering from a circular target above or below rough surface,” Prog. Electromagn. Res. 40, 207–227 (2003).
[CrossRef]

Radio Sci. (1)

G. S. Brown, “The validity of shadowing corrections in rough surface scattering,” Radio Sci. 19, 1461–1468 (1984).
[CrossRef]

Sci. China: Phys., Mech. Astron. (1)

H. X. Ye and Y. Q. Jin, “Fast iterative approach to the difference scattering from a dielectric target above a rough surface,” Sci. China: Phys., Mech. Astron. 48, 723–738 (2005).

Waves Random Complex Media (1)

G. Kubicke, C. Bourlier, and J. Saillard, “Scattering by an object above a randomly rough surface from a fast numerical method: extended PILE method combined with FB-SA,” Waves Random Complex Media 18, 495–519 (2008).
[CrossRef]

Other (4)

H. Chen and W. J. Ji, “Fast calculation of EM scattering from a dielectric target above the dielectric Gauss rough surface based on the cross coupling iterative approach,” 2011 Cross Strait Quad-Regional Radio Science and Wireless Technology Conference (2011), pp. 168–170.

L. Tsang, J. A. Kong, K. H. Ding, and C. O. Ao, Scattering of Electromagnetic Waves: Numerical Simulations (Wiley-Interscience, 2001).

A. F. Peterson, S. L. Ray, and R. Mittra, Computational Methods for Electromagnetics (Wiley-IEEE, 1997).

F. Ticconi, L. Pulvirenti, and N. Pierdicca, “Models for scattering from rough surfaces,” in Electromagnetic Waves, V. Zhurbenko, ed. (InTech, 2011), pp. 203–226.

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Figures (6)

Fig. 1.
Fig. 1.

Scattering model of a target above a rough surface.

Fig. 2.
Fig. 2.

Underlying rough surface taken account of the surface scattering to the target.

Fig. 3.
Fig. 3.

Bistatic NRCS comparison of a cylinder with r=λ and h=4λ above the Gaussian rough surface (θi=20°).

Fig. 4.
Fig. 4.

Bistatic NRCS comparison of a cylinder with r=λ and h=4λ above the Gaussian rough surface (θi=60°).

Fig. 5.
Fig. 5.

Bistatic NRCS comparison of a cylinder with r=1.5λ and h=4λ above the Gaussian rough surface (θi=60°).

Fig. 6.
Fig. 6.

Bistatic NRCS comparison of a cylinder with r=λ and h=6λ above the Gaussian rough surface (θi=60°).

Tables (1)

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Table 1. Comparison of the Effectiveness of MoM and the Hybrid Method

Equations (26)

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Hi(r¯)=yHi(r¯)=yexp(jk0(xsinθizcosθi)(1+w(r¯)))·exp((x+ztanθi)2g2),
w(r¯)=2(x+ztanθi)2g21(k0gcosθi)2,
g>6(cosθi)1.5,
L15lc,
L4g,
L2(rcosθm+htanθm).
g4(rcosθi+htanθi).
Js=p=1PtpJspfp,
Jo=n=1NtnJonfn,
Ko=yn=1NKonfn,
Hso(r¯)=yHso(r¯)=y[iωε0Ao(r¯)(Fz(r¯)xFx(r¯)z)],
Ao(r¯)=cKo(r¯)i4H0(1)(k0R)dr¯,
Fo(r¯)=cJo(r¯)i4H0(1)(k0R)dr¯,
Hin(r¯)=Hi(r¯)+Hso(r¯),r¯S.
tJs=n×yHS(r¯)=n×y2Hin(r¯),r¯S,
Js=p=1Ptp(2Hi(rp)+2Hso(rp))fp.
[Js]=[Ji]+[ZJ][Jo]+[ZK][Ko],
Ji=p=1P2Hi(rp)fp,
ZKpn=ωε02H0(1)(k0|r¯pr¯n|)dr¯n,
ZJpn=i2[(z·tn)H0(1)(k0|r¯pr¯n|)dr¯nx(x·tn)H0(1)(k0|r¯pr¯n|)dr¯nz]|r¯=r¯p.
12Jo(r¯)=Hi(r¯)+c[Jo(r¯)G0(r¯,r¯)n+G0(r¯,r¯)×iωε0Ko(r¯)]dr¯+SJs(r¯)G0(r¯,r¯)ndr¯(r¯c+),
12Jo(r¯)=c[Jo(r¯)G1(r¯,r¯)n+G1(r¯,r¯)iωε0εdKo(r¯)]dr¯(r¯c),
SJs(r¯)G0(r¯,r¯)ndr¯=[Z][Jsp]=[Z][Ji]+[Z][ZJpn][Jo]+[Z][ZKpn][Ko],r¯pL1L2,
Znp=idr¯p4[H0(1)(k0|r¯nr¯p|)x(ς(xp))+H0(1)(k0|r¯nr¯p|)z]|r¯=r¯p(r¯nc,r¯pL1L2).
Hs(r¯)=c[Jo(r¯)G0(r¯,r¯)n+G0(r¯,r¯)iωε0Ko(r¯)]dr¯+SJs(r¯)G0(r¯,r¯)ndr¯,
σ(θs,θi)=limρρ|Hs(θs,θi)|22ηPi=limρρ|Hs(θs,θi)|2g2/πcosθi[11+2tan2θi2k2g2cos2θi],

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