Abstract

The problem of electromagnetic (EM) scattering between the time-varying lossy dielectric ocean and a moving target is always solved by using some numerical algorithm. However, the elements of the impedance matrix and the surface electric and magnetic currents of the lossy dielectric ocean must be determined and evaluated again at different moments due to the varying of the ocean with time, and the numerical algorithm will produce an enormous amount of calculation. To overcome this shortcoming, the reciprocity theorem is used to solve the coupling field between a time-varying lossy dielectric ocean and a moving conducting plate above it. Due to the advantage of the reciprocity theorem, the difficulty in computing the secondary scattered fields is reduced. The polarization currents of the ocean and the first scattered field from the conducting plate are both evaluated by using the physical optics (PO) method. The backscattered field from the ocean is evaluated by using the Kirchhoff approximation (KA) method. The characteristics of the coupling backscattered field and the Doppler spectrum are analyzed in detail for different incident conditions.

© 2009 Optical Society of America

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  1. J. C. West and Z. Q. Zhao, “Electromagnetic modeling of multipath scattering from breaking water waves with rough faces,” IEEE Trans. Geosci. Remote Sens. 40, 583-592 (2002).
    [CrossRef]
  2. J. V. Toporkov and G. S. Brown, “Numerical simulations of scattering from time-varying randomly rough surfaces,” IEEE Trans. Geosci. Remote Sens. 38, 1616-1625 (2000).
    [CrossRef]
  3. L. X. Guo and Z. S. 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]
  4. D. Colak, R. J. Burkholder, and E. H. Newman, “Multiple sweep method of moments analysis of electromagnetic scattering from 3D targets on ocean-like rough surfaces,” Microwave Opt. Technol. Lett. 49, 241-247 (2007).
    [CrossRef]
  5. T. Chiu and K. Sarabandi, “Electromagnetic scattering interaction between a dielectric cylinder and slightly rough surface,” IEEE Trans. Antennas Propag. 47, 902-913 (1999).
    [CrossRef]
  6. K. Jamil and R. J. Burkholder, “Radar scattering from a rolling target floating on a time-evolving rough sea surface,” IEEE Trans. Geosci. Remote Sens. 44, 3330-3337 (2006).
    [CrossRef]
  7. D. Holliday, L. L. DeRaad, and G. J. St-Cyr, “Forward-backward: a new method for computing low-grazing angle scattering,” IEEE Trans. Antennas Propag. 44, 722-729 (1996).
    [CrossRef]
  8. P. Liu and Y. Q. Jin, “Numerical simulation of the Doppler spectrum of a flying target above dynamic oceanic surface by using the FEM-DDM method,” IEEE Trans. Antennas Propag. 53, 825-832 (2005).
    [CrossRef]
  9. H. 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]
  10. P. M. Rodriguez, L. Landesa, J. L. Rodriguez, F. Obelleiro, and R. J. Burkholder, “The generalized forward-backward method for analyzing the scattering from targets on ocean-like rough surfaces,” IEEE Trans. Antennas Propag. 47, 961-963 (1999).
    [CrossRef]
  11. L. X. Guo and C. Y. Kim, “Light scattering models for a spherical particle above a slightly dielectric rough surface,” Microwave Opt. Technol. Lett. 33, 142-146 (2002).
    [CrossRef]
  12. L. Li, J. Q. He, Z. J. Liu, 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]
  13. J. V. Bladel, “Electromagnetic fields in the presence of rotating bodies,” in Proceedings of the IEEE (IEEE, 1976), pp. 301-318.
    [CrossRef]
  14. K. Sarabandi and P. F. Polatin, “Electromagnetic scattering from two adjacent objects,” IEEE Trans. Antennas Propag. 42, 510-517 (1994).
    [CrossRef]
  15. Y. H. Wang, L. X. Guo, and Q. Wu, “Electromagnetic scattering from two parallel 2D targets arbitrarily located in a Gaussian beam,” Chin. Phys. 15, 1755-1765 (2006).
    [CrossRef]
  16. J. A. Kong, Electromagnetic Wave Theory (Wiley, 2000), pp. 649-776.
  17. A. K. Fung, Microwave Scattering and Emission Models and Their Applications (Artech House, 1994).
  18. J. Chen, K. Y. Lo, H. Leung, and J. Litva, “The use of fractal for modeling EM waves scattering from rough sea surface,” IEEE Trans. Geosci. Remote Sens. 34, 966-972 (1996).
    [CrossRef]
  19. M. G. Wang, Theory of Geometry Diffraction (Xidian U. Press, 1994).
  20. T. Chiu and K. Sarabandi, “Electromagnetic scattering interaction between a dielectric cylinder and a slightly rough surface,” IEEE Trans. Antennas Propag. 47, 902-913 (1999).
    [CrossRef]
  21. J. C. Chao, F. J. Rizzo, I. Elshafiey, Y. J. Liu, L. Upda, and P. A. Martin, “General formulation for light scattering by a dielectric body near a perfectly conducting surface,” J. Opt. Soc. Am. A 13, 338-344 (1996).
    [CrossRef]
  22. A. D. Rozenberg, D. C. Quigley, and W. K. Melville, “Laboratory study of polarized micro-wave scattering by surface waves at grazing incidence: part I-wind waves,” IEEE Trans. Geosci. Remote Sens. 33, 1037-1046 (1995).
    [CrossRef]
  23. J. T. Johnson, J. V. Toporkov, and G. S. Brown, “A numerical study of backscattering from time-evolving sea surfaces: comparison of hydrodynamic models,” IEEE Trans. Geosci. Remote Sens. 39, 2411-2419 (2001).
    [CrossRef]
  24. J. V. Toporkov 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 Propag. 50, 417-425 (2002).
    [CrossRef]
  25. L. X. Guo, Y. H. Wang, and Z. S. Wu, “Study on the electromagnetic scattering and Doppler spectra from two-scale time-varying fractal rough sea surface,” Acta Phys. Sin. 54, 96-101 (2005).
  26. F. Bass, I. Fuks, A. Kalmykov, I. Ostrovsky, and A. Rosenberg, “Very high frequency radiowave scattering by a disturbed sea surface,” IEEE Trans. Antennas Propag. 16, 554-568 (1968).
    [CrossRef]

2007 (1)

D. Colak, R. J. Burkholder, and E. H. Newman, “Multiple sweep method of moments analysis of electromagnetic scattering from 3D targets on ocean-like rough surfaces,” Microwave Opt. Technol. Lett. 49, 241-247 (2007).
[CrossRef]

2006 (3)

K. Jamil and R. J. Burkholder, “Radar scattering from a rolling target floating on a time-evolving rough sea surface,” IEEE Trans. Geosci. Remote Sens. 44, 3330-3337 (2006).
[CrossRef]

H. 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]

Y. H. Wang, L. X. Guo, and Q. Wu, “Electromagnetic scattering from two parallel 2D targets arbitrarily located in a Gaussian beam,” Chin. Phys. 15, 1755-1765 (2006).
[CrossRef]

2005 (2)

P. Liu and Y. Q. Jin, “Numerical simulation of the Doppler spectrum of a flying target above dynamic oceanic surface by using the FEM-DDM method,” IEEE Trans. Antennas Propag. 53, 825-832 (2005).
[CrossRef]

L. X. Guo, Y. H. Wang, and Z. S. Wu, “Study on the electromagnetic scattering and Doppler spectra from two-scale time-varying fractal rough sea surface,” Acta Phys. Sin. 54, 96-101 (2005).

2004 (1)

L. X. Guo and Z. S. 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 (1)

L. Li, J. Q. He, Z. J. Liu, 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 (3)

J. C. West and Z. Q. Zhao, “Electromagnetic modeling of multipath scattering from breaking water waves with rough faces,” IEEE Trans. Geosci. Remote Sens. 40, 583-592 (2002).
[CrossRef]

L. X. Guo and C. Y. Kim, “Light scattering models for a spherical particle above a slightly dielectric rough surface,” Microwave Opt. Technol. Lett. 33, 142-146 (2002).
[CrossRef]

J. V. Toporkov 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 Propag. 50, 417-425 (2002).
[CrossRef]

2001 (1)

J. T. Johnson, J. V. Toporkov, and G. S. Brown, “A numerical study of backscattering from time-evolving sea surfaces: comparison of hydrodynamic models,” IEEE Trans. Geosci. Remote Sens. 39, 2411-2419 (2001).
[CrossRef]

2000 (1)

J. V. Toporkov and G. S. Brown, “Numerical simulations of scattering from time-varying randomly rough surfaces,” IEEE Trans. Geosci. Remote Sens. 38, 1616-1625 (2000).
[CrossRef]

1999 (3)

T. Chiu and K. Sarabandi, “Electromagnetic scattering interaction between a dielectric cylinder and slightly rough surface,” IEEE Trans. Antennas Propag. 47, 902-913 (1999).
[CrossRef]

P. M. Rodriguez, L. Landesa, J. L. Rodriguez, F. Obelleiro, and R. J. Burkholder, “The generalized forward-backward method for analyzing the scattering from targets on ocean-like rough surfaces,” IEEE Trans. Antennas Propag. 47, 961-963 (1999).
[CrossRef]

T. Chiu and K. Sarabandi, “Electromagnetic scattering interaction between a dielectric cylinder and a slightly rough surface,” IEEE Trans. Antennas Propag. 47, 902-913 (1999).
[CrossRef]

1996 (3)

J. C. Chao, F. J. Rizzo, I. Elshafiey, Y. J. Liu, L. Upda, and P. A. Martin, “General formulation for light scattering by a dielectric body near a perfectly conducting surface,” J. Opt. Soc. Am. A 13, 338-344 (1996).
[CrossRef]

J. Chen, K. Y. Lo, H. Leung, and J. Litva, “The use of fractal for modeling EM waves scattering from rough sea surface,” IEEE Trans. Geosci. Remote Sens. 34, 966-972 (1996).
[CrossRef]

D. Holliday, L. L. DeRaad, and G. J. St-Cyr, “Forward-backward: a new method for computing low-grazing angle scattering,” IEEE Trans. Antennas Propag. 44, 722-729 (1996).
[CrossRef]

1995 (1)

A. D. Rozenberg, D. C. Quigley, and W. K. Melville, “Laboratory study of polarized micro-wave scattering by surface waves at grazing incidence: part I-wind waves,” IEEE Trans. Geosci. Remote Sens. 33, 1037-1046 (1995).
[CrossRef]

1994 (1)

K. Sarabandi and P. F. Polatin, “Electromagnetic scattering from two adjacent objects,” IEEE Trans. Antennas Propag. 42, 510-517 (1994).
[CrossRef]

1968 (1)

F. Bass, I. Fuks, A. Kalmykov, I. Ostrovsky, and A. Rosenberg, “Very high frequency radiowave scattering by a disturbed sea surface,” IEEE Trans. Antennas Propag. 16, 554-568 (1968).
[CrossRef]

Bass, F.

F. Bass, I. Fuks, A. Kalmykov, I. Ostrovsky, and A. Rosenberg, “Very high frequency radiowave scattering by a disturbed sea surface,” IEEE Trans. Antennas Propag. 16, 554-568 (1968).
[CrossRef]

Bladel, J. V.

J. V. Bladel, “Electromagnetic fields in the presence of rotating bodies,” in Proceedings of the IEEE (IEEE, 1976), pp. 301-318.
[CrossRef]

Brown, G. S.

J. V. Toporkov 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 Propag. 50, 417-425 (2002).
[CrossRef]

J. T. Johnson, J. V. Toporkov, and G. S. Brown, “A numerical study of backscattering from time-evolving sea surfaces: comparison of hydrodynamic models,” IEEE Trans. Geosci. Remote Sens. 39, 2411-2419 (2001).
[CrossRef]

J. V. Toporkov and G. S. Brown, “Numerical simulations of scattering from time-varying randomly rough surfaces,” IEEE Trans. Geosci. Remote Sens. 38, 1616-1625 (2000).
[CrossRef]

Burkholder, R. J.

D. Colak, R. J. Burkholder, and E. H. Newman, “Multiple sweep method of moments analysis of electromagnetic scattering from 3D targets on ocean-like rough surfaces,” Microwave Opt. Technol. Lett. 49, 241-247 (2007).
[CrossRef]

K. Jamil and R. J. Burkholder, “Radar scattering from a rolling target floating on a time-evolving rough sea surface,” IEEE Trans. Geosci. Remote Sens. 44, 3330-3337 (2006).
[CrossRef]

P. M. Rodriguez, L. Landesa, J. L. Rodriguez, F. Obelleiro, and R. J. Burkholder, “The generalized forward-backward method for analyzing the scattering from targets on ocean-like rough surfaces,” IEEE Trans. Antennas Propag. 47, 961-963 (1999).
[CrossRef]

Carin, L.

L. Li, J. Q. He, Z. J. Liu, 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]

Chao, J. C.

Chen, J.

J. Chen, K. Y. Lo, H. Leung, and J. Litva, “The use of fractal for modeling EM waves scattering from rough sea surface,” IEEE Trans. Geosci. Remote Sens. 34, 966-972 (1996).
[CrossRef]

Chiu, T.

T. Chiu and K. Sarabandi, “Electromagnetic scattering interaction between a dielectric cylinder and a slightly rough surface,” IEEE Trans. Antennas Propag. 47, 902-913 (1999).
[CrossRef]

T. Chiu and K. Sarabandi, “Electromagnetic scattering interaction between a dielectric cylinder and slightly rough surface,” IEEE Trans. Antennas Propag. 47, 902-913 (1999).
[CrossRef]

Colak, D.

D. Colak, R. J. Burkholder, and E. H. Newman, “Multiple sweep method of moments analysis of electromagnetic scattering from 3D targets on ocean-like rough surfaces,” Microwave Opt. Technol. Lett. 49, 241-247 (2007).
[CrossRef]

DeRaad, L. L.

D. Holliday, L. L. DeRaad, and G. J. St-Cyr, “Forward-backward: a new method for computing low-grazing angle scattering,” IEEE Trans. Antennas Propag. 44, 722-729 (1996).
[CrossRef]

Elshafiey, I.

Fuks, I.

F. Bass, I. Fuks, A. Kalmykov, I. Ostrovsky, and A. Rosenberg, “Very high frequency radiowave scattering by a disturbed sea surface,” IEEE Trans. Antennas Propag. 16, 554-568 (1968).
[CrossRef]

Fung, A. K.

A. K. Fung, Microwave Scattering and Emission Models and Their Applications (Artech House, 1994).

Guo, L. X.

Y. H. Wang, L. X. Guo, and Q. Wu, “Electromagnetic scattering from two parallel 2D targets arbitrarily located in a Gaussian beam,” Chin. Phys. 15, 1755-1765 (2006).
[CrossRef]

L. X. Guo, Y. H. Wang, and Z. S. Wu, “Study on the electromagnetic scattering and Doppler spectra from two-scale time-varying fractal rough sea surface,” Acta Phys. Sin. 54, 96-101 (2005).

L. X. Guo and Z. S. 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]

L. X. Guo and C. Y. Kim, “Light scattering models for a spherical particle above a slightly dielectric rough surface,” Microwave Opt. Technol. Lett. 33, 142-146 (2002).
[CrossRef]

He, J. Q.

L. Li, J. Q. He, Z. J. Liu, 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]

Holliday, D.

D. Holliday, L. L. DeRaad, and G. J. St-Cyr, “Forward-backward: a new method for computing low-grazing angle scattering,” IEEE Trans. Antennas Propag. 44, 722-729 (1996).
[CrossRef]

Jamil, K.

K. Jamil and R. J. Burkholder, “Radar scattering from a rolling target floating on a time-evolving rough sea surface,” IEEE Trans. Geosci. Remote Sens. 44, 3330-3337 (2006).
[CrossRef]

Jin, Y. Q.

H. 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]

P. Liu and Y. Q. Jin, “Numerical simulation of the Doppler spectrum of a flying target above dynamic oceanic surface by using the FEM-DDM method,” IEEE Trans. Antennas Propag. 53, 825-832 (2005).
[CrossRef]

Johnson, J. T.

J. T. Johnson, J. V. Toporkov, and G. S. Brown, “A numerical study of backscattering from time-evolving sea surfaces: comparison of hydrodynamic models,” IEEE Trans. Geosci. Remote Sens. 39, 2411-2419 (2001).
[CrossRef]

Kalmykov, A.

F. Bass, I. Fuks, A. Kalmykov, I. Ostrovsky, and A. Rosenberg, “Very high frequency radiowave scattering by a disturbed sea surface,” IEEE Trans. Antennas Propag. 16, 554-568 (1968).
[CrossRef]

Kim, C. Y.

L. X. Guo and C. Y. Kim, “Light scattering models for a spherical particle above a slightly dielectric rough surface,” Microwave Opt. Technol. Lett. 33, 142-146 (2002).
[CrossRef]

Kong, J. A.

J. A. Kong, Electromagnetic Wave Theory (Wiley, 2000), pp. 649-776.

Landesa, L.

P. M. Rodriguez, L. Landesa, J. L. Rodriguez, F. Obelleiro, and R. J. Burkholder, “The generalized forward-backward method for analyzing the scattering from targets on ocean-like rough surfaces,” IEEE Trans. Antennas Propag. 47, 961-963 (1999).
[CrossRef]

Leung, H.

J. Chen, K. Y. Lo, H. Leung, and J. Litva, “The use of fractal for modeling EM waves scattering from rough sea surface,” IEEE Trans. Geosci. Remote Sens. 34, 966-972 (1996).
[CrossRef]

Li, L.

L. Li, J. Q. He, Z. J. Liu, 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]

Litva, J.

J. Chen, K. Y. Lo, H. Leung, and J. Litva, “The use of fractal for modeling EM waves scattering from rough sea surface,” IEEE Trans. Geosci. Remote Sens. 34, 966-972 (1996).
[CrossRef]

Liu, P.

P. Liu and Y. Q. Jin, “Numerical simulation of the Doppler spectrum of a flying target above dynamic oceanic surface by using the FEM-DDM method,” IEEE Trans. Antennas Propag. 53, 825-832 (2005).
[CrossRef]

Liu, Y. J.

Liu, Z. J.

L. Li, J. Q. He, Z. J. Liu, 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]

Lo, K. Y.

J. Chen, K. Y. Lo, H. Leung, and J. Litva, “The use of fractal for modeling EM waves scattering from rough sea surface,” IEEE Trans. Geosci. Remote Sens. 34, 966-972 (1996).
[CrossRef]

Martin, P. A.

Melville, W. K.

A. D. Rozenberg, D. C. Quigley, and W. K. Melville, “Laboratory study of polarized micro-wave scattering by surface waves at grazing incidence: part I-wind waves,” IEEE Trans. Geosci. Remote Sens. 33, 1037-1046 (1995).
[CrossRef]

Newman, E. H.

D. Colak, R. J. Burkholder, and E. H. Newman, “Multiple sweep method of moments analysis of electromagnetic scattering from 3D targets on ocean-like rough surfaces,” Microwave Opt. Technol. Lett. 49, 241-247 (2007).
[CrossRef]

Obelleiro, F.

P. M. Rodriguez, L. Landesa, J. L. Rodriguez, F. Obelleiro, and R. J. Burkholder, “The generalized forward-backward method for analyzing the scattering from targets on ocean-like rough surfaces,” IEEE Trans. Antennas Propag. 47, 961-963 (1999).
[CrossRef]

Ostrovsky, I.

F. Bass, I. Fuks, A. Kalmykov, I. Ostrovsky, and A. Rosenberg, “Very high frequency radiowave scattering by a disturbed sea surface,” IEEE Trans. Antennas Propag. 16, 554-568 (1968).
[CrossRef]

Polatin, P. F.

K. Sarabandi and P. F. Polatin, “Electromagnetic scattering from two adjacent objects,” IEEE Trans. Antennas Propag. 42, 510-517 (1994).
[CrossRef]

Quigley, D. C.

A. D. Rozenberg, D. C. Quigley, and W. K. Melville, “Laboratory study of polarized micro-wave scattering by surface waves at grazing incidence: part I-wind waves,” IEEE Trans. Geosci. Remote Sens. 33, 1037-1046 (1995).
[CrossRef]

Rizzo, F. J.

Rodriguez, J. L.

P. M. Rodriguez, L. Landesa, J. L. Rodriguez, F. Obelleiro, and R. J. Burkholder, “The generalized forward-backward method for analyzing the scattering from targets on ocean-like rough surfaces,” IEEE Trans. Antennas Propag. 47, 961-963 (1999).
[CrossRef]

Rodriguez, P. M.

P. M. Rodriguez, L. Landesa, J. L. Rodriguez, F. Obelleiro, and R. J. Burkholder, “The generalized forward-backward method for analyzing the scattering from targets on ocean-like rough surfaces,” IEEE Trans. Antennas Propag. 47, 961-963 (1999).
[CrossRef]

Rosenberg, A.

F. Bass, I. Fuks, A. Kalmykov, I. Ostrovsky, and A. Rosenberg, “Very high frequency radiowave scattering by a disturbed sea surface,” IEEE Trans. Antennas Propag. 16, 554-568 (1968).
[CrossRef]

Rozenberg, A. D.

A. D. Rozenberg, D. C. Quigley, and W. K. Melville, “Laboratory study of polarized micro-wave scattering by surface waves at grazing incidence: part I-wind waves,” IEEE Trans. Geosci. Remote Sens. 33, 1037-1046 (1995).
[CrossRef]

Sarabandi, K.

T. Chiu and K. Sarabandi, “Electromagnetic scattering interaction between a dielectric cylinder and a slightly rough surface,” IEEE Trans. Antennas Propag. 47, 902-913 (1999).
[CrossRef]

T. Chiu and K. Sarabandi, “Electromagnetic scattering interaction between a dielectric cylinder and slightly rough surface,” IEEE Trans. Antennas Propag. 47, 902-913 (1999).
[CrossRef]

K. Sarabandi and P. F. Polatin, “Electromagnetic scattering from two adjacent objects,” IEEE Trans. Antennas Propag. 42, 510-517 (1994).
[CrossRef]

St-Cyr, G. J.

D. Holliday, L. L. DeRaad, and G. J. St-Cyr, “Forward-backward: a new method for computing low-grazing angle scattering,” IEEE Trans. Antennas Propag. 44, 722-729 (1996).
[CrossRef]

Toporkov, J. V.

J. V. Toporkov 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 Propag. 50, 417-425 (2002).
[CrossRef]

J. T. Johnson, J. V. Toporkov, and G. S. Brown, “A numerical study of backscattering from time-evolving sea surfaces: comparison of hydrodynamic models,” IEEE Trans. Geosci. Remote Sens. 39, 2411-2419 (2001).
[CrossRef]

J. V. Toporkov and G. S. Brown, “Numerical simulations of scattering from time-varying randomly rough surfaces,” IEEE Trans. Geosci. Remote Sens. 38, 1616-1625 (2000).
[CrossRef]

Upda, L.

Wang, M. G.

M. G. Wang, Theory of Geometry Diffraction (Xidian U. Press, 1994).

Wang, Y. H.

Y. H. Wang, L. X. Guo, and Q. Wu, “Electromagnetic scattering from two parallel 2D targets arbitrarily located in a Gaussian beam,” Chin. Phys. 15, 1755-1765 (2006).
[CrossRef]

L. X. Guo, Y. H. Wang, and Z. S. Wu, “Study on the electromagnetic scattering and Doppler spectra from two-scale time-varying fractal rough sea surface,” Acta Phys. Sin. 54, 96-101 (2005).

West, J. C.

J. C. West and Z. Q. Zhao, “Electromagnetic modeling of multipath scattering from breaking water waves with rough faces,” IEEE Trans. Geosci. Remote Sens. 40, 583-592 (2002).
[CrossRef]

Wu, Q.

Y. H. Wang, L. X. Guo, and Q. Wu, “Electromagnetic scattering from two parallel 2D targets arbitrarily located in a Gaussian beam,” Chin. Phys. 15, 1755-1765 (2006).
[CrossRef]

Wu, Z. S.

L. X. Guo, Y. H. Wang, and Z. S. Wu, “Study on the electromagnetic scattering and Doppler spectra from two-scale time-varying fractal rough sea surface,” Acta Phys. Sin. 54, 96-101 (2005).

L. X. Guo and Z. S. 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]

Ye, H.

H. 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]

Zhao, Z. Q.

J. C. West and Z. Q. Zhao, “Electromagnetic modeling of multipath scattering from breaking water waves with rough faces,” IEEE Trans. Geosci. Remote Sens. 40, 583-592 (2002).
[CrossRef]

Acta Phys. Sin. (1)

L. X. Guo, Y. H. Wang, and Z. S. Wu, “Study on the electromagnetic scattering and Doppler spectra from two-scale time-varying fractal rough sea surface,” Acta Phys. Sin. 54, 96-101 (2005).

Chin. Phys. (1)

Y. H. Wang, L. X. Guo, and Q. Wu, “Electromagnetic scattering from two parallel 2D targets arbitrarily located in a Gaussian beam,” Chin. Phys. 15, 1755-1765 (2006).
[CrossRef]

IEEE Trans. Antennas Propag. (9)

P. M. Rodriguez, L. Landesa, J. L. Rodriguez, F. Obelleiro, and R. J. Burkholder, “The generalized forward-backward method for analyzing the scattering from targets on ocean-like rough surfaces,” IEEE Trans. Antennas Propag. 47, 961-963 (1999).
[CrossRef]

L. Li, J. Q. He, Z. J. Liu, 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]

T. Chiu and K. Sarabandi, “Electromagnetic scattering interaction between a dielectric cylinder and slightly rough surface,” IEEE Trans. Antennas Propag. 47, 902-913 (1999).
[CrossRef]

D. Holliday, L. L. DeRaad, and G. J. St-Cyr, “Forward-backward: a new method for computing low-grazing angle scattering,” IEEE Trans. Antennas Propag. 44, 722-729 (1996).
[CrossRef]

P. Liu and Y. Q. Jin, “Numerical simulation of the Doppler spectrum of a flying target above dynamic oceanic surface by using the FEM-DDM method,” IEEE Trans. Antennas Propag. 53, 825-832 (2005).
[CrossRef]

F. Bass, I. Fuks, A. Kalmykov, I. Ostrovsky, and A. Rosenberg, “Very high frequency radiowave scattering by a disturbed sea surface,” IEEE Trans. Antennas Propag. 16, 554-568 (1968).
[CrossRef]

K. Sarabandi and P. F. Polatin, “Electromagnetic scattering from two adjacent objects,” IEEE Trans. Antennas Propag. 42, 510-517 (1994).
[CrossRef]

J. V. Toporkov 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 Propag. 50, 417-425 (2002).
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IEEE Trans. Geosci. Remote Sens. (7)

A. D. Rozenberg, D. C. Quigley, and W. K. Melville, “Laboratory study of polarized micro-wave scattering by surface waves at grazing incidence: part I-wind waves,” IEEE Trans. Geosci. Remote Sens. 33, 1037-1046 (1995).
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J. T. Johnson, J. V. Toporkov, and G. S. Brown, “A numerical study of backscattering from time-evolving sea surfaces: comparison of hydrodynamic models,” IEEE Trans. Geosci. Remote Sens. 39, 2411-2419 (2001).
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H. 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).
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K. Jamil and R. J. Burkholder, “Radar scattering from a rolling target floating on a time-evolving rough sea surface,” IEEE Trans. Geosci. Remote Sens. 44, 3330-3337 (2006).
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Supplementary Material (21)

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Figures (15)

Fig. 1
Fig. 1

Configuration of the scattering problem.

Fig. 2
Fig. 2

Composite scattering model.

Fig. 3
Fig. 3

Comparison of the coupling RCS by the reciprocity theorem and the image method for a different tilted angle α.

Fig. 4
Fig. 4

Angular distribution of coupling RCS for a different windspeed.

Fig. 5
Fig. 5

Angular distribution of total backscattering RCS with a different size of the plate.

Fig. 6
Fig. 6

Angular distribution of total backscattering RCS with a different height of the plate.

Fig. 7
Fig. 7

Angular distribution of total backscattering RCS with a different tilted angle α.

Fig. 8
Fig. 8

Doppler spectrum of the backscattered field for a different windspeed.

Fig. 9
Fig. 9

Doppler spectrum of the total backscattered field for a different size of the plate.

Fig. 10
Fig. 10

Doppler spectrum of the total backscattered field for a different height of the plate.

Fig. 11
Fig. 11

Doppler spectrum of the total backscattered field for a different incident angle.

Fig. 12
Fig. 12

Doppler spectrum of the backscattered field for V = 10 m s .

Fig. 13
Fig. 13

Normalized Doppler spectrum of the total backscattered field for a different moving velocity of the plate.

Fig. 14
Fig. 14

Doppler spectrum of the backscattered field for a different windspeed with V = 10 m s .

Fig. 15
Fig. 15

Comparison of the Doppler spectrum of the backscattered field from the composite model with different incident angles.

Equations (59)

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p ̂ E pr s = S c J r E ep s d S ,
q ̂ H pr s = S c M r H mp s d S .
W ( K x ) = { α 2 K x 3 exp ( β g 2 K x 2 U 19.5 4 ) 0 K x , 0 K x < 0 , }
{ f ( x , t ) = m = 0 N A m cos ( K m x ω m t + Φ m ) f x ( x , t ) = m = 0 N A m K m sin ( K m x ω m t + Φ m ) } ,
E r s ( r 0 , t ) = i k exp ( i k r 0 ) 4 π r 0 L f L f ( p f x ( x , t ) q ) exp i [ v x x + v z f ( x , t ) ] d x ,
p = ( 1 R ) sin θ i + ( 1 + R ) sin θ s ,
q = ( 1 + R ) cos θ s ( 1 R ) cos θ i ,
v x = k ( sin θ i sin θ s ) ,
v z = k ( cos θ i + cos θ s ) ,
R vv = ε r cos θ l ( ε r sin 2 θ l ) 1 2 ε r cos θ l + ( ε r sin 2 θ l ) 1 2 , R hh = cos θ l ( ε r sin 2 θ l ) 1 2 cos θ l + ( ε r sin 2 θ l ) 1 2 ,
J rte = ( 1 R hh ) n ̂ × H i = ( 1 R hh ) ε μ ( cos θ i + f x sin θ i ) 1 + f x 2 exp ( j k x sin θ i j k f cos θ i ) y ̂ ,
M rte = ( 1 + R hh ) n ̂ × E i = ( 1 + R hh ) x ̂ + f x z ̂ 1 + f x 2 exp ( j k x sin θ i j k f cos θ i ) .
E r s ( r , r ) = i ω μ s [ G ̿ ( r , r ) exp ( j k r r ) 4 π r r J rte + × G ̿ ( r , r ) M rte ] d s ;
J rtm = ( 1 + R ) n ̂ × H i = ( 1 + R ) x ̂ + f x z ̂ 1 + f x 2 exp ( j k sin θ i j k f cos θ i ) ,
M rtm = ( 1 R ) n ̂ × E i = ( 1 R ) cos θ i + f sin θ i 1 + f x 2 exp ( j k x sin θ i j k f cos θ i ) y ̂ .
{ x 0 = x 00 + V t sin ϴ cos Φ y 0 = y 00 + V t sin ϴ sin Φ z 0 = z 00 + V t cos ϴ } ,
z = z 0 ( x x 0 ) tan α ,
x = x 0 .
J p = 2 n ̂ × H i = 2 ε μ cos ( θ i + α ) exp ( j k x sin θ i j k z cos θ i ) y ̂ = 2 ε μ cos ( θ i + α ) exp [ j k ( sin θ i + cos θ i tan α ) x j k ( z 0 cos θ i + x 0 cos θ i tan α ) ] y ̂ .
E p s = j ε μ ω cos ( α + θ i ) exp ( i k r ) y ̂ exp [ j k ( cos θ i + cos θ s ) ( z 0 + tan α x 0 ) ] W exp { j k [ ( sin θ i sin θ s ) + ( cos θ i + cos θ s ) tan α ] x 0 } sin [ ( k sin θ i + k cos θ i tan α k sin θ s + k cos θ s tan α ) cos α L 2 ] [ π r cos α ( k sin θ i + k cos θ i tan α k sin θ s + k cos θ s tan α ) ] ,
J p = 2 n ̂ × H i = 2 ε μ cos ( θ i + α ) exp ( j k x 0 sin θ i j k z cos θ i ) y ̂ ,
E p s = j ε μ ω W sin θ i exp [ j k ( cos θ i + cos θ s ) z 0 ] exp [ j k ( sin θ i sin θ s ) x 0 ] sin [ ( k cos θ i + k cos θ s ) L 2 ] [ π r ( k cos θ i + k cos θ s ) ] exp ( j k r ) y ̂ .
E p s = j ε μ ω exp ( j k r ) exp [ j k ( cos θ i + cos θ s ) ( z 0 + tan α x 0 ) ] W exp { j k [ ( sin θ i sin θ s ) + ( cos θ i + cos θ s ) tan α ] x 0 } ( sin α sin θ s + cos α cos θ s ) sin [ ( k sin θ i + k cos θ i tan α k sin θ s + k cos θ s tan α ) cos α L 2 ] θ ̂ s [ π r cos α ( k sin θ i + k cos θ i tan α k sin θ s + k cos θ s tan α ) ] .
E p s = j sin θ s ε μ ω exp ( j k r ) exp [ j k ( cos θ i + cos θ s ) z 0 ] sin [ ( k cos θ i + k cos θ s ) L 2 ] W θ ̂ s exp [ j k ( sin θ i sin θ s ) x 0 ] [ π r ( k cos θ i + k cos θ s ) ] .
E ed ( r ) = j k Z 0 4 π r 0 exp ( j k 0 r 0 ) exp ( j k s r ) y ̂ ,
H md ( r ) = j k Y 0 4 π r 0 exp ( j k 0 r 0 ) exp ( j k s r ) θ ̂ ;
E ed ( r ) = E 0 exp ( i k s r ) y ̂ , H md ( r ) = H 0 exp ( i k s r ) θ ̂ .
A ̃ = x x 0 , B ̃ = y y 0 , C ̃ = z z 0 , D ̃ = A ̃ 2 + B ̃ 2 + C ̃ 2 ,
E ̃ = f ( x ) z 0 ,
F ̃ = ( A ̃ E ̃ tan α ) D ̃ sin θ i tan α cos θ i ,
G ̃ = ( 1 sin 2 θ ss sin 2 φ ss ) y ̂ sin 2 θ ss cos φ ss sin φ ss x ̂ sin θ ss cos θ ss sin φ ss z ̂ ,
E ep sh = j ω μ ( I ̿ r ̂ r ̂ ) cos α s p [ exp ( j k r r ) 4 π r r 2 E 0 ε μ cos ( θ i + α ) exp ( j k x sin θ i j k cos θ i z ) y ̂ ] d x d y j ( I ̿ r ̂ r ̂ ) y ̂ ω μ E 0 ε μ cos ( θ i + α ) k B ̃ π cos α sin ( k B ̃ W 2 A ̃ 2 + B ̃ 2 + C ̃ 2 ) x 0 L cos α 2 x 0 + L cos α 2 exp { j k [ D ̃ A ̃ ( x x 0 ) + E ̃ ( z z 0 ) D ̃ + x sin θ i z cos θ i ] } d x = j E 0 cos ( θ i + α ) π sin ( k B ̃ W 2 D ̃ ) 2 G ̃ k B ̃ sin [ k ( sin θ i + tan α cos θ i A ̃ E ̃ tan α D ̃ ) cos α L 2 ] cos α F ̃ exp { j k [ ( E ̃ D ̃ + cos θ i ) ( z 0 + x 0 tan α ) + D ̃ + A ̃ x 0 + E ̃ z 0 D ̃ F ̃ x 0 ] } ,
H mp sh = ( sin θ ss cos φ ss z ̂ cos θ ss x ̂ ) j H 0 cos ( θ i + α ) π 2 k B ̃ exp ( j k A ̃ 2 + E ̃ 2 ) exp ( j k A ̃ x 0 + E ̃ z 0 D ̃ ) exp [ j k ( E ̃ D ̃ + cos θ i ) ( z 0 + x 0 tan α ) ] exp ( j k F ̃ x 0 ) sin ( k F ̃ cos α L 2 ) sin ( k B ̃ W 2 D ̃ ) ( cos α F ̃ ) .
E ep sh = G ̃ j 2 E 0 sin θ i π sin ( W k B ̃ 2 D ̃ ) 1 k B ̃ sin [ k ( E ̃ D ̃ + cos θ i ) L 2 ] exp [ j k ( cos θ i z 0 + sin θ i x 0 + D ̃ ) ] ( E ̃ D ̃ + cos θ i ) ,
H mp sh = ( cos θ ss x ̂ + sin θ ss cos φ ss z ̂ ) j H 0 sin θ i π k B ̃ sin [ k ( E ̃ D ̃ + cos θ i ) L 2 ] 2 sin ( k W B ̃ 2 D ̃ ) exp [ j k ( sin θ i x 0 cos θ i z 0 + D ̃ ) ] ( E ̃ D ̃ + cos θ i ) .
E ep sv = j [ ( sin 2 θ ss cos 2 φ ss 1 ) x ̂ + sin 2 θ ss sin φ ss cos φ ss y ̂ + sin θ ss cos θ ss cos φ ss z ̂ ] E 0 π sin ( k W B ̃ 2 D ̃ ) 2 k B ̃ exp ( j k D ̃ ) exp ( j k A ̃ x 0 + E ̃ z 0 D ̃ ) exp [ j k ( E ̃ D ̃ + cos θ i ) ( z 0 + x 0 tan α ) ] exp ( j k F ̃ x 0 ) sin ( k F ̃ cos α L 2 ) ( cos α F ̃ ) ,
H mp sv = j 2 H 0 k B ̃ ( sin θ ss sin φ ss z ̂ cos θ ss y ̂ ) π sin ( W k B ̃ 2 D ̃ ) exp ( j k A ̃ x 0 + E ̃ z 0 D ̃ ) exp ( j k D ̃ ) exp [ j k ( E ̃ D ̃ + cos θ i ) ( z 0 + x 0 tan α ) ] exp ( j k F ̃ x 0 ) sin ( k F ̃ cos α L 2 ) ( cos α F ̃ ) ,
E ep sv = [ ( sin 2 θ ss cos 2 φ ss 1 ) x ̂ + sin 2 θ ss sin φ ss cos φ ss y ̂ + sin θ ss cos θ ss cos φ ss z ̂ ] π sin ( k W B ̃ 2 D ̃ ) j E 0 2 k B ̃ exp ( j k D ̃ ) exp ( j k cos θ i z 0 + j k sin θ i x 0 ) sin { k [ E ̃ D ̃ + cos θ i ] L 2 } [ E ̃ D ̃ + cos θ i ] ,
H mp sv = j ( cos θ ss y ̂ + sin θ ss sin φ ss z ̂ ) H 0 π k B ̃ sin ( k W B ̃ 2 D ̃ ) exp ( j k D ̃ ) sin [ k ( E ̃ D ̃ + cos θ i ) L 2 ] 2 exp ( j k cos θ i z 0 + j k sin θ i x 0 ) ( E ̃ D ̃ + cos θ i ) ,
h ̂ E pr sh = s r J rte E ep sh d s = j ε μ E 0 cos ( θ i + α ) ( 1 R h h ) s r ( cos θ i + f x sin θ i ) exp [ j k x sin θ i j k f cos θ i ] 1 + f x sin ( k W B ̃ 2 D ̃ ) 2 D ̃ k B ̃ ( 1 sin 2 θ ss sin 2 φ ss ) exp [ ( j k A ̃ x 0 + E ̃ z 0 D ̃ j k ( E ̃ D ̃ + cos θ i ) ( z 0 + x 0 tan α ) ) ] exp ( j k D ̃ j k F ̃ x 0 ) sin ( k F ̃ cos α L 2 ) { cos α π tan α [ A ̃ E ̃ ( sin θ i + tan α cos θ i ) D ̃ ] } d x d y ,
v ̂ H pr sh = s r M rte H ep sh d s = j H 0 cos ( θ i + α ) ( 1 + R h h ) π s r ( ( f x sin α cos α ) cos θ ss + ( f x cos α + sin α ) sin θ ss cos φ ss ) 1 + f x 2 exp { j k [ x sin θ i f ( x ) cos θ i + D ̃ + A ̃ x 0 + E ̃ z 0 D ̃ D ̃ k B ̃ ( E ̃ D ̃ + cos θ i ) ( z 0 + x 0 tan α ) F ̃ x 0 ] } 2 sin ( k W B ̃ 2 D ̃ ) sin ( k F ̃ cos α L 2 ) { cos α [ A ̃ E ̃ tan α ( sin θ i + tan α cos θ i ) D ̃ ] } d x d y ,
h ̂ E pr sh = s r J rte E ep sh d s = j ε μ E 0 sin θ i ( 1 R h h ) π s r exp { j k [ x sin θ i f ( x ) cos θ i + D ̃ cos θ i z 0 + sin θ i x 0 ] } ( cos θ i + f x sin θ i ) 1 + f x 2 D ̃ k B ̃ sin ( k W B ̃ 2 D ̃ ) sin [ k ( E ̃ D ̃ + cos θ i ) L 2 ] ( 1 sin 2 θ ss sin 2 φ ss ) [ E ̃ + D ̃ cos θ i ] d x d y ,
v ̂ H pr sh = s r M rte H ep sh d s = s r ( ( f x sin α cos α ) cos θ ss + ( f x cos α + sin α ) sin θ ss cos φ ss ) 1 + f x 2 exp { j k [ x sin θ i f ( x ) cos θ i cos θ i z 0 + sin θ i x 0 + D ̃ ] } D ̃ sin [ k W B ̃ 2 D ̃ ] j 2 H 0 sin θ i ( 1 + R h h ) π sin { k [ E ̃ D ̃ + cos θ ] L 2 } k B ̃ [ E ̃ + cos θ i D ̃ ] d x d y .
h ̂ E pr ̱ total sh = h ̂ E pr sh + μ ε v ̂ H pr sh .
v ̂ E pr sv = s r J rtm E ep sv d s = ε μ ( 1 + R v v ) s r j E 0 1 + f x 2 { ( 1 sin 2 θ ss cos 2 φ ss ) cos α + sin α sin θ ss cos θ ss cos φ ss f x [ ( 1 sin 2 θ ss cos 2 φ ss ) sin α + f x cos α sin θ ss cos θ ss cos φ ss ] } sin [ k W B ̃ 2 D ̃ ] 2 D ̃ k B ̃ exp { j k [ x sin θ i f ( x ) cos θ i + D ̃ + A ̃ x 0 + E ̃ z 0 D ̃ ( E ̃ D ̃ + cos θ i ) ( z 0 + x 0 tan α ) F ̃ x 0 ] } sin { k F ̃ cos α L 2 } { cos α π [ A ̃ E ̃ tan α ( sin θ i + tan α cos θ i ) D ̃ ] } d x d y ,
h ̂ H pr sv = s r M rtm H ep sv d s = j H 0 ( 1 R v v ) π s r ( cos θ i + f x sin θ i ) cos θ ss exp [ j k x sin θ i j k f cos θ i ] 1 + f x 2 sin ( k W B ̃ 2 D ̃ ) 2 D ̃ k B ̃ exp { j k [ D ̃ + A ̃ x 0 + E ̃ z 0 D ̃ ( E ̃ D ̃ + cos θ i ) ( z 0 + x 0 tan α ) ( A ̃ E ̃ tan α D ̃ sin θ i tan α cos θ i ) x 0 ] } sin ( k F ̃ cos α L 2 ) { π cos α [ A ̃ E ̃ tan α ( sin θ i + tan α cos θ i ) D ̃ ] } d x d y ,
v ̂ E pr sv = s r J rtm E ep sv d s r = ε μ s r 2 D ̃ k B ̃ j E 0 ( 1 + R v v ) π 1 + f x 2 { ( 1 sin 2 θ ss cos 2 φ ss ) cos α + sin α sin θ ss cos θ ss cos φ ss f x [ ( 1 sin 2 θ ss cos 2 φ ss ) sin α + f x cos α sin θ ss cos θ ss cos φ ss ] } sin [ k ( E ̃ D ̃ + cos θ i ) L 2 ] exp { j k [ x sin θ i f ( x ) cos θ i + D ̃ cos θ i z 0 + sin θ i x 0 ] } sin ( k W B ̃ 2 D ̃ ) [ E ̃ + cos θ i D ̃ ] d x d y ,
h ̂ H pr sv = s r M rtm H ep sv d s = j H 0 ( 1 R v v ) π s r ( cos θ i + f x sin θ i ) cos θ ss 1 + f x 2 sin ( k W B ̃ 2 D ̃ ) 2 D ̃ k B ̃ sin [ k ( E ̃ D ̃ + cos θ i ) L 2 ] exp { j k [ D ̃ cos θ i z 0 + sin θ i x 0 + x sin θ i f ( x ) cos θ i ] } ( E ̃ + cos θ i D ̃ ) d x d y .
v ̂ E pr ̱ total sv = v ̂ E pr sv + μ ε h ̂ H pr sv .
y 2 = y 0 + W 2 ,
y 1 = y 0 W 2 ,
x 2 = x 0 + L 2 sin ( π 2 α ) [ z 0 L 2 cos ( π 2 α ) ] cot ( 3 2 π θ i 2 α + β ) ,
x 1 = x 0 L 2 sin ( π 2 α ) [ z 0 + L 2 cos ( π 2 α ) ] cot ( 3 2 π θ i 2 α β ) .
E s = [ exp ( j k r ) r ] S ̿ E i ,
S ̿ rp ( k ̂ s , k ̂ i ) = S ̿ pr ( t ) ( k ̂ i , k ̂ s ) ,
( S rp v v ( k ̂ i , k ̂ s ) S rp vh ( k ̂ i , k ̂ s ) S rp hv ( k ̂ i , k ̂ s ) S rp h h ( k ̂ i , k ̂ s ) ) = ( S pr v v ( k ̂ s , k ̂ i ) S pr hv ( k ̂ s , k ̂ i ) S pr vh ( k ̂ s , k ̂ i ) S pr h h ( k ̂ s , k ̂ i ) ) .
( S rp v v 0 0 S rp h h ) = ( S pr v v 0 0 S pr h h ) .
σ pr = 4 π 2 S pr 2 , σ = 4 π S r + 2 S pr + S p 2 ,
S ( f ) = 1 T 0 T E s ( t , θ i , θ s ) exp ( j 2 π f t ) d t 2

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