Abstract

A two-dimensional beam is scattered by a cylinder buried below a slightly rough surface. The cylindrical wave approach is applied, i.e., cylindrical waves are employed as basis functions of the fields scattered by the cylinder. Moreover, a spectral representation of both the incident field and the cylindrical waves is used. Rough surface deviation is coped with by the first-order small perturbation method. Therefore, to a zeroth-order solution relevant to scattering in the case of a flat surface, a first-order approximation is superimposed. The theoretical approach has been implemented for a periodic surface with Gaussian roughness spectrum.

© 2013 Optical Society of America

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  1. D. J. Daniels, Ground Penetrating Radar, 2nd ed. (IET, 2004).
  2. B. P. D’Yakonov, “The diffraction of electromagnetic waves by a circular cylinder in a homogeneous half-space,” Atmos. Oceanic Phys.950–955 (1959).
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    [CrossRef]
  4. S. O. Ogunade, “Electromagnetic response of an embedded cylinder for line current excitation,” Geophysics 46, 45–52 (1981).
    [CrossRef]
  5. S. F. Mahmoud, S. M. Ali, and J. R. Wait, “Electromagnetic scattering from a buried cylindrical inhomogeneity inside a lossy earth,” Radio Sci. 16, 1285–1298 (1981).
    [CrossRef]
  6. C. M. Butler, X.-B. Xu, and A. W. Glisson, “Current induced on a conducting cylinder located near the planar interface between two semi-infinite half-spaces,” IEEE Trans. Antennas Propag. 33, 616–624 (1985).
    [CrossRef]
  7. K. Hongo and A. Hamamura, “Asymptotic solutions for the scattered field of plane wave by a cylindrical obstacle buried in a dielectric half-space,” IEEE Trans. Antennas Propag. 34, 1306–1312 (1986).
    [CrossRef]
  8. M. Di Vico, F. Frezza, L. Pajewski, and G. Schettini, “Scattering by buried dielectric cylindrical structures,” Radio Sci. 40, RS6S18 (2005).
    [CrossRef]
  9. S. Ahmed and Q. A. Naqvi, “Electromagnetic scattering from a perfect electromagnetic conductor cylinder buried in a dielectric half-space,” Prog. Electromagn. Res. 78, 25–38 (2008).
    [CrossRef]
  10. F. Frezza, L. Pajewski, C. Ponti, and G. Schettini, “Line source scattering by buried perfectly conducting circular cylinders,” Int. J. Antennas Propag. 2012, 1–7 (2012).
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  11. L. Tsang, J. A. Kong, and K.-H. Ding, Scattering of Electromagnetic Waves: Theories and Applications (Wiley, 2001).
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    [CrossRef]
  13. F. G. Bass and I. M. Fuks, Wave Scattering from Statistically Rough Surfaces (Pergamon, 1979).
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    [CrossRef]
  17. P. G. Cottis and J. D. Kanellopoulos, “Scattering of electromagnetic waves from cylindrical inhomogeneities embedded inside a lossy medium with a sinusoidal surface,” J. Electromagn. Waves. Appl. 6, 445–458 (1992).
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  20. K. O’Neill, R. F. Lussky, and K. D. Paulsen, “Scattering from a metallic object embedded near the randomly rough surface of a lossy dielectric,” IEEE Trans. Geosci. Remote Sens. 34, 367–376 (1996).
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    [CrossRef]
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  24. Z.-X. Li, “Bistatic scattering from rough dielectric soil surface with a conducting object partially buried by using the gfbm/saa method,” IEEE Trans. Antennas Propag. 54, 2072–2080 (2006).
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  25. J. T. Johson and R. J. Burkholder, “A study of scattering from an object below a rough surface,” IEEE Trans. Geosci. Remote Sens. 42, 59–66 (2004).
    [CrossRef]
  26. C. Bourlier, G. Kubick, and N. Pinel, “PILE method combined with PO for the scattering by coated cylinders, a rough layer and an object below a rough surface,” J. Opt. Soc. Am. A 30, 1727–1737 (2013).
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    [CrossRef]
  29. M. A. Fiaz, F. Frezza, L. Pajewski, C. Ponti, and G. Schettini, “Asymptotic solution for a scattered field by cylindrical objects buried beneath a slightly rough surface,” Near Surf. Geophys. 11, 177–183 (2013).
  30. F. Frezza, L. Pajewski, C. Ponti, G. Schettini, and N. Tedeschi, “Electromagnetic scattering by a metallic cylinder buried in a lossy medium with the cylindrical wave approach,” Geosci. Remote Sens. Lett. 10, 179–183 (2013).
  31. F. Frezza, L. Pajewski, C. Ponti, G. Schettini, and N. Tedeschi, “Cylindrical-wave approach for electromagnetic scattering by subsurface metallic targets in a lossy medium,” J. Appl. Geophys. 97, 55–59 (2013).
    [CrossRef]
  32. F. Frezza, L. Pajewski, C. Ponti, and G. Schettini, “Scattering by dielectric circular cylinders in a dielectric slab,” J. Opt. Soc. Am. A 27, 687–695 (2010).
    [CrossRef]
  33. R. Borghi, F. Frezza, P. Oliverio, M. Santarsiero, and G. Schettini, “Scattering of a generic two-dimensional field by cylindrical structures in the presence of a plane interface,” Int. J. Infrared Millim. Waves 21, 805–827 (2000).
    [CrossRef]
  34. A. Papoulis, Probability, Random Variables, and Stochastic Processes (McGraw-Hill, 1984).
  35. A. Z. Elsherbeni, “A comparative study of two-dimensional multiple scattering techniques,” Radio Sci. 29, 1023–1033 (1994).
    [CrossRef]
  36. F. Frezza, L. Pajewski, C. Ponti, and G. Schettini, “Accurate wire-grid modelling of buried conducting cylindrical scatterers,” Nondestr. Test. Eval. 27, 199–207 (2012), Special issue on Civil Engineering Applications of Ground Penetrating Radar.
    [CrossRef]

2013 (4)

M. A. Fiaz, F. Frezza, L. Pajewski, C. Ponti, and G. Schettini, “Asymptotic solution for a scattered field by cylindrical objects buried beneath a slightly rough surface,” Near Surf. Geophys. 11, 177–183 (2013).

F. Frezza, L. Pajewski, C. Ponti, G. Schettini, and N. Tedeschi, “Electromagnetic scattering by a metallic cylinder buried in a lossy medium with the cylindrical wave approach,” Geosci. Remote Sens. Lett. 10, 179–183 (2013).

F. Frezza, L. Pajewski, C. Ponti, G. Schettini, and N. Tedeschi, “Cylindrical-wave approach for electromagnetic scattering by subsurface metallic targets in a lossy medium,” J. Appl. Geophys. 97, 55–59 (2013).
[CrossRef]

C. Bourlier, G. Kubick, and N. Pinel, “PILE method combined with PO for the scattering by coated cylinders, a rough layer and an object below a rough surface,” J. Opt. Soc. Am. A 30, 1727–1737 (2013).
[CrossRef]

2012 (3)

F. Frezza, L. Pajewski, C. Ponti, and G. Schettini, “Accurate wire-grid modelling of buried conducting cylindrical scatterers,” Nondestr. Test. Eval. 27, 199–207 (2012), Special issue on Civil Engineering Applications of Ground Penetrating Radar.
[CrossRef]

M. A. Fiaz, F. Frezza, L. Pajewski, C. Ponti, and G. Schettini, “Scattering by a circular cylinder buried under a slightly rough surface: the cylindrical-wave approach,” IEEE Trans. Antennas Propag. 60, 2834–2842 (2012).
[CrossRef]

F. Frezza, L. Pajewski, C. Ponti, and G. Schettini, “Line source scattering by buried perfectly conducting circular cylinders,” Int. J. Antennas Propag. 2012, 1–7 (2012).
[CrossRef]

2010 (1)

2008 (1)

S. Ahmed and Q. A. Naqvi, “Electromagnetic scattering from a perfect electromagnetic conductor cylinder buried in a dielectric half-space,” Prog. Electromagn. Res. 78, 25–38 (2008).
[CrossRef]

2006 (3)

Y. Altuncu, A. Yapar, and I. Akduman, “On the scattering of electromagnetic waves by bodies buried in a half-space with locally rough interface,” IEEE Trans. Geosci. Remote Sens. 44, 1435–1443 (2006).
[CrossRef]

C.-H. Kuo and M. Moghaddam, “Electromagnetic scattering from a buried cylinder in layered media with rough interfaces,” IEEE Trans. Antennas Propag. 54, 2392–2401 (2006).
[CrossRef]

Z.-X. Li, “Bistatic scattering from rough dielectric soil surface with a conducting object partially buried by using the gfbm/saa method,” IEEE Trans. Antennas Propag. 54, 2072–2080 (2006).
[CrossRef]

2005 (1)

M. Di Vico, F. Frezza, L. Pajewski, and G. Schettini, “Scattering by buried dielectric cylindrical structures,” Radio Sci. 40, RS6S18 (2005).
[CrossRef]

2004 (1)

J. T. Johson and R. J. Burkholder, “A study of scattering from an object below a rough surface,” IEEE Trans. Geosci. Remote Sens. 42, 59–66 (2004).
[CrossRef]

2003 (1)

M. El-Shenawee and K. Rappaport, “Electromagnetic scattering interference between two shallow objects buried under 2-D random rough surfaces,” IEEE Microw. Wirel. Compon. Lett. 13, 223–225 (2003).
[CrossRef]

2002 (1)

D. E. Lawrence and K. Sarabandi, “Electromagnetic scattering from a dielectric cylinder buried beneath a slightly rough surface,” IEEE Trans. Antennas Propag. 50, 1368–1376 (2002).
[CrossRef]

2000 (1)

R. Borghi, F. Frezza, P. Oliverio, M. Santarsiero, and G. Schettini, “Scattering of a generic two-dimensional field by cylindrical structures in the presence of a plane interface,” Int. J. Infrared Millim. Waves 21, 805–827 (2000).
[CrossRef]

1996 (1)

K. O’Neill, R. F. Lussky, and K. D. Paulsen, “Scattering from a metallic object embedded near the randomly rough surface of a lossy dielectric,” IEEE Trans. Geosci. Remote Sens. 34, 367–376 (1996).
[CrossRef]

1994 (1)

A. Z. Elsherbeni, “A comparative study of two-dimensional multiple scattering techniques,” Radio Sci. 29, 1023–1033 (1994).
[CrossRef]

1992 (2)

P. G. Cottis and J. D. Kanellopoulos, “Scattering of electromagnetic waves from cylindrical inhomogeneities embedded inside a lossy medium with a sinusoidal surface,” J. Electromagn. Waves. Appl. 6, 445–458 (1992).
[CrossRef]

R. E. Collin, “Electromagnetic scattering from perfectly conducting rough surface (A new full-wave method),” IEEE Trans. Antennas Propag. 40, 1466–1477 (1992).
[CrossRef]

1988 (2)

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]

M. F. Chen and A. K. Fung, “A numerical study of the regions of validity of the Kirchhoff and small-perturbation rough surface scattering models,” Radio Sci. 23, 163–170 (1988).
[CrossRef]

1986 (1)

K. Hongo and A. Hamamura, “Asymptotic solutions for the scattered field of plane wave by a cylindrical obstacle buried in a dielectric half-space,” IEEE Trans. Antennas Propag. 34, 1306–1312 (1986).
[CrossRef]

1985 (1)

C. M. Butler, X.-B. Xu, and A. W. Glisson, “Current induced on a conducting cylinder located near the planar interface between two semi-infinite half-spaces,” IEEE Trans. Antennas Propag. 33, 616–624 (1985).
[CrossRef]

1981 (2)

S. O. Ogunade, “Electromagnetic response of an embedded cylinder for line current excitation,” Geophysics 46, 45–52 (1981).
[CrossRef]

S. F. Mahmoud, S. M. Ali, and J. R. Wait, “Electromagnetic scattering from a buried cylindrical inhomogeneity inside a lossy earth,” Radio Sci. 16, 1285–1298 (1981).
[CrossRef]

1972 (1)

A. Q. Howard, “The electromagnetic fields of a subterranean cylindrical inhomogeneity excited by a line source,” Geophysics 37, 975–984 (1972).
[CrossRef]

1951 (1)

S. O. Rice, “Reflection of electromagnetic waves by slightly rough surfaces,” Commun. Pure Appl. Math. 4, 351–378 (1951).
[CrossRef]

Ahmed, S.

S. Ahmed and Q. A. Naqvi, “Electromagnetic scattering from a perfect electromagnetic conductor cylinder buried in a dielectric half-space,” Prog. Electromagn. Res. 78, 25–38 (2008).
[CrossRef]

Akduman, I.

Y. Altuncu, A. Yapar, and I. Akduman, “On the scattering of electromagnetic waves by bodies buried in a half-space with locally rough interface,” IEEE Trans. Geosci. Remote Sens. 44, 1435–1443 (2006).
[CrossRef]

Ali, S. M.

S. F. Mahmoud, S. M. Ali, and J. R. Wait, “Electromagnetic scattering from a buried cylindrical inhomogeneity inside a lossy earth,” Radio Sci. 16, 1285–1298 (1981).
[CrossRef]

Altuncu, Y.

Y. Altuncu, A. Yapar, and I. Akduman, “On the scattering of electromagnetic waves by bodies buried in a half-space with locally rough interface,” IEEE Trans. Geosci. Remote Sens. 44, 1435–1443 (2006).
[CrossRef]

Bass, F. G.

F. G. Bass and I. M. Fuks, Wave Scattering from Statistically Rough Surfaces (Pergamon, 1979).

Borghi, R.

R. Borghi, F. Frezza, P. Oliverio, M. Santarsiero, and G. Schettini, “Scattering of a generic two-dimensional field by cylindrical structures in the presence of a plane interface,” Int. J. Infrared Millim. Waves 21, 805–827 (2000).
[CrossRef]

Bourlier, C.

Burkholder, R. J.

J. T. Johson and R. J. Burkholder, “A study of scattering from an object below a rough surface,” IEEE Trans. Geosci. Remote Sens. 42, 59–66 (2004).
[CrossRef]

Butler, C. M.

C. M. Butler, X.-B. Xu, and A. W. Glisson, “Current induced on a conducting cylinder located near the planar interface between two semi-infinite half-spaces,” IEEE Trans. Antennas Propag. 33, 616–624 (1985).
[CrossRef]

Chen, M. F.

M. F. Chen and A. K. Fung, “A numerical study of the regions of validity of the Kirchhoff and small-perturbation rough surface scattering models,” Radio Sci. 23, 163–170 (1988).
[CrossRef]

Collin, R. E.

R. E. Collin, “Electromagnetic scattering from perfectly conducting rough surface (A new full-wave method),” IEEE Trans. Antennas Propag. 40, 1466–1477 (1992).
[CrossRef]

Cottis, P. G.

P. G. Cottis and J. D. Kanellopoulos, “Scattering of electromagnetic waves from cylindrical inhomogeneities embedded inside a lossy medium with a sinusoidal surface,” J. Electromagn. Waves. Appl. 6, 445–458 (1992).
[CrossRef]

D’Yakonov, B. P.

B. P. D’Yakonov, “The diffraction of electromagnetic waves by a circular cylinder in a homogeneous half-space,” Atmos. Oceanic Phys.950–955 (1959).

Daniels, D. J.

D. J. Daniels, Ground Penetrating Radar, 2nd ed. (IET, 2004).

Di Vico, M.

M. Di Vico, F. Frezza, L. Pajewski, and G. Schettini, “Scattering by buried dielectric cylindrical structures,” Radio Sci. 40, RS6S18 (2005).
[CrossRef]

Ding, K.-H.

L. Tsang, J. A. Kong, and K.-H. Ding, Scattering of Electromagnetic Waves: Theories and Applications (Wiley, 2001).

El-Shenawee, M.

M. El-Shenawee and K. Rappaport, “Electromagnetic scattering interference between two shallow objects buried under 2-D random rough surfaces,” IEEE Microw. Wirel. Compon. Lett. 13, 223–225 (2003).
[CrossRef]

Elsherbeni, A. Z.

A. Z. Elsherbeni, “A comparative study of two-dimensional multiple scattering techniques,” Radio Sci. 29, 1023–1033 (1994).
[CrossRef]

Fiaz, M. A.

M. A. Fiaz, F. Frezza, L. Pajewski, C. Ponti, and G. Schettini, “Asymptotic solution for a scattered field by cylindrical objects buried beneath a slightly rough surface,” Near Surf. Geophys. 11, 177–183 (2013).

M. A. Fiaz, F. Frezza, L. Pajewski, C. Ponti, and G. Schettini, “Scattering by a circular cylinder buried under a slightly rough surface: the cylindrical-wave approach,” IEEE Trans. Antennas Propag. 60, 2834–2842 (2012).
[CrossRef]

Frezza, F.

M. A. Fiaz, F. Frezza, L. Pajewski, C. Ponti, and G. Schettini, “Asymptotic solution for a scattered field by cylindrical objects buried beneath a slightly rough surface,” Near Surf. Geophys. 11, 177–183 (2013).

F. Frezza, L. Pajewski, C. Ponti, G. Schettini, and N. Tedeschi, “Electromagnetic scattering by a metallic cylinder buried in a lossy medium with the cylindrical wave approach,” Geosci. Remote Sens. Lett. 10, 179–183 (2013).

F. Frezza, L. Pajewski, C. Ponti, G. Schettini, and N. Tedeschi, “Cylindrical-wave approach for electromagnetic scattering by subsurface metallic targets in a lossy medium,” J. Appl. Geophys. 97, 55–59 (2013).
[CrossRef]

F. Frezza, L. Pajewski, C. Ponti, and G. Schettini, “Accurate wire-grid modelling of buried conducting cylindrical scatterers,” Nondestr. Test. Eval. 27, 199–207 (2012), Special issue on Civil Engineering Applications of Ground Penetrating Radar.
[CrossRef]

M. A. Fiaz, F. Frezza, L. Pajewski, C. Ponti, and G. Schettini, “Scattering by a circular cylinder buried under a slightly rough surface: the cylindrical-wave approach,” IEEE Trans. Antennas Propag. 60, 2834–2842 (2012).
[CrossRef]

F. Frezza, L. Pajewski, C. Ponti, and G. Schettini, “Line source scattering by buried perfectly conducting circular cylinders,” Int. J. Antennas Propag. 2012, 1–7 (2012).
[CrossRef]

F. Frezza, L. Pajewski, C. Ponti, and G. Schettini, “Scattering by dielectric circular cylinders in a dielectric slab,” J. Opt. Soc. Am. A 27, 687–695 (2010).
[CrossRef]

M. Di Vico, F. Frezza, L. Pajewski, and G. Schettini, “Scattering by buried dielectric cylindrical structures,” Radio Sci. 40, RS6S18 (2005).
[CrossRef]

R. Borghi, F. Frezza, P. Oliverio, M. Santarsiero, and G. Schettini, “Scattering of a generic two-dimensional field by cylindrical structures in the presence of a plane interface,” Int. J. Infrared Millim. Waves 21, 805–827 (2000).
[CrossRef]

Fuks, I. M.

F. G. Bass and I. M. Fuks, Wave Scattering from Statistically Rough Surfaces (Pergamon, 1979).

Fung, A. K.

M. F. Chen and A. K. Fung, “A numerical study of the regions of validity of the Kirchhoff and small-perturbation rough surface scattering models,” Radio Sci. 23, 163–170 (1988).
[CrossRef]

Glisson, A. W.

C. M. Butler, X.-B. Xu, and A. W. Glisson, “Current induced on a conducting cylinder located near the planar interface between two semi-infinite half-spaces,” IEEE Trans. Antennas Propag. 33, 616–624 (1985).
[CrossRef]

Hamamura, A.

K. Hongo and A. Hamamura, “Asymptotic solutions for the scattered field of plane wave by a cylindrical obstacle buried in a dielectric half-space,” IEEE Trans. Antennas Propag. 34, 1306–1312 (1986).
[CrossRef]

Hongo, K.

K. Hongo and A. Hamamura, “Asymptotic solutions for the scattered field of plane wave by a cylindrical obstacle buried in a dielectric half-space,” IEEE Trans. Antennas Propag. 34, 1306–1312 (1986).
[CrossRef]

Howard, A. Q.

A. Q. Howard, “The electromagnetic fields of a subterranean cylindrical inhomogeneity excited by a line source,” Geophysics 37, 975–984 (1972).
[CrossRef]

Johson, J. T.

J. T. Johson and R. J. Burkholder, “A study of scattering from an object below a rough surface,” IEEE Trans. Geosci. Remote Sens. 42, 59–66 (2004).
[CrossRef]

Kanellopoulos, J. D.

P. G. Cottis and J. D. Kanellopoulos, “Scattering of electromagnetic waves from cylindrical inhomogeneities embedded inside a lossy medium with a sinusoidal surface,” J. Electromagn. Waves. Appl. 6, 445–458 (1992).
[CrossRef]

Kong, J. A.

L. Tsang, J. A. Kong, and K.-H. Ding, Scattering of Electromagnetic Waves: Theories and Applications (Wiley, 2001).

Kubick, G.

Kuo, C.-H.

C.-H. Kuo and M. Moghaddam, “Electromagnetic scattering from a buried cylinder in layered media with rough interfaces,” IEEE Trans. Antennas Propag. 54, 2392–2401 (2006).
[CrossRef]

Lawrence, D. E.

D. E. Lawrence and K. Sarabandi, “Electromagnetic scattering from a dielectric cylinder buried beneath a slightly rough surface,” IEEE Trans. Antennas Propag. 50, 1368–1376 (2002).
[CrossRef]

Li, Z.-X.

Z.-X. Li, “Bistatic scattering from rough dielectric soil surface with a conducting object partially buried by using the gfbm/saa method,” IEEE Trans. Antennas Propag. 54, 2072–2080 (2006).
[CrossRef]

Lussky, R. F.

K. O’Neill, R. F. Lussky, and K. D. Paulsen, “Scattering from a metallic object embedded near the randomly rough surface of a lossy dielectric,” IEEE Trans. Geosci. Remote Sens. 34, 367–376 (1996).
[CrossRef]

Mahmoud, S. F.

S. F. Mahmoud, S. M. Ali, and J. R. Wait, “Electromagnetic scattering from a buried cylindrical inhomogeneity inside a lossy earth,” Radio Sci. 16, 1285–1298 (1981).
[CrossRef]

Moghaddam, M.

C.-H. Kuo and M. Moghaddam, “Electromagnetic scattering from a buried cylinder in layered media with rough interfaces,” IEEE Trans. Antennas Propag. 54, 2392–2401 (2006).
[CrossRef]

Naqvi, Q. A.

S. Ahmed and Q. A. Naqvi, “Electromagnetic scattering from a perfect electromagnetic conductor cylinder buried in a dielectric half-space,” Prog. Electromagn. Res. 78, 25–38 (2008).
[CrossRef]

O’Neill, K.

K. O’Neill, R. F. Lussky, and K. D. Paulsen, “Scattering from a metallic object embedded near the randomly rough surface of a lossy dielectric,” IEEE Trans. Geosci. Remote Sens. 34, 367–376 (1996).
[CrossRef]

Ogunade, S. O.

S. O. Ogunade, “Electromagnetic response of an embedded cylinder for line current excitation,” Geophysics 46, 45–52 (1981).
[CrossRef]

Oliverio, P.

R. Borghi, F. Frezza, P. Oliverio, M. Santarsiero, and G. Schettini, “Scattering of a generic two-dimensional field by cylindrical structures in the presence of a plane interface,” Int. J. Infrared Millim. Waves 21, 805–827 (2000).
[CrossRef]

Pajewski, L.

F. Frezza, L. Pajewski, C. Ponti, G. Schettini, and N. Tedeschi, “Cylindrical-wave approach for electromagnetic scattering by subsurface metallic targets in a lossy medium,” J. Appl. Geophys. 97, 55–59 (2013).
[CrossRef]

F. Frezza, L. Pajewski, C. Ponti, G. Schettini, and N. Tedeschi, “Electromagnetic scattering by a metallic cylinder buried in a lossy medium with the cylindrical wave approach,” Geosci. Remote Sens. Lett. 10, 179–183 (2013).

M. A. Fiaz, F. Frezza, L. Pajewski, C. Ponti, and G. Schettini, “Asymptotic solution for a scattered field by cylindrical objects buried beneath a slightly rough surface,” Near Surf. Geophys. 11, 177–183 (2013).

M. A. Fiaz, F. Frezza, L. Pajewski, C. Ponti, and G. Schettini, “Scattering by a circular cylinder buried under a slightly rough surface: the cylindrical-wave approach,” IEEE Trans. Antennas Propag. 60, 2834–2842 (2012).
[CrossRef]

F. Frezza, L. Pajewski, C. Ponti, and G. Schettini, “Line source scattering by buried perfectly conducting circular cylinders,” Int. J. Antennas Propag. 2012, 1–7 (2012).
[CrossRef]

F. Frezza, L. Pajewski, C. Ponti, and G. Schettini, “Accurate wire-grid modelling of buried conducting cylindrical scatterers,” Nondestr. Test. Eval. 27, 199–207 (2012), Special issue on Civil Engineering Applications of Ground Penetrating Radar.
[CrossRef]

F. Frezza, L. Pajewski, C. Ponti, and G. Schettini, “Scattering by dielectric circular cylinders in a dielectric slab,” J. Opt. Soc. Am. A 27, 687–695 (2010).
[CrossRef]

M. Di Vico, F. Frezza, L. Pajewski, and G. Schettini, “Scattering by buried dielectric cylindrical structures,” Radio Sci. 40, RS6S18 (2005).
[CrossRef]

Papoulis, A.

A. Papoulis, Probability, Random Variables, and Stochastic Processes (McGraw-Hill, 1984).

Paulsen, K. D.

K. O’Neill, R. F. Lussky, and K. D. Paulsen, “Scattering from a metallic object embedded near the randomly rough surface of a lossy dielectric,” IEEE Trans. Geosci. Remote Sens. 34, 367–376 (1996).
[CrossRef]

Pinel, N.

Ponti, C.

M. A. Fiaz, F. Frezza, L. Pajewski, C. Ponti, and G. Schettini, “Asymptotic solution for a scattered field by cylindrical objects buried beneath a slightly rough surface,” Near Surf. Geophys. 11, 177–183 (2013).

F. Frezza, L. Pajewski, C. Ponti, G. Schettini, and N. Tedeschi, “Electromagnetic scattering by a metallic cylinder buried in a lossy medium with the cylindrical wave approach,” Geosci. Remote Sens. Lett. 10, 179–183 (2013).

F. Frezza, L. Pajewski, C. Ponti, G. Schettini, and N. Tedeschi, “Cylindrical-wave approach for electromagnetic scattering by subsurface metallic targets in a lossy medium,” J. Appl. Geophys. 97, 55–59 (2013).
[CrossRef]

F. Frezza, L. Pajewski, C. Ponti, and G. Schettini, “Accurate wire-grid modelling of buried conducting cylindrical scatterers,” Nondestr. Test. Eval. 27, 199–207 (2012), Special issue on Civil Engineering Applications of Ground Penetrating Radar.
[CrossRef]

M. A. Fiaz, F. Frezza, L. Pajewski, C. Ponti, and G. Schettini, “Scattering by a circular cylinder buried under a slightly rough surface: the cylindrical-wave approach,” IEEE Trans. Antennas Propag. 60, 2834–2842 (2012).
[CrossRef]

F. Frezza, L. Pajewski, C. Ponti, and G. Schettini, “Line source scattering by buried perfectly conducting circular cylinders,” Int. J. Antennas Propag. 2012, 1–7 (2012).
[CrossRef]

F. Frezza, L. Pajewski, C. Ponti, and G. Schettini, “Scattering by dielectric circular cylinders in a dielectric slab,” J. Opt. Soc. Am. A 27, 687–695 (2010).
[CrossRef]

Rappaport, K.

M. El-Shenawee and K. Rappaport, “Electromagnetic scattering interference between two shallow objects buried under 2-D random rough surfaces,” IEEE Microw. Wirel. Compon. Lett. 13, 223–225 (2003).
[CrossRef]

Rice, S. O.

S. O. Rice, “Reflection of electromagnetic waves by slightly rough surfaces,” Commun. Pure Appl. Math. 4, 351–378 (1951).
[CrossRef]

Santarsiero, M.

R. Borghi, F. Frezza, P. Oliverio, M. Santarsiero, and G. Schettini, “Scattering of a generic two-dimensional field by cylindrical structures in the presence of a plane interface,” Int. J. Infrared Millim. Waves 21, 805–827 (2000).
[CrossRef]

Sarabandi, K.

D. E. Lawrence and K. Sarabandi, “Electromagnetic scattering from a dielectric cylinder buried beneath a slightly rough surface,” IEEE Trans. Antennas Propag. 50, 1368–1376 (2002).
[CrossRef]

Schettini, G.

F. Frezza, L. Pajewski, C. Ponti, G. Schettini, and N. Tedeschi, “Electromagnetic scattering by a metallic cylinder buried in a lossy medium with the cylindrical wave approach,” Geosci. Remote Sens. Lett. 10, 179–183 (2013).

M. A. Fiaz, F. Frezza, L. Pajewski, C. Ponti, and G. Schettini, “Asymptotic solution for a scattered field by cylindrical objects buried beneath a slightly rough surface,” Near Surf. Geophys. 11, 177–183 (2013).

F. Frezza, L. Pajewski, C. Ponti, G. Schettini, and N. Tedeschi, “Cylindrical-wave approach for electromagnetic scattering by subsurface metallic targets in a lossy medium,” J. Appl. Geophys. 97, 55–59 (2013).
[CrossRef]

F. Frezza, L. Pajewski, C. Ponti, and G. Schettini, “Accurate wire-grid modelling of buried conducting cylindrical scatterers,” Nondestr. Test. Eval. 27, 199–207 (2012), Special issue on Civil Engineering Applications of Ground Penetrating Radar.
[CrossRef]

M. A. Fiaz, F. Frezza, L. Pajewski, C. Ponti, and G. Schettini, “Scattering by a circular cylinder buried under a slightly rough surface: the cylindrical-wave approach,” IEEE Trans. Antennas Propag. 60, 2834–2842 (2012).
[CrossRef]

F. Frezza, L. Pajewski, C. Ponti, and G. Schettini, “Line source scattering by buried perfectly conducting circular cylinders,” Int. J. Antennas Propag. 2012, 1–7 (2012).
[CrossRef]

F. Frezza, L. Pajewski, C. Ponti, and G. Schettini, “Scattering by dielectric circular cylinders in a dielectric slab,” J. Opt. Soc. Am. A 27, 687–695 (2010).
[CrossRef]

M. Di Vico, F. Frezza, L. Pajewski, and G. Schettini, “Scattering by buried dielectric cylindrical structures,” Radio Sci. 40, RS6S18 (2005).
[CrossRef]

R. Borghi, F. Frezza, P. Oliverio, M. Santarsiero, and G. Schettini, “Scattering of a generic two-dimensional field by cylindrical structures in the presence of a plane interface,” Int. J. Infrared Millim. Waves 21, 805–827 (2000).
[CrossRef]

Tedeschi, N.

F. Frezza, L. Pajewski, C. Ponti, G. Schettini, and N. Tedeschi, “Cylindrical-wave approach for electromagnetic scattering by subsurface metallic targets in a lossy medium,” J. Appl. Geophys. 97, 55–59 (2013).
[CrossRef]

F. Frezza, L. Pajewski, C. Ponti, G. Schettini, and N. Tedeschi, “Electromagnetic scattering by a metallic cylinder buried in a lossy medium with the cylindrical wave approach,” Geosci. Remote Sens. Lett. 10, 179–183 (2013).

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]

Tsang, L.

L. Tsang, J. A. Kong, and K.-H. Ding, Scattering of Electromagnetic Waves: Theories and Applications (Wiley, 2001).

Wait, J. R.

S. F. Mahmoud, S. M. Ali, and J. R. Wait, “Electromagnetic scattering from a buried cylindrical inhomogeneity inside a lossy earth,” Radio Sci. 16, 1285–1298 (1981).
[CrossRef]

Watanabe, K.

K. Watanabe and K. Yasumoto, “Formulation of electromagnetic scattering from cylinder located near periodic surface,” in Proceedings of URSI International Symposium Electromagnetic Theory, Berlin, August16–19, 2010, pp. 660–663.

Xu, X.-B.

C. M. Butler, X.-B. Xu, and A. W. Glisson, “Current induced on a conducting cylinder located near the planar interface between two semi-infinite half-spaces,” IEEE Trans. Antennas Propag. 33, 616–624 (1985).
[CrossRef]

Yapar, A.

Y. Altuncu, A. Yapar, and I. Akduman, “On the scattering of electromagnetic waves by bodies buried in a half-space with locally rough interface,” IEEE Trans. Geosci. Remote Sens. 44, 1435–1443 (2006).
[CrossRef]

Yasumoto, K.

K. Watanabe and K. Yasumoto, “Formulation of electromagnetic scattering from cylinder located near periodic surface,” in Proceedings of URSI International Symposium Electromagnetic Theory, Berlin, August16–19, 2010, pp. 660–663.

Commun. Pure Appl. Math. (1)

S. O. Rice, “Reflection of electromagnetic waves by slightly rough surfaces,” Commun. Pure Appl. Math. 4, 351–378 (1951).
[CrossRef]

Geophysics (2)

A. Q. Howard, “The electromagnetic fields of a subterranean cylindrical inhomogeneity excited by a line source,” Geophysics 37, 975–984 (1972).
[CrossRef]

S. O. Ogunade, “Electromagnetic response of an embedded cylinder for line current excitation,” Geophysics 46, 45–52 (1981).
[CrossRef]

Geosci. Remote Sens. Lett. (1)

F. Frezza, L. Pajewski, C. Ponti, G. Schettini, and N. Tedeschi, “Electromagnetic scattering by a metallic cylinder buried in a lossy medium with the cylindrical wave approach,” Geosci. Remote Sens. Lett. 10, 179–183 (2013).

IEEE Microw. Wirel. Compon. Lett. (1)

M. El-Shenawee and K. Rappaport, “Electromagnetic scattering interference between two shallow objects buried under 2-D random rough surfaces,” IEEE Microw. Wirel. Compon. Lett. 13, 223–225 (2003).
[CrossRef]

IEEE Trans. Antennas Propag. (7)

D. E. Lawrence and K. Sarabandi, “Electromagnetic scattering from a dielectric cylinder buried beneath a slightly rough surface,” IEEE Trans. Antennas Propag. 50, 1368–1376 (2002).
[CrossRef]

C.-H. Kuo and M. Moghaddam, “Electromagnetic scattering from a buried cylinder in layered media with rough interfaces,” IEEE Trans. Antennas Propag. 54, 2392–2401 (2006).
[CrossRef]

Z.-X. Li, “Bistatic scattering from rough dielectric soil surface with a conducting object partially buried by using the gfbm/saa method,” IEEE Trans. Antennas Propag. 54, 2072–2080 (2006).
[CrossRef]

M. A. Fiaz, F. Frezza, L. Pajewski, C. Ponti, and G. Schettini, “Scattering by a circular cylinder buried under a slightly rough surface: the cylindrical-wave approach,” IEEE Trans. Antennas Propag. 60, 2834–2842 (2012).
[CrossRef]

C. M. Butler, X.-B. Xu, and A. W. Glisson, “Current induced on a conducting cylinder located near the planar interface between two semi-infinite half-spaces,” IEEE Trans. Antennas Propag. 33, 616–624 (1985).
[CrossRef]

K. Hongo and A. Hamamura, “Asymptotic solutions for the scattered field of plane wave by a cylindrical obstacle buried in a dielectric half-space,” IEEE Trans. Antennas Propag. 34, 1306–1312 (1986).
[CrossRef]

R. E. Collin, “Electromagnetic scattering from perfectly conducting rough surface (A new full-wave method),” IEEE Trans. Antennas Propag. 40, 1466–1477 (1992).
[CrossRef]

IEEE Trans. Geosci. Remote Sens. (3)

Y. Altuncu, A. Yapar, and I. Akduman, “On the scattering of electromagnetic waves by bodies buried in a half-space with locally rough interface,” IEEE Trans. Geosci. Remote Sens. 44, 1435–1443 (2006).
[CrossRef]

K. O’Neill, R. F. Lussky, and K. D. Paulsen, “Scattering from a metallic object embedded near the randomly rough surface of a lossy dielectric,” IEEE Trans. Geosci. Remote Sens. 34, 367–376 (1996).
[CrossRef]

J. T. Johson and R. J. Burkholder, “A study of scattering from an object below a rough surface,” IEEE Trans. Geosci. Remote Sens. 42, 59–66 (2004).
[CrossRef]

Int. J. Antennas Propag. (1)

F. Frezza, L. Pajewski, C. Ponti, and G. Schettini, “Line source scattering by buried perfectly conducting circular cylinders,” Int. J. Antennas Propag. 2012, 1–7 (2012).
[CrossRef]

Int. J. Infrared Millim. Waves (1)

R. Borghi, F. Frezza, P. Oliverio, M. Santarsiero, and G. Schettini, “Scattering of a generic two-dimensional field by cylindrical structures in the presence of a plane interface,” Int. J. Infrared Millim. Waves 21, 805–827 (2000).
[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. Appl. Geophys. (1)

F. Frezza, L. Pajewski, C. Ponti, G. Schettini, and N. Tedeschi, “Cylindrical-wave approach for electromagnetic scattering by subsurface metallic targets in a lossy medium,” J. Appl. Geophys. 97, 55–59 (2013).
[CrossRef]

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P. G. Cottis and J. D. Kanellopoulos, “Scattering of electromagnetic waves from cylindrical inhomogeneities embedded inside a lossy medium with a sinusoidal surface,” J. Electromagn. Waves. Appl. 6, 445–458 (1992).
[CrossRef]

J. Opt. Soc. Am. A (2)

Near Surf. Geophys. (1)

M. A. Fiaz, F. Frezza, L. Pajewski, C. Ponti, and G. Schettini, “Asymptotic solution for a scattered field by cylindrical objects buried beneath a slightly rough surface,” Near Surf. Geophys. 11, 177–183 (2013).

Nondestr. Test. Eval. (1)

F. Frezza, L. Pajewski, C. Ponti, and G. Schettini, “Accurate wire-grid modelling of buried conducting cylindrical scatterers,” Nondestr. Test. Eval. 27, 199–207 (2012), Special issue on Civil Engineering Applications of Ground Penetrating Radar.
[CrossRef]

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S. Ahmed and Q. A. Naqvi, “Electromagnetic scattering from a perfect electromagnetic conductor cylinder buried in a dielectric half-space,” Prog. Electromagn. Res. 78, 25–38 (2008).
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[CrossRef]

M. Di Vico, F. Frezza, L. Pajewski, and G. Schettini, “Scattering by buried dielectric cylindrical structures,” Radio Sci. 40, RS6S18 (2005).
[CrossRef]

S. F. Mahmoud, S. M. Ali, and J. R. Wait, “Electromagnetic scattering from a buried cylindrical inhomogeneity inside a lossy earth,” Radio Sci. 16, 1285–1298 (1981).
[CrossRef]

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K. Watanabe and K. Yasumoto, “Formulation of electromagnetic scattering from cylinder located near periodic surface,” in Proceedings of URSI International Symposium Electromagnetic Theory, Berlin, August16–19, 2010, pp. 660–663.

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Figures (5)

Fig. 1.
Fig. 1.

Geometry of the scattering problem.

Fig. 2.
Fig. 2.

Decomposition of the total field.

Fig. 3.
Fig. 3.

Comparison between our results and the ones of Fig. 10 in [23]. Cylinder’s parameters are nc=1.5, α=0.32π, and (χ=2.6π, η=0). The incident beam has normalized beam waist wn=Ln/4(φi=60°), TM polarization. The lower medium has refraction index n1=2; the parameters of the Gaussian rough surface are n=0.6π, hn=0.02π, Ln=80π.

Fig. 4.
Fig. 4.

Scattering cross section of a buried dielectric cylinder (nc=7, α=1, χ=3, η=0, n1=2). Incident beam: wn=Ln/10, φi=30°, TM polarization. Statistics of the Gaussian rough surface: n=1.8, Ln=80, and: (a) hn=0.03 and (b) hn=0.10.

Fig. 5.
Fig. 5.

Scattering cross section of a buried PEC cylinder (α=1, χ=3, η=0, n1=2). Incident beam: wn=Ln/10, φi=0, TM polarization. Gaussian rough surface of length Ln=80 and (a) n=1.8, hn=0.06 and (b) n=3.6, hn=0.12.

Equations (44)

Equations on this page are rendered with MathJax. Learn more.

G(n)=g(ζ)einζdζ.
Vi(ξ,ζ)=12πV0i(n)ei[n(ξξ0)+n(ζζ0)](cosφi+nnsinφi)dn,
V0i(n)=V0πwne[wn(ncosφinsinφi)/2]2,
Vr(ξ,ζ)=12πΓ01(n)V0i(n)ei[n(ξ+ξ0)+n(ζζ0)](cosφi+nnsinφi)dn+ΔA.
ΔA=1(2π)2γ01(nn)V0i(n)ei(nξ0nζ0)ei(nξ+nζ)(cosφi+nnsinφi)dndn,
Vt(ξ,ζ)=12πT01(n)V0i(n)ei(1n2ξ0nζ0)ei(n12n2ξ+nζ)(cosφi+n1n2sinφi)dn+1(2π)2τ01(n,n)V0i(n)ei(1n2ξ0nζ0)ei(n12n2ξ+nζ)(cosφi+n1n2sinφi)dndn,
Vt(ξ,ζ)==iJ(n1ρq)eiθq[TWi(χq,ζ0;ξ0)+ΔB],
TWi(χq,ζ0;ξ0)=12πT01(n)V0i(n)ei(1n2ξ0nζ0)×ein12n2χq(cosφi+n1n2sinφi)dn
ΔB=1(2π)2τ01(n,n)V0i(n)×ei(1n2ξ0nζ0)ein12n2χq×eilarctan(n/n12n2)(cosφi+n1n2sinφi)dndn.
Vs(ξq,ζq)=V0m=imcqmCWm(n1ξq,n1ζq).
CWm(ξ,ζ)=12π+Fm(ξ,n)einζdn,
Fm(ξ,n)=21(n)2ei|ξ|1(n)2{eimarccosn,ξ0eimarccosn,ξ0.
Vsr(ξ,ζ)=V0m=imcqmRWm[n1(ξq2χq),n1ζq,χq].
RWm(ξ,ζ,χ)=RWmun(ξ,ζ)+RWmper(ξ,ζ,χ).
RWmun(ξ,ζ)=12πΓ10(n)Fm(ξ,n)einζdn
RWmper(ξ,ζ,χ)=1(2π)2γ10(n,n)Fm(n1χ,n)ei(nξ+nζ)dndn.
Vsr(ξ,ζ)=V0=J(n1ρq)eiθqm=imcqm[RWm+un(2n1χq,0)+RWm,per(n1χq,0,χq)].
RWmun(2n1χq,0)=12πΓ10(n)Fm(2n1χq,n)dn
RWm,per(n1χq,0,χq)=1(2π)2γ10(n,n)Fm(n1χq,n)einχqeiφsrdndn.
TWm(ξ,ζ,χ)=TWmun(ξ,ζ,χ)+TWmper(ξ,ζ,χ),
TWmun(ξ,ζ,χ)=12πT10(n)Fm(n1χ,n)ei1(n1n)2(ξ+χ)ein1nζdn
TWmper(ξ,ζ,χ)=1(2π)2τ10(n,n)Fm(n1χ,n)ei1(n1n)2(ξ+χ)ein1nζdndn.
Vst(ξ,ζ)=V0m=imcqmTWm(ξχq,ζηq,χq).
Vcq(ξq,ζq)=V0=idqJ(ncqρq)eiθq.
Vt+Vs+Vsr|ρq=αq=Vcq|ρq=αqρq(Vt+Vs+Vsr)|ρq=αq=tqVcqρq|ρq=αq.
m=Amq(1)cqmBq(1)=dqLq(1)m=Amq(2)cqmBq(2)=dqLq(2)=0;±1;±2.,
Amq(1,2)=imeimφt{[RWm+un(2n1χq,0)+RWm,per(n1χq,0,χq)]G(1,2)(n1αq)+δm}
Bq(1,2)=[TWi(χq,ζ0;ξ0)+ΔB]G(1,2)(n1αq)
Lq(1)=eiφtJq(ncqαq)H(1)(n1αq)Lq(2)=qeiφtJq(ncqαq)H(1)(n1αq).
m=Dmqcqm=Mq,
Dmq=Lq(2)Amq(1)Lq(1)Amq(2)Mq=Bq(1)Lq(2)Bq(2)Lq(1).
dq=m=Amq(1)cqmBq(1)Lq(1).
Vt+Vs+Vsr|ρq=αq=0.
ρq(Vt+Vs+Vsr)|ρq=αq=0.
m=Amq(TM,TE)cqm=Bq(TM,TE),
Amq(TM,TE)=imeimφt{[RWm+un(2n1χq,0)+RWm,per(n1χq,0,χq)]G(TM,TE)(n1αq)+δm}
Bq(TM,TE)=[TWi(χq,ζ0;ξ0)+ΔB]G(TM,TE)(n1αq),
g(ζ)=g(ζ+Ln).
g(ζ)=1Lnu=G(2πuLn)ei2πuLnζ,
G(2πuLn)=LnW(2πuLn),
W(2πuLn)=πhn2ne(2πuLnn2)2,
ΔB=12πLnu=τ01(n,u)V0i(n)ei(1n2ξ0nζ0)ein12(n+2πuLn)2χqeilarctan[(n+2πuLn)/n12(n+2πuLn)2](cosφi+n1n2sinφi)dn.
RWm,per(n1χq,0,χq)=12πLnu=γ10(n,u)Fm(n1χq,n)×ei1(n+2πuLn)2χqeilarctan[(n+2πuLn)/1(n+2πuLn)2]dn
TWmper(ξ,ζ,χ)=12πLnu=τ10(n,u)Fm(n1χ,n)×ei1[n1(n+2πun1Ln)]2(ξ+χ)ein1(n+2πun1Ln)ζdn.

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