Abstract

We present a statistical study of the electric field scattered from a three-dimensional penetrable object buried under a two-dimensional random rough surface. Monte Carlo simulations using the steepest-descent fast multipole method (SDFMM) are conducted to calculate the average and the standard deviation of the near-zone scattered fields. The SDFMM, originally developed at the University of Illinois at Urbana–Champaign, has been modified to calculate the unknown surface currents both on the rough ground and on the buried object that are due to excitation by a tapered Gaussian beam. The rough ground medium used is an experimentally measured typical dry Bosnian soil with 3.8% moisture, while the buried object represents a plastic land mine modeled as an oblate spheroid with dimensions and burial depth smaller than the free-space wavelength. Both vertical and horizontal polarizations for the incident waves are studied. The numerical results show that the TNT mine signature is almost 5% of the total field scattered from the ground. Moreover, relatively recognizable object signatures are observed even when the object is buried under the tail of the incident beam. Interestingly, even for the small surface roughness parameters considered, the standard deviation of the object signature is almost 30% of the signal itself, indicating significant clutter distortion that is due to the roughness of the ground.

© 2001 Optical Society of America

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  1. L. Tsang, C. H. Chan, K. Pak, H. Sangani, A. Ishimaru, P. Phu, “Monte Carlo simulations of large-scale composite random rough-surface scattering based on the banded-matrix iterative approach,” J. Opt. Soc. Am. A 11, 691–696 (1994).
    [CrossRef]
  2. R. L. Wagner, J. Song, W. C. Chew, “Monte Carlo simulation of electromagnetic scattering from two-dimensional random rough surfaces,” IEEE Trans. Antennas Propag. 45, 235–245 (1997).
    [CrossRef]
  3. C. H. Chan, L. Tsang, Q. Li, “Monte Carlo simulations of large-scale one dimensional random rough-surface scattering at near grazing incidence: penetrable case,” IEEE Trans. Antennas Propag. 46, 142–149 (1998).
    [CrossRef]
  4. F. D. Hastings, J. B. Schneider, S. L. Broschat, “A Monte Carlo FDTD technique for rough surface scattering,” IEEE Trans. Antennas Propag. 43, 1183–1191 (1995).
    [CrossRef]
  5. J. T. Johnson, L. Tsang, R. T. Shin, K. Pak, C. H. Chan, A. Ishimaru, Y. Kuga, “Backscattering enhancement of electromagnetic waves from two-dimensional perfectly conducting random rough surfaces: comparison of Monte Carlo simulations with experimental data,” IEEE Trans. Antennas Propag. 44, 748–756 (1996).
    [CrossRef]
  6. K. O’Neill, R. F. Lussky, 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]
  7. G. Zhang, L. Tsang, Y. Kuga, “Studies of the angular correlation function of scattering by random rough surfaces with and without a buried object,” IEEE Trans. Geosci. Remote Sens. 35, 444–453 (1997).
    [CrossRef]
  8. A. Madrazo, M. Nieto-Vesperinas, “Scattering of light and other electromagnetic waves from a body buried beneath a highly rough random surface,” J. Opt. Soc. Am. A 14, 1859–1866 (1997).
    [CrossRef]
  9. N. Geng, A. Sullivan, L. Carin, “Multilevel fast-multipole algorithm for scattering from conducting targets above or embedded in a lossy half space,” IEEE Trans. Geosci. Remote Sens. 38, 1561–1573 (2000).
    [CrossRef]
  10. G. Zhang, L. Tsang, K. Pak, “Angular correlation function and scattering coefficient of electromagnetic waves scattered by a buried object under a two-dimensional rough surface,” J. Opt. Soc. Am. A 15, 2995–3002 (1998).
    [CrossRef]
  11. M. El-Shenawee, C. Rappaport, E. Miller, M. Silevitch, “3-D subsurface analysis of electromagnetic scattering from penetrable/PEC objects buried under rough surfaces: use of the steepest descent fast multipole method (SDFMM),” IEEE Trans. Geosci. Remote Sens. 39, 1174–1182 (2001).
    [CrossRef]
  12. V. Rokhlin, “Rapid solution of integral equations of scattering theory in two dimensions,” J. Comput. Phys. 36, 414–439 (1990).
    [CrossRef]
  13. R. Coifman, V. Rokhlin, S. Wandzura, “The fast multipole method for the wave equation: a pedestrian description,” IEEE Antennas Propag. Mag. 35 (No. 3), 7–12 (1993).
    [CrossRef]
  14. C. C. Lu, W. C. Chew, “Fast algorithm for solving hybrid integral equations,” IEE Proc. Pt. H 140, 455–460 (1993).
  15. C. C. Lu, W. C. Chew, “A multilevel fast-algorithm for solving a boundary integral equation of wave scattering,” Microwave Opt. Technol. Lett. 7, 466–470 (1994).
    [CrossRef]
  16. J. M. Song, W. C. Chew, “Multilevel fast-multipole algorithm for solving combined field integral equations of electromagnetic scattering,” Microwave Opt. Technol. Lett. 10, 14–19 (1995).
    [CrossRef]
  17. V. Jandhyala, “Fast multilevel algorithms for the efficient electromagnetic analysis of quasi-planar structures,” Ph.D. thesis (Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign, Urbana Champaign, Ill., 1998).
  18. V. Jandhyala, E. Michielssen, B. Shanker, W. C. Chew, “A combined steepest descent–fast multipole algorithm for the fast analysis of three-dimensional scattering by rough surfaces,” IEEE Trans. Geosci. Remote Sens. 36, 738–748 (1998).
    [CrossRef]
  19. V. Jandhyala, B. Shanker, E. Michielssen, W. C. Chew, “A fast algorithm for the analysis of scattering by dielectric rough surfaces,” J. Opt. Soc. Am. A 15, 1877–1885 (1998).
    [CrossRef]
  20. M. El-Shenawee, V. Jandhyala, E. Michielssen, W. C. Chew, “The steepest descent fast multipole method (SDFMM) for solving combined field integral equation pertinent to rough surface scattering,” in Proceedings of the IEEE APS/URSI ’99 Conference (Institute of Electrical and Electronics Engineers, New York, 1999), pp. 534–537.
  21. L. Medgyesti-Mitschang, J. Putnam, M. Gedera, “Generalized method of moments for three-dimensional penetrable scatterers,” J. Opt. Soc. Am. A 11, 1383–1398 (1994).
    [CrossRef]
  22. J. R. Mautz, R. F. Harrington, “H-field, E-field, and combined field solutions for conducting bodies of revolutions,” Arch. Elektr. Uebertrag. 32, 157–164 (1978).
  23. P. L. Huddleston, L. N. Medgyesi-Mitschang, J. M. Putnam, “Combined field integral equation formulation for scattering from dielectrically coated conducting bodies,” IEEE Trans. Antennas Propag. AP-34, 510–520 (1986).
    [CrossRef]
  24. S. M. Rao, D. R. Wilton, A. W. Glisson, “Electromagnetic scattering by surfaces of arbitrary shape,” IEEE Trans. Antennas Propag. AP-30, 409–418 (1982).
    [CrossRef]
  25. P. Tran, A. A. Maradudin, “Scattering of a scalar beamfrom a two-dimensional randomly rough hard wall: enhanced backscatter,” Phys. Rev. B 45, 3936–3939 (1992).
    [CrossRef]
  26. J. Curtis, “Dielectric properties of soils; various sites in Bosnia,” (U.S. Army Corps of Engineers, Waterways Experiment, Washington, D.C., 1996).
  27. C. A. Balanis, Advanced Engineering Electromagnetics (Wiley, New York, 1989), Chap. 6, pp. 254–309.
  28. R. W. Freund, “A transpose-free quasi-minimal residual algorithm for non-Hermitian linear systems,” SIAM J. Sci. Comput. 14, 470–482 (1993).
    [CrossRef]
  29. S. Li, C. H. Chan, L. Tsang, Q. Li, L. Zhou, “Parallel implementation of the parse matrix/canonical grid method for the analysis of two-dimensional random rough surfaces (three-dimensional scattering problem) on a Beowulf system,” IEEE Trans. Geosci. Remote Sens. 38, 1600–1608 (2000).
    [CrossRef]

2001 (1)

M. El-Shenawee, C. Rappaport, E. Miller, M. Silevitch, “3-D subsurface analysis of electromagnetic scattering from penetrable/PEC objects buried under rough surfaces: use of the steepest descent fast multipole method (SDFMM),” IEEE Trans. Geosci. Remote Sens. 39, 1174–1182 (2001).
[CrossRef]

2000 (2)

N. Geng, A. Sullivan, L. Carin, “Multilevel fast-multipole algorithm for scattering from conducting targets above or embedded in a lossy half space,” IEEE Trans. Geosci. Remote Sens. 38, 1561–1573 (2000).
[CrossRef]

S. Li, C. H. Chan, L. Tsang, Q. Li, L. Zhou, “Parallel implementation of the parse matrix/canonical grid method for the analysis of two-dimensional random rough surfaces (three-dimensional scattering problem) on a Beowulf system,” IEEE Trans. Geosci. Remote Sens. 38, 1600–1608 (2000).
[CrossRef]

1998 (4)

V. Jandhyala, E. Michielssen, B. Shanker, W. C. Chew, “A combined steepest descent–fast multipole algorithm for the fast analysis of three-dimensional scattering by rough surfaces,” IEEE Trans. Geosci. Remote Sens. 36, 738–748 (1998).
[CrossRef]

V. Jandhyala, B. Shanker, E. Michielssen, W. C. Chew, “A fast algorithm for the analysis of scattering by dielectric rough surfaces,” J. Opt. Soc. Am. A 15, 1877–1885 (1998).
[CrossRef]

G. Zhang, L. Tsang, K. Pak, “Angular correlation function and scattering coefficient of electromagnetic waves scattered by a buried object under a two-dimensional rough surface,” J. Opt. Soc. Am. A 15, 2995–3002 (1998).
[CrossRef]

C. H. Chan, L. Tsang, Q. Li, “Monte Carlo simulations of large-scale one dimensional random rough-surface scattering at near grazing incidence: penetrable case,” IEEE Trans. Antennas Propag. 46, 142–149 (1998).
[CrossRef]

1997 (3)

R. L. Wagner, J. Song, W. C. Chew, “Monte Carlo simulation of electromagnetic scattering from two-dimensional random rough surfaces,” IEEE Trans. Antennas Propag. 45, 235–245 (1997).
[CrossRef]

G. Zhang, L. Tsang, Y. Kuga, “Studies of the angular correlation function of scattering by random rough surfaces with and without a buried object,” IEEE Trans. Geosci. Remote Sens. 35, 444–453 (1997).
[CrossRef]

A. Madrazo, M. Nieto-Vesperinas, “Scattering of light and other electromagnetic waves from a body buried beneath a highly rough random surface,” J. Opt. Soc. Am. A 14, 1859–1866 (1997).
[CrossRef]

1996 (2)

J. T. Johnson, L. Tsang, R. T. Shin, K. Pak, C. H. Chan, A. Ishimaru, Y. Kuga, “Backscattering enhancement of electromagnetic waves from two-dimensional perfectly conducting random rough surfaces: comparison of Monte Carlo simulations with experimental data,” IEEE Trans. Antennas Propag. 44, 748–756 (1996).
[CrossRef]

K. O’Neill, R. F. Lussky, 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]

1995 (2)

F. D. Hastings, J. B. Schneider, S. L. Broschat, “A Monte Carlo FDTD technique for rough surface scattering,” IEEE Trans. Antennas Propag. 43, 1183–1191 (1995).
[CrossRef]

J. M. Song, W. C. Chew, “Multilevel fast-multipole algorithm for solving combined field integral equations of electromagnetic scattering,” Microwave Opt. Technol. Lett. 10, 14–19 (1995).
[CrossRef]

1994 (3)

1993 (3)

R. W. Freund, “A transpose-free quasi-minimal residual algorithm for non-Hermitian linear systems,” SIAM J. Sci. Comput. 14, 470–482 (1993).
[CrossRef]

R. Coifman, V. Rokhlin, S. Wandzura, “The fast multipole method for the wave equation: a pedestrian description,” IEEE Antennas Propag. Mag. 35 (No. 3), 7–12 (1993).
[CrossRef]

C. C. Lu, W. C. Chew, “Fast algorithm for solving hybrid integral equations,” IEE Proc. Pt. H 140, 455–460 (1993).

1992 (1)

P. Tran, A. A. Maradudin, “Scattering of a scalar beamfrom a two-dimensional randomly rough hard wall: enhanced backscatter,” Phys. Rev. B 45, 3936–3939 (1992).
[CrossRef]

1990 (1)

V. Rokhlin, “Rapid solution of integral equations of scattering theory in two dimensions,” J. Comput. Phys. 36, 414–439 (1990).
[CrossRef]

1986 (1)

P. L. Huddleston, L. N. Medgyesi-Mitschang, J. M. Putnam, “Combined field integral equation formulation for scattering from dielectrically coated conducting bodies,” IEEE Trans. Antennas Propag. AP-34, 510–520 (1986).
[CrossRef]

1982 (1)

S. M. Rao, D. R. Wilton, A. W. Glisson, “Electromagnetic scattering by surfaces of arbitrary shape,” IEEE Trans. Antennas Propag. AP-30, 409–418 (1982).
[CrossRef]

1978 (1)

J. R. Mautz, R. F. Harrington, “H-field, E-field, and combined field solutions for conducting bodies of revolutions,” Arch. Elektr. Uebertrag. 32, 157–164 (1978).

Balanis, C. A.

C. A. Balanis, Advanced Engineering Electromagnetics (Wiley, New York, 1989), Chap. 6, pp. 254–309.

Broschat, S. L.

F. D. Hastings, J. B. Schneider, S. L. Broschat, “A Monte Carlo FDTD technique for rough surface scattering,” IEEE Trans. Antennas Propag. 43, 1183–1191 (1995).
[CrossRef]

Carin, L.

N. Geng, A. Sullivan, L. Carin, “Multilevel fast-multipole algorithm for scattering from conducting targets above or embedded in a lossy half space,” IEEE Trans. Geosci. Remote Sens. 38, 1561–1573 (2000).
[CrossRef]

Chan, C. H.

S. Li, C. H. Chan, L. Tsang, Q. Li, L. Zhou, “Parallel implementation of the parse matrix/canonical grid method for the analysis of two-dimensional random rough surfaces (three-dimensional scattering problem) on a Beowulf system,” IEEE Trans. Geosci. Remote Sens. 38, 1600–1608 (2000).
[CrossRef]

C. H. Chan, L. Tsang, Q. Li, “Monte Carlo simulations of large-scale one dimensional random rough-surface scattering at near grazing incidence: penetrable case,” IEEE Trans. Antennas Propag. 46, 142–149 (1998).
[CrossRef]

J. T. Johnson, L. Tsang, R. T. Shin, K. Pak, C. H. Chan, A. Ishimaru, Y. Kuga, “Backscattering enhancement of electromagnetic waves from two-dimensional perfectly conducting random rough surfaces: comparison of Monte Carlo simulations with experimental data,” IEEE Trans. Antennas Propag. 44, 748–756 (1996).
[CrossRef]

L. Tsang, C. H. Chan, K. Pak, H. Sangani, A. Ishimaru, P. Phu, “Monte Carlo simulations of large-scale composite random rough-surface scattering based on the banded-matrix iterative approach,” J. Opt. Soc. Am. A 11, 691–696 (1994).
[CrossRef]

Chew, W. C.

V. Jandhyala, E. Michielssen, B. Shanker, W. C. Chew, “A combined steepest descent–fast multipole algorithm for the fast analysis of three-dimensional scattering by rough surfaces,” IEEE Trans. Geosci. Remote Sens. 36, 738–748 (1998).
[CrossRef]

V. Jandhyala, B. Shanker, E. Michielssen, W. C. Chew, “A fast algorithm for the analysis of scattering by dielectric rough surfaces,” J. Opt. Soc. Am. A 15, 1877–1885 (1998).
[CrossRef]

R. L. Wagner, J. Song, W. C. Chew, “Monte Carlo simulation of electromagnetic scattering from two-dimensional random rough surfaces,” IEEE Trans. Antennas Propag. 45, 235–245 (1997).
[CrossRef]

J. M. Song, W. C. Chew, “Multilevel fast-multipole algorithm for solving combined field integral equations of electromagnetic scattering,” Microwave Opt. Technol. Lett. 10, 14–19 (1995).
[CrossRef]

C. C. Lu, W. C. Chew, “A multilevel fast-algorithm for solving a boundary integral equation of wave scattering,” Microwave Opt. Technol. Lett. 7, 466–470 (1994).
[CrossRef]

C. C. Lu, W. C. Chew, “Fast algorithm for solving hybrid integral equations,” IEE Proc. Pt. H 140, 455–460 (1993).

M. El-Shenawee, V. Jandhyala, E. Michielssen, W. C. Chew, “The steepest descent fast multipole method (SDFMM) for solving combined field integral equation pertinent to rough surface scattering,” in Proceedings of the IEEE APS/URSI ’99 Conference (Institute of Electrical and Electronics Engineers, New York, 1999), pp. 534–537.

Coifman, R.

R. Coifman, V. Rokhlin, S. Wandzura, “The fast multipole method for the wave equation: a pedestrian description,” IEEE Antennas Propag. Mag. 35 (No. 3), 7–12 (1993).
[CrossRef]

Curtis, J.

J. Curtis, “Dielectric properties of soils; various sites in Bosnia,” (U.S. Army Corps of Engineers, Waterways Experiment, Washington, D.C., 1996).

El-Shenawee, M.

M. El-Shenawee, C. Rappaport, E. Miller, M. Silevitch, “3-D subsurface analysis of electromagnetic scattering from penetrable/PEC objects buried under rough surfaces: use of the steepest descent fast multipole method (SDFMM),” IEEE Trans. Geosci. Remote Sens. 39, 1174–1182 (2001).
[CrossRef]

M. El-Shenawee, V. Jandhyala, E. Michielssen, W. C. Chew, “The steepest descent fast multipole method (SDFMM) for solving combined field integral equation pertinent to rough surface scattering,” in Proceedings of the IEEE APS/URSI ’99 Conference (Institute of Electrical and Electronics Engineers, New York, 1999), pp. 534–537.

Freund, R. W.

R. W. Freund, “A transpose-free quasi-minimal residual algorithm for non-Hermitian linear systems,” SIAM J. Sci. Comput. 14, 470–482 (1993).
[CrossRef]

Gedera, M.

Geng, N.

N. Geng, A. Sullivan, L. Carin, “Multilevel fast-multipole algorithm for scattering from conducting targets above or embedded in a lossy half space,” IEEE Trans. Geosci. Remote Sens. 38, 1561–1573 (2000).
[CrossRef]

Glisson, A. W.

S. M. Rao, D. R. Wilton, A. W. Glisson, “Electromagnetic scattering by surfaces of arbitrary shape,” IEEE Trans. Antennas Propag. AP-30, 409–418 (1982).
[CrossRef]

Harrington, R. F.

J. R. Mautz, R. F. Harrington, “H-field, E-field, and combined field solutions for conducting bodies of revolutions,” Arch. Elektr. Uebertrag. 32, 157–164 (1978).

Hastings, F. D.

F. D. Hastings, J. B. Schneider, S. L. Broschat, “A Monte Carlo FDTD technique for rough surface scattering,” IEEE Trans. Antennas Propag. 43, 1183–1191 (1995).
[CrossRef]

Huddleston, P. L.

P. L. Huddleston, L. N. Medgyesi-Mitschang, J. M. Putnam, “Combined field integral equation formulation for scattering from dielectrically coated conducting bodies,” IEEE Trans. Antennas Propag. AP-34, 510–520 (1986).
[CrossRef]

Ishimaru, A.

J. T. Johnson, L. Tsang, R. T. Shin, K. Pak, C. H. Chan, A. Ishimaru, Y. Kuga, “Backscattering enhancement of electromagnetic waves from two-dimensional perfectly conducting random rough surfaces: comparison of Monte Carlo simulations with experimental data,” IEEE Trans. Antennas Propag. 44, 748–756 (1996).
[CrossRef]

L. Tsang, C. H. Chan, K. Pak, H. Sangani, A. Ishimaru, P. Phu, “Monte Carlo simulations of large-scale composite random rough-surface scattering based on the banded-matrix iterative approach,” J. Opt. Soc. Am. A 11, 691–696 (1994).
[CrossRef]

Jandhyala, V.

V. Jandhyala, B. Shanker, E. Michielssen, W. C. Chew, “A fast algorithm for the analysis of scattering by dielectric rough surfaces,” J. Opt. Soc. Am. A 15, 1877–1885 (1998).
[CrossRef]

V. Jandhyala, E. Michielssen, B. Shanker, W. C. Chew, “A combined steepest descent–fast multipole algorithm for the fast analysis of three-dimensional scattering by rough surfaces,” IEEE Trans. Geosci. Remote Sens. 36, 738–748 (1998).
[CrossRef]

V. Jandhyala, “Fast multilevel algorithms for the efficient electromagnetic analysis of quasi-planar structures,” Ph.D. thesis (Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign, Urbana Champaign, Ill., 1998).

M. El-Shenawee, V. Jandhyala, E. Michielssen, W. C. Chew, “The steepest descent fast multipole method (SDFMM) for solving combined field integral equation pertinent to rough surface scattering,” in Proceedings of the IEEE APS/URSI ’99 Conference (Institute of Electrical and Electronics Engineers, New York, 1999), pp. 534–537.

Johnson, J. T.

J. T. Johnson, L. Tsang, R. T. Shin, K. Pak, C. H. Chan, A. Ishimaru, Y. Kuga, “Backscattering enhancement of electromagnetic waves from two-dimensional perfectly conducting random rough surfaces: comparison of Monte Carlo simulations with experimental data,” IEEE Trans. Antennas Propag. 44, 748–756 (1996).
[CrossRef]

Kuga, Y.

G. Zhang, L. Tsang, Y. Kuga, “Studies of the angular correlation function of scattering by random rough surfaces with and without a buried object,” IEEE Trans. Geosci. Remote Sens. 35, 444–453 (1997).
[CrossRef]

J. T. Johnson, L. Tsang, R. T. Shin, K. Pak, C. H. Chan, A. Ishimaru, Y. Kuga, “Backscattering enhancement of electromagnetic waves from two-dimensional perfectly conducting random rough surfaces: comparison of Monte Carlo simulations with experimental data,” IEEE Trans. Antennas Propag. 44, 748–756 (1996).
[CrossRef]

Li, Q.

S. Li, C. H. Chan, L. Tsang, Q. Li, L. Zhou, “Parallel implementation of the parse matrix/canonical grid method for the analysis of two-dimensional random rough surfaces (three-dimensional scattering problem) on a Beowulf system,” IEEE Trans. Geosci. Remote Sens. 38, 1600–1608 (2000).
[CrossRef]

C. H. Chan, L. Tsang, Q. Li, “Monte Carlo simulations of large-scale one dimensional random rough-surface scattering at near grazing incidence: penetrable case,” IEEE Trans. Antennas Propag. 46, 142–149 (1998).
[CrossRef]

Li, S.

S. Li, C. H. Chan, L. Tsang, Q. Li, L. Zhou, “Parallel implementation of the parse matrix/canonical grid method for the analysis of two-dimensional random rough surfaces (three-dimensional scattering problem) on a Beowulf system,” IEEE Trans. Geosci. Remote Sens. 38, 1600–1608 (2000).
[CrossRef]

Lu, C. C.

C. C. Lu, W. C. Chew, “A multilevel fast-algorithm for solving a boundary integral equation of wave scattering,” Microwave Opt. Technol. Lett. 7, 466–470 (1994).
[CrossRef]

C. C. Lu, W. C. Chew, “Fast algorithm for solving hybrid integral equations,” IEE Proc. Pt. H 140, 455–460 (1993).

Lussky, R. F.

K. O’Neill, R. F. Lussky, 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]

Madrazo, A.

Maradudin, A. A.

P. Tran, A. A. Maradudin, “Scattering of a scalar beamfrom a two-dimensional randomly rough hard wall: enhanced backscatter,” Phys. Rev. B 45, 3936–3939 (1992).
[CrossRef]

Mautz, J. R.

J. R. Mautz, R. F. Harrington, “H-field, E-field, and combined field solutions for conducting bodies of revolutions,” Arch. Elektr. Uebertrag. 32, 157–164 (1978).

Medgyesi-Mitschang, L. N.

P. L. Huddleston, L. N. Medgyesi-Mitschang, J. M. Putnam, “Combined field integral equation formulation for scattering from dielectrically coated conducting bodies,” IEEE Trans. Antennas Propag. AP-34, 510–520 (1986).
[CrossRef]

Medgyesti-Mitschang, L.

Michielssen, E.

V. Jandhyala, B. Shanker, E. Michielssen, W. C. Chew, “A fast algorithm for the analysis of scattering by dielectric rough surfaces,” J. Opt. Soc. Am. A 15, 1877–1885 (1998).
[CrossRef]

V. Jandhyala, E. Michielssen, B. Shanker, W. C. Chew, “A combined steepest descent–fast multipole algorithm for the fast analysis of three-dimensional scattering by rough surfaces,” IEEE Trans. Geosci. Remote Sens. 36, 738–748 (1998).
[CrossRef]

M. El-Shenawee, V. Jandhyala, E. Michielssen, W. C. Chew, “The steepest descent fast multipole method (SDFMM) for solving combined field integral equation pertinent to rough surface scattering,” in Proceedings of the IEEE APS/URSI ’99 Conference (Institute of Electrical and Electronics Engineers, New York, 1999), pp. 534–537.

Miller, E.

M. El-Shenawee, C. Rappaport, E. Miller, M. Silevitch, “3-D subsurface analysis of electromagnetic scattering from penetrable/PEC objects buried under rough surfaces: use of the steepest descent fast multipole method (SDFMM),” IEEE Trans. Geosci. Remote Sens. 39, 1174–1182 (2001).
[CrossRef]

Nieto-Vesperinas, M.

O’Neill, K.

K. O’Neill, R. F. Lussky, 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]

Pak, K.

Paulsen, K. D.

K. O’Neill, R. F. Lussky, 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]

Phu, P.

Putnam, J.

Putnam, J. M.

P. L. Huddleston, L. N. Medgyesi-Mitschang, J. M. Putnam, “Combined field integral equation formulation for scattering from dielectrically coated conducting bodies,” IEEE Trans. Antennas Propag. AP-34, 510–520 (1986).
[CrossRef]

Rao, S. M.

S. M. Rao, D. R. Wilton, A. W. Glisson, “Electromagnetic scattering by surfaces of arbitrary shape,” IEEE Trans. Antennas Propag. AP-30, 409–418 (1982).
[CrossRef]

Rappaport, C.

M. El-Shenawee, C. Rappaport, E. Miller, M. Silevitch, “3-D subsurface analysis of electromagnetic scattering from penetrable/PEC objects buried under rough surfaces: use of the steepest descent fast multipole method (SDFMM),” IEEE Trans. Geosci. Remote Sens. 39, 1174–1182 (2001).
[CrossRef]

Rokhlin, V.

R. Coifman, V. Rokhlin, S. Wandzura, “The fast multipole method for the wave equation: a pedestrian description,” IEEE Antennas Propag. Mag. 35 (No. 3), 7–12 (1993).
[CrossRef]

V. Rokhlin, “Rapid solution of integral equations of scattering theory in two dimensions,” J. Comput. Phys. 36, 414–439 (1990).
[CrossRef]

Sangani, H.

Schneider, J. B.

F. D. Hastings, J. B. Schneider, S. L. Broschat, “A Monte Carlo FDTD technique for rough surface scattering,” IEEE Trans. Antennas Propag. 43, 1183–1191 (1995).
[CrossRef]

Shanker, B.

V. Jandhyala, E. Michielssen, B. Shanker, W. C. Chew, “A combined steepest descent–fast multipole algorithm for the fast analysis of three-dimensional scattering by rough surfaces,” IEEE Trans. Geosci. Remote Sens. 36, 738–748 (1998).
[CrossRef]

V. Jandhyala, B. Shanker, E. Michielssen, W. C. Chew, “A fast algorithm for the analysis of scattering by dielectric rough surfaces,” J. Opt. Soc. Am. A 15, 1877–1885 (1998).
[CrossRef]

Shin, R. T.

J. T. Johnson, L. Tsang, R. T. Shin, K. Pak, C. H. Chan, A. Ishimaru, Y. Kuga, “Backscattering enhancement of electromagnetic waves from two-dimensional perfectly conducting random rough surfaces: comparison of Monte Carlo simulations with experimental data,” IEEE Trans. Antennas Propag. 44, 748–756 (1996).
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[CrossRef]

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[CrossRef]

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S. Li, C. H. Chan, L. Tsang, Q. Li, L. Zhou, “Parallel implementation of the parse matrix/canonical grid method for the analysis of two-dimensional random rough surfaces (three-dimensional scattering problem) on a Beowulf system,” IEEE Trans. Geosci. Remote Sens. 38, 1600–1608 (2000).
[CrossRef]

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[CrossRef]

C. H. Chan, L. Tsang, Q. Li, “Monte Carlo simulations of large-scale one dimensional random rough-surface scattering at near grazing incidence: penetrable case,” IEEE Trans. Antennas Propag. 46, 142–149 (1998).
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[CrossRef]

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P. Tran, A. A. Maradudin, “Scattering of a scalar beamfrom a two-dimensional randomly rough hard wall: enhanced backscatter,” Phys. Rev. B 45, 3936–3939 (1992).
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Figures (7)

Fig. 1
Fig. 1

Cross section of 2-D rough surface ground with 3-D object buried under the interface.

Fig. 2
Fig. 2

Penetrable 3-D scatterer R3 immersed in scatterer R2 immersed in region R1.

Fig. 3
Fig. 3

(a) Average of near electric field scattered at z=0.5λ0 above rough ground of rms height σ=0.04λ0 and correlation length lc=0.5λ0 with incidence angle θi=0° for horizontal polarization. (b) Average of near electric field scattered at z=0.5λ0 above rough ground of rms height σ=0.04λ0 and correlation length lc=0.5λ0 with incidence angle θi=0° for horizontal polarization. The oblate spheroid object has dimensions a=0.3λ0 and b=0.15λ0 and is buried at depth d=0.3λ0 under the mean plane of the surface.

Fig. 4
Fig. 4

Near electric field scattered at z=0.5λ0 (a) from two individual rough surface realizations with buried spheroid selected from Fig. 3(b) (surfaces 1 and 2), the average of 65 electric fields scattered from a rough surface with and without the buried spheroid [Figs. 3(b) and 3(a), respectively], and the scattered electric field from flat ground with and without the buried spheroid, all plotted at Y=4.0λ0; (b) that is due to just the buried object under a flat ground obtained by subtraction; (c) that is due to just the buried object obtained by subtracting the average electric field of Fig. 3(a) from the field scattered from only one surface (with buried spheroid) selected from the 65 realizations used to obtain Fig. 3(b); (d) that is due to just the buried object obtained by subtracting fields scattered from only one surface selected from the 65 realizations used to obtain Fig. 3(a) (surface only) from fields scattered from the same surface (with buried spheroid) selected from the 65 realizations used to obtain Fig. 3(b); (e) average scattered near electric field that is due to just the buried object obtained by subtracting fields scattered from the 65 realizations used to obtain Fig. 3(a) from fields scattered from the same 65 realizations and used to obtain Fig. 3(b) and then take the statistical average. For (a)–(e) the incidence angle is θi=0° for horizontal polarization, where the spheroid is buried at x=y=4.0λ0, z=-0.3λ0.

Fig. 5
Fig. 5

Comparison between signatures of three objects located at x=y=4.0λ0, x=y=5.0λ0, and x=6.5λ0, y=4.0λ0.

Fig. 6
Fig. 6

STD of scattered near electric fields that are due to just the buried spheroid for the same data as those in Fig. 4(e).

Fig. 7
Fig. 7

(a) Average of near electric field scattered at z=0.5λ0 above rough ground of rms height σ=0.04λ0 and correlation length lc=0.5λ0 with incidence angle θi=10° for vertical polarization. (b) Average of near electric field scattered at z=0.5λ0 above rough ground of rms height σ=0.04λ0 and correlation length lc=0.5λ0 with incidence angle θi=10° for vertical polarization. The object has dimensions a=0.3λ0 and b=0.15λ0 and is buried at depth d=0.3λ0 under the mean plane of the surface. (c) Average scattered near electric field that is due to just the buried object obtained by subtracting fields scattered from the 65 realizations used to obtain Fig. 7(a) from fields scattered from the same 65 realizations and used to obtain Fig. 7(b) and then by taking the statistical average. The incidence angle is θi=10° for vertical polarization. (d) Average scattered near electric field that is due to just the buried object for data similar to those shown in Fig. 7(c) but for horizontal polarization.

Equations (11)

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

Einc(r)|tang.=[(L1+L2)J1-(K1+K2)M1-L3J3+K3M3]tang.,
Hinc(r)|tang.=(K1+K2)J1+L1η12+L2η22M1-K3J3-L3η22M3tang.,
0=[-L2J1+K2M1+(L3+L4)J3-(K3+K4)M3]tang.,
0=-K2J1-L2M1η22+(K3+K4)J3+L3η22+L4η32M3tang.,
J1(r)=n=iNI1nj1n(r),
M1(r)=ξ1n=1NI2nj1n(r),rS1,
J3(r)=m=1PI3mj2m(r),
M3(r)=ξ1m=1PI4mj2m(r),rS2,
ZI=V.
Average=1Mi=1MEi,
STD=1Mi=1M|Ei|2-|1Mi=1MEi|21/2,

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