Abstract

We study three-dimensional (3-D) electromagnetic wave scattering from a buried object under a two-dimensional (2-D) random rough surface. The surface integral equations of wave fields are used for the rough surface and the surface of the buried object. The surface fields are then solved by the method of moments. The scattered wave field from the object is represented by the rough-surface field so that the matrix equation can be solved efficiently by means of the sparse-matrix canonical-grid method. Numerical simulations are illustrated for a perfectly conducting sphere buried under a 2-D rough surface. Both the scattering coefficient (normalized radar cross section) and the angular correlation function (ACF) are calculated. The study of 3-D electromagnetic scattering allows the use of azimuthal angular averaging and the study of cross polarization and the polarization angular correlation function (PACF). It is found that the ACF is more effective in suppressing the clutter that is due to the rough-surface scattering, and the PACF is more useful for the detection of the buried object.

© 1998 Optical Society of America

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  1. L. Peters, J. Daniels, J. Young, “Ground penetrating radar as a subsurface environmental sensing tool,” Proc. IEEE 82, 1802–1822 (1994).
    [CrossRef]
  2. S. Vitebskiy, L. Carin, M. A. Ressler, F. H. Le, “Ultra-wideband, short-pulse ground-penetrating radar: simulation and measurement,” IEEE Trans. Geosci. Remote Sens. 35, 762–772 (1997).
    [CrossRef]
  3. X. Yang, D. A. Gregory, P. S. Erbach, “Clutter reduction and target detection enhancement using wavelet transform techniques,” in Optical Pattern Recognition VI, D. P. Casasent, T.-H. Chao, eds., Proc. SPIE2490, 125–139 (1995).
    [CrossRef]
  4. Y. Yamaguchi, T. Moriyama, “Polarimetric detection of objects buried in snowpack by a synthetic aperture FM–CM radar,” IEEE Trans. Geosci. Remote Sens. 34, 45–51 (1996).
    [CrossRef]
  5. A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978), Vols. I and II.
  6. L. Tsang, J. A. Kong, R. T. Shin, Theory of Microwave Remote Sensing (Wiley-Interscience, New York, 1985).
  7. L. Tsang, C. H. Chan, K. Pak, “Backscattering enhancement of a two-dimensional random rough surface (three-dimensional scattering) based on Monte Carlo simulations,” J. Opt. Soc. Am. A 11, 711–715 (1994).
    [CrossRef]
  8. P. Tran, A. A. Maradudin, “The scattering of electromagnetic waves from 2D metallic surface,” Opt. Commun. 110, 269–273 (1994).
    [CrossRef]
  9. K. O’Neill, R. Lussky, K. D. Paulsen, “Scattering from a metallic reflector embedded in a lossy dielectric beneath a random rough surface,” IEEE Trans. Geosci. Remote Sens. 34, 367–376 (1996).
    [CrossRef]
  10. 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]
  11. G. Videen, “Light scattering from a sphere behind a plane,” J. Opt. Soc. Am. A 10, 110–117 (1993).
    [CrossRef]
  12. S. Tjuatja, A. K. Fung, S. Wu, P. Zhou, Z. Li, “Remote sensing of buried objects: an analysis using FD–TD simulation,” presented at the International Geoscience and Remote Sensing Symposium ’97, Singapore, August 3–8, 1997.
  13. Y. H. Chen, W. C. Chew, M. L. Oristaglio, “Application of perfectly matched layers to the transient modeling of subsurface EM problems,” Geophysics 62, 1730–1736 (1997).
    [CrossRef]
  14. 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]
  15. K. Pak, “Studies of large-scale random rough surface scattering problems based on Monte Carlo simulations with efficient computational integral equation methods,” Ph.D. dissertation (University of Washington, Seattle, Wash., 1996).
  16. K. Pak, L. Tsang, C. H. Chan, J. Johnson, “Backscattering enhancement of electromagnetic waves from two-dimensional perfectly conducting random rough surfaces based on Monte Carlo simulations,” J. Opt. Soc. Am. A 12, 2491–2499 (1995).
    [CrossRef]
  17. K. Pak, L. Tsang, J. Johnson, “Numerical simulations and backscattering enhancement of scattered waves from two-dimensional dielectric random rough surfaces with sparse-matrix canonical grid method,” J. Opt. Soc. Am. A 14, 1515–1529 (1997).
    [CrossRef]
  18. S. Feng, C. Kane, P. A. Lee, A. D. Stone, “Correlations and fluctuations of coherent wave transmission through disordered media,” Phys. Rev. Lett. 61, 834–837 (1988).
    [CrossRef] [PubMed]
  19. T. R. Michel, K. A. O’Donnell, “Angular correlation functions of amplitudes scattered from a one-dimensional, perfectly conducting rough surface,” J. Opt. Soc. Am. A 9, 1374–1384 (1992).
    [CrossRef]
  20. M. Nieto-Vesperinas, J. A. Sanchez-Gil, “Intensity angular correlations of light multiply scattered from random rough surfaces,” J. Opt. Soc. Am. A 10, 150–157 (1993).
    [CrossRef]
  21. A. A. Maradudin, M. Nieto-Vesperinas, E. Thorsos, “Enhanced backscattering of light from randomly rough surfaces and related phenomena I: one-dimensional surfaces and angular correlation function of scattered fields,” Comments Condens. Matter Phys. 17, 13–37 (1994).
  22. L. Tsang, G. Zhang, K. Pak, “Detection of a buried object under a single random rough surface with angular correlation function in EM wave scattering,” Microwave Opt. Technol. Lett. 11, 300–304 (1996).
    [CrossRef]
  23. G. Zhang, L. Tsang, Y. Kuga, “Angular correlation function of wave scattering by a buried object embedded in random discrete scatterers under a rough surface,” Microwave Opt. Technol. Lett. 14, 144–151 (1997).
    [CrossRef]
  24. 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]
  25. G. Zhang, L. Tsang, “Application of the angular correlation function of clutter scattering and correlation imaging in target detection,” IEEE Trans. Geosci. Remote Sens. 36(5) (1998).

1998 (1)

G. Zhang, L. Tsang, “Application of the angular correlation function of clutter scattering and correlation imaging in target detection,” IEEE Trans. Geosci. Remote Sens. 36(5) (1998).

1997 (7)

G. Zhang, L. Tsang, Y. Kuga, “Angular correlation function of wave scattering by a buried object embedded in random discrete scatterers under a rough surface,” Microwave Opt. Technol. Lett. 14, 144–151 (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]

K. Pak, L. Tsang, J. Johnson, “Numerical simulations and backscattering enhancement of scattered waves from two-dimensional dielectric random rough surfaces with sparse-matrix canonical grid method,” J. Opt. Soc. Am. A 14, 1515–1529 (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]

S. Vitebskiy, L. Carin, M. A. Ressler, F. H. Le, “Ultra-wideband, short-pulse ground-penetrating radar: simulation and measurement,” IEEE Trans. Geosci. Remote Sens. 35, 762–772 (1997).
[CrossRef]

Y. H. Chen, W. C. Chew, M. L. Oristaglio, “Application of perfectly matched layers to the transient modeling of subsurface EM problems,” Geophysics 62, 1730–1736 (1997).
[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]

1996 (3)

L. Tsang, G. Zhang, K. Pak, “Detection of a buried object under a single random rough surface with angular correlation function in EM wave scattering,” Microwave Opt. Technol. Lett. 11, 300–304 (1996).
[CrossRef]

Y. Yamaguchi, T. Moriyama, “Polarimetric detection of objects buried in snowpack by a synthetic aperture FM–CM radar,” IEEE Trans. Geosci. Remote Sens. 34, 45–51 (1996).
[CrossRef]

K. O’Neill, R. Lussky, K. D. Paulsen, “Scattering from a metallic reflector embedded in a lossy dielectric beneath a random rough surface,” IEEE Trans. Geosci. Remote Sens. 34, 367–376 (1996).
[CrossRef]

1995 (1)

1994 (4)

L. Tsang, C. H. Chan, K. Pak, “Backscattering enhancement of a two-dimensional random rough surface (three-dimensional scattering) based on Monte Carlo simulations,” J. Opt. Soc. Am. A 11, 711–715 (1994).
[CrossRef]

L. Peters, J. Daniels, J. Young, “Ground penetrating radar as a subsurface environmental sensing tool,” Proc. IEEE 82, 1802–1822 (1994).
[CrossRef]

P. Tran, A. A. Maradudin, “The scattering of electromagnetic waves from 2D metallic surface,” Opt. Commun. 110, 269–273 (1994).
[CrossRef]

A. A. Maradudin, M. Nieto-Vesperinas, E. Thorsos, “Enhanced backscattering of light from randomly rough surfaces and related phenomena I: one-dimensional surfaces and angular correlation function of scattered fields,” Comments Condens. Matter Phys. 17, 13–37 (1994).

1993 (2)

1992 (1)

1988 (1)

S. Feng, C. Kane, P. A. Lee, A. D. Stone, “Correlations and fluctuations of coherent wave transmission through disordered media,” Phys. Rev. Lett. 61, 834–837 (1988).
[CrossRef] [PubMed]

Carin, L.

S. Vitebskiy, L. Carin, M. A. Ressler, F. H. Le, “Ultra-wideband, short-pulse ground-penetrating radar: simulation and measurement,” IEEE Trans. Geosci. Remote Sens. 35, 762–772 (1997).
[CrossRef]

Chan, C. H.

Chen, Y. H.

Y. H. Chen, W. C. Chew, M. L. Oristaglio, “Application of perfectly matched layers to the transient modeling of subsurface EM problems,” Geophysics 62, 1730–1736 (1997).
[CrossRef]

Chew, W. C.

Y. H. Chen, W. C. Chew, M. L. Oristaglio, “Application of perfectly matched layers to the transient modeling of subsurface EM problems,” Geophysics 62, 1730–1736 (1997).
[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]

Daniels, J.

L. Peters, J. Daniels, J. Young, “Ground penetrating radar as a subsurface environmental sensing tool,” Proc. IEEE 82, 1802–1822 (1994).
[CrossRef]

Erbach, P. S.

X. Yang, D. A. Gregory, P. S. Erbach, “Clutter reduction and target detection enhancement using wavelet transform techniques,” in Optical Pattern Recognition VI, D. P. Casasent, T.-H. Chao, eds., Proc. SPIE2490, 125–139 (1995).
[CrossRef]

Feng, S.

S. Feng, C. Kane, P. A. Lee, A. D. Stone, “Correlations and fluctuations of coherent wave transmission through disordered media,” Phys. Rev. Lett. 61, 834–837 (1988).
[CrossRef] [PubMed]

Fung, A. K.

S. Tjuatja, A. K. Fung, S. Wu, P. Zhou, Z. Li, “Remote sensing of buried objects: an analysis using FD–TD simulation,” presented at the International Geoscience and Remote Sensing Symposium ’97, Singapore, August 3–8, 1997.

Gregory, D. A.

X. Yang, D. A. Gregory, P. S. Erbach, “Clutter reduction and target detection enhancement using wavelet transform techniques,” in Optical Pattern Recognition VI, D. P. Casasent, T.-H. Chao, eds., Proc. SPIE2490, 125–139 (1995).
[CrossRef]

Ishimaru, A.

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978), Vols. I and II.

Johnson, J.

Kane, C.

S. Feng, C. Kane, P. A. Lee, A. D. Stone, “Correlations and fluctuations of coherent wave transmission through disordered media,” Phys. Rev. Lett. 61, 834–837 (1988).
[CrossRef] [PubMed]

Kong, J. A.

L. Tsang, J. A. Kong, R. T. Shin, Theory of Microwave Remote Sensing (Wiley-Interscience, New York, 1985).

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]

G. Zhang, L. Tsang, Y. Kuga, “Angular correlation function of wave scattering by a buried object embedded in random discrete scatterers under a rough surface,” Microwave Opt. Technol. Lett. 14, 144–151 (1997).
[CrossRef]

Le, F. H.

S. Vitebskiy, L. Carin, M. A. Ressler, F. H. Le, “Ultra-wideband, short-pulse ground-penetrating radar: simulation and measurement,” IEEE Trans. Geosci. Remote Sens. 35, 762–772 (1997).
[CrossRef]

Lee, P. A.

S. Feng, C. Kane, P. A. Lee, A. D. Stone, “Correlations and fluctuations of coherent wave transmission through disordered media,” Phys. Rev. Lett. 61, 834–837 (1988).
[CrossRef] [PubMed]

Li, Z.

S. Tjuatja, A. K. Fung, S. Wu, P. Zhou, Z. Li, “Remote sensing of buried objects: an analysis using FD–TD simulation,” presented at the International Geoscience and Remote Sensing Symposium ’97, Singapore, August 3–8, 1997.

Lussky, R.

K. O’Neill, R. Lussky, K. D. Paulsen, “Scattering from a metallic reflector embedded in a lossy dielectric beneath a random rough surface,” IEEE Trans. Geosci. Remote Sens. 34, 367–376 (1996).
[CrossRef]

Madrazo, A.

Maradudin, A. A.

P. Tran, A. A. Maradudin, “The scattering of electromagnetic waves from 2D metallic surface,” Opt. Commun. 110, 269–273 (1994).
[CrossRef]

A. A. Maradudin, M. Nieto-Vesperinas, E. Thorsos, “Enhanced backscattering of light from randomly rough surfaces and related phenomena I: one-dimensional surfaces and angular correlation function of scattered fields,” Comments Condens. Matter Phys. 17, 13–37 (1994).

Michel, T. R.

Moriyama, T.

Y. Yamaguchi, T. Moriyama, “Polarimetric detection of objects buried in snowpack by a synthetic aperture FM–CM radar,” IEEE Trans. Geosci. Remote Sens. 34, 45–51 (1996).
[CrossRef]

Nieto-Vesperinas, M.

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]

A. A. Maradudin, M. Nieto-Vesperinas, E. Thorsos, “Enhanced backscattering of light from randomly rough surfaces and related phenomena I: one-dimensional surfaces and angular correlation function of scattered fields,” Comments Condens. Matter Phys. 17, 13–37 (1994).

M. Nieto-Vesperinas, J. A. Sanchez-Gil, “Intensity angular correlations of light multiply scattered from random rough surfaces,” J. Opt. Soc. Am. A 10, 150–157 (1993).
[CrossRef]

O’Donnell, K. A.

O’Neill, K.

K. O’Neill, R. Lussky, K. D. Paulsen, “Scattering from a metallic reflector embedded in a lossy dielectric beneath a random rough surface,” IEEE Trans. Geosci. Remote Sens. 34, 367–376 (1996).
[CrossRef]

Oristaglio, M. L.

Y. H. Chen, W. C. Chew, M. L. Oristaglio, “Application of perfectly matched layers to the transient modeling of subsurface EM problems,” Geophysics 62, 1730–1736 (1997).
[CrossRef]

Pak, K.

Paulsen, K. D.

K. O’Neill, R. Lussky, K. D. Paulsen, “Scattering from a metallic reflector embedded in a lossy dielectric beneath a random rough surface,” IEEE Trans. Geosci. Remote Sens. 34, 367–376 (1996).
[CrossRef]

Peters, L.

L. Peters, J. Daniels, J. Young, “Ground penetrating radar as a subsurface environmental sensing tool,” Proc. IEEE 82, 1802–1822 (1994).
[CrossRef]

Ressler, M. A.

S. Vitebskiy, L. Carin, M. A. Ressler, F. H. Le, “Ultra-wideband, short-pulse ground-penetrating radar: simulation and measurement,” IEEE Trans. Geosci. Remote Sens. 35, 762–772 (1997).
[CrossRef]

Sanchez-Gil, J. A.

Shin, R. T.

L. Tsang, J. A. Kong, R. T. Shin, Theory of Microwave Remote Sensing (Wiley-Interscience, New York, 1985).

Song, J.

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]

Stone, A. D.

S. Feng, C. Kane, P. A. Lee, A. D. Stone, “Correlations and fluctuations of coherent wave transmission through disordered media,” Phys. Rev. Lett. 61, 834–837 (1988).
[CrossRef] [PubMed]

Thorsos, E.

A. A. Maradudin, M. Nieto-Vesperinas, E. Thorsos, “Enhanced backscattering of light from randomly rough surfaces and related phenomena I: one-dimensional surfaces and angular correlation function of scattered fields,” Comments Condens. Matter Phys. 17, 13–37 (1994).

Tjuatja, S.

S. Tjuatja, A. K. Fung, S. Wu, P. Zhou, Z. Li, “Remote sensing of buried objects: an analysis using FD–TD simulation,” presented at the International Geoscience and Remote Sensing Symposium ’97, Singapore, August 3–8, 1997.

Tran, P.

P. Tran, A. A. Maradudin, “The scattering of electromagnetic waves from 2D metallic surface,” Opt. Commun. 110, 269–273 (1994).
[CrossRef]

Tsang, L.

G. Zhang, L. Tsang, “Application of the angular correlation function of clutter scattering and correlation imaging in target detection,” IEEE Trans. Geosci. Remote Sens. 36(5) (1998).

G. Zhang, L. Tsang, Y. Kuga, “Angular correlation function of wave scattering by a buried object embedded in random discrete scatterers under a rough surface,” Microwave Opt. Technol. Lett. 14, 144–151 (1997).
[CrossRef]

K. Pak, L. Tsang, J. Johnson, “Numerical simulations and backscattering enhancement of scattered waves from two-dimensional dielectric random rough surfaces with sparse-matrix canonical grid method,” J. Opt. Soc. Am. A 14, 1515–1529 (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]

L. Tsang, G. Zhang, K. Pak, “Detection of a buried object under a single random rough surface with angular correlation function in EM wave scattering,” Microwave Opt. Technol. Lett. 11, 300–304 (1996).
[CrossRef]

K. Pak, L. Tsang, C. H. Chan, J. Johnson, “Backscattering enhancement of electromagnetic waves from two-dimensional perfectly conducting random rough surfaces based on Monte Carlo simulations,” J. Opt. Soc. Am. A 12, 2491–2499 (1995).
[CrossRef]

L. Tsang, C. H. Chan, K. Pak, “Backscattering enhancement of a two-dimensional random rough surface (three-dimensional scattering) based on Monte Carlo simulations,” J. Opt. Soc. Am. A 11, 711–715 (1994).
[CrossRef]

L. Tsang, J. A. Kong, R. T. Shin, Theory of Microwave Remote Sensing (Wiley-Interscience, New York, 1985).

Videen, G.

Vitebskiy, S.

S. Vitebskiy, L. Carin, M. A. Ressler, F. H. Le, “Ultra-wideband, short-pulse ground-penetrating radar: simulation and measurement,” IEEE Trans. Geosci. Remote Sens. 35, 762–772 (1997).
[CrossRef]

Wagner, R. L.

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]

Wu, S.

S. Tjuatja, A. K. Fung, S. Wu, P. Zhou, Z. Li, “Remote sensing of buried objects: an analysis using FD–TD simulation,” presented at the International Geoscience and Remote Sensing Symposium ’97, Singapore, August 3–8, 1997.

Yamaguchi, Y.

Y. Yamaguchi, T. Moriyama, “Polarimetric detection of objects buried in snowpack by a synthetic aperture FM–CM radar,” IEEE Trans. Geosci. Remote Sens. 34, 45–51 (1996).
[CrossRef]

Yang, X.

X. Yang, D. A. Gregory, P. S. Erbach, “Clutter reduction and target detection enhancement using wavelet transform techniques,” in Optical Pattern Recognition VI, D. P. Casasent, T.-H. Chao, eds., Proc. SPIE2490, 125–139 (1995).
[CrossRef]

Young, J.

L. Peters, J. Daniels, J. Young, “Ground penetrating radar as a subsurface environmental sensing tool,” Proc. IEEE 82, 1802–1822 (1994).
[CrossRef]

Zhang, G.

G. Zhang, L. Tsang, “Application of the angular correlation function of clutter scattering and correlation imaging in target detection,” IEEE Trans. Geosci. Remote Sens. 36(5) (1998).

G. Zhang, L. Tsang, Y. Kuga, “Angular correlation function of wave scattering by a buried object embedded in random discrete scatterers under a rough surface,” Microwave Opt. Technol. Lett. 14, 144–151 (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]

L. Tsang, G. Zhang, K. Pak, “Detection of a buried object under a single random rough surface with angular correlation function in EM wave scattering,” Microwave Opt. Technol. Lett. 11, 300–304 (1996).
[CrossRef]

Zhou, P.

S. Tjuatja, A. K. Fung, S. Wu, P. Zhou, Z. Li, “Remote sensing of buried objects: an analysis using FD–TD simulation,” presented at the International Geoscience and Remote Sensing Symposium ’97, Singapore, August 3–8, 1997.

Comments Condens. Matter Phys. (1)

A. A. Maradudin, M. Nieto-Vesperinas, E. Thorsos, “Enhanced backscattering of light from randomly rough surfaces and related phenomena I: one-dimensional surfaces and angular correlation function of scattered fields,” Comments Condens. Matter Phys. 17, 13–37 (1994).

Geophysics (1)

Y. H. Chen, W. C. Chew, M. L. Oristaglio, “Application of perfectly matched layers to the transient modeling of subsurface EM problems,” Geophysics 62, 1730–1736 (1997).
[CrossRef]

IEEE Trans. Antennas Propag. (1)

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]

IEEE Trans. Geosci. Remote Sens. (5)

S. Vitebskiy, L. Carin, M. A. Ressler, F. H. Le, “Ultra-wideband, short-pulse ground-penetrating radar: simulation and measurement,” IEEE Trans. Geosci. Remote Sens. 35, 762–772 (1997).
[CrossRef]

Y. Yamaguchi, T. Moriyama, “Polarimetric detection of objects buried in snowpack by a synthetic aperture FM–CM radar,” IEEE Trans. Geosci. Remote Sens. 34, 45–51 (1996).
[CrossRef]

K. O’Neill, R. Lussky, K. D. Paulsen, “Scattering from a metallic reflector embedded in a lossy dielectric beneath a random rough surface,” IEEE Trans. Geosci. Remote Sens. 34, 367–376 (1996).
[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]

G. Zhang, L. Tsang, “Application of the angular correlation function of clutter scattering and correlation imaging in target detection,” IEEE Trans. Geosci. Remote Sens. 36(5) (1998).

J. Opt. Soc. Am. A (7)

Microwave Opt. Technol. Lett. (2)

L. Tsang, G. Zhang, K. Pak, “Detection of a buried object under a single random rough surface with angular correlation function in EM wave scattering,” Microwave Opt. Technol. Lett. 11, 300–304 (1996).
[CrossRef]

G. Zhang, L. Tsang, Y. Kuga, “Angular correlation function of wave scattering by a buried object embedded in random discrete scatterers under a rough surface,” Microwave Opt. Technol. Lett. 14, 144–151 (1997).
[CrossRef]

Opt. Commun. (1)

P. Tran, A. A. Maradudin, “The scattering of electromagnetic waves from 2D metallic surface,” Opt. Commun. 110, 269–273 (1994).
[CrossRef]

Phys. Rev. Lett. (1)

S. Feng, C. Kane, P. A. Lee, A. D. Stone, “Correlations and fluctuations of coherent wave transmission through disordered media,” Phys. Rev. Lett. 61, 834–837 (1988).
[CrossRef] [PubMed]

Proc. IEEE (1)

L. Peters, J. Daniels, J. Young, “Ground penetrating radar as a subsurface environmental sensing tool,” Proc. IEEE 82, 1802–1822 (1994).
[CrossRef]

Other (5)

K. Pak, “Studies of large-scale random rough surface scattering problems based on Monte Carlo simulations with efficient computational integral equation methods,” Ph.D. dissertation (University of Washington, Seattle, Wash., 1996).

S. Tjuatja, A. K. Fung, S. Wu, P. Zhou, Z. Li, “Remote sensing of buried objects: an analysis using FD–TD simulation,” presented at the International Geoscience and Remote Sensing Symposium ’97, Singapore, August 3–8, 1997.

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978), Vols. I and II.

L. Tsang, J. A. Kong, R. T. Shin, Theory of Microwave Remote Sensing (Wiley-Interscience, New York, 1985).

X. Yang, D. A. Gregory, P. S. Erbach, “Clutter reduction and target detection enhancement using wavelet transform techniques,” in Optical Pattern Recognition VI, D. P. Casasent, T.-H. Chao, eds., Proc. SPIE2490, 125–139 (1995).
[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

Configuration of EM wave scattering by a 3-D object buried under a 2-D rough surface.

Fig. 2
Fig. 2

Discretization of a sphere into 80 triangle patches.

Fig. 3
Fig. 3

Comparison of MoM and Mie scattering for the RCS of a PEC sphere (a=0.36).

Fig. 4
Fig. 4

Comparison of the solution of the matrix equation for the object on the left-hand side and the object on the right-hand side.

Fig. 5
Fig. 5

(a) RCS and (b) ACF for EM wave scattering by a PEC sphere buried under a 2-D rough surface for the hh polarization component. Parameters are a=0.3λ, d=0.6λ, Lx=Ly=8.0λ, h=0.02λ, lx=ly=0.5.0λ, rd=3.5λ, g=Lx/4=Ly/4, θi1=20°, θs1=-40°, and θi2=20°.

Fig. 6
Fig. 6

RCS for EM wave scattering by a PEC sphere buried under a 2-D rough surface for co-polarized and cross-polarized components. (a) hh, (b) vv, (c) vh, (d) hv. Parameters are a=0.3λ, d=0.6λ, Lx=Ly=8.0λ, h=0.02λ, lx=ly=0.5.0λ, rd=3.5λ, g=Lx/4=Ly/4, θi1=20°, θs1=-40°, and θi2=20°.

Fig. 7
Fig. 7

ACF for EM wave scattering by a PEC sphere buried under a 2-D rough surface for co-polarized and cross-polarized components. (a) hh, (b) vv, (c) vh, (d) hv. Parameters are a=0.3λ, d=0.6λ, Lx=Ly=8.0λ, h=0.02λ, lx=ly=0.5.0λ, rd=3.5λ, g=Lx/4=Ly/4, θi1=20°, θs1=-40°, and θi2=20°.

Fig. 8
Fig. 8

PACF for EM wave scattering by a PEC sphere buried under a 2-D rough surface with co-polarized and cross-polarized components. (a) hhvh, (b) vvhv. Parameters are a=0.3λ, d=0.6λ, Lx=Ly=8.0λ, h=0.02λ, lx=ly=0.5.0λ, rd=3.5λ, g=Lx/4=Ly/4, θi1=20°, θs1=-40°, and θi2=20°.

Equations (43)

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Eαi(x, y, z)=-+dkx-+dky×exp(ikxx+ikyy-ikzz)×Ei(kx, ky)eˆα(-kz),
Hαi(x, y, z)=-1η -+dkx-+dky×exp(ikxx+ikyy-ikzz)×Ei(kx, ky)hˆα(-kz)
eˆh(-kz)=1kρ(xˆky-yˆkx),
hˆh(-kz)=kzkkρ(xˆkx+yˆky)+kρkzˆ,
eˆv(-kz)=kzkkρ(xˆkx+yˆky)+kρkzˆ,
hˆv(-kz)=1kρ(-xˆky+yˆkx),
Ei(kx, ky)=14π2 -+dx-+dy exp(-ikxx-ikyy)×exp[i(kixx+kiyy)(1+w)]exp(-t),
tx=(cos θi cos ϕix+cos θi sin ϕiy)2g2 cos2 θi,
ty=(-sin ϕix+cos ϕiy)2g2,
w=1k2 (2tx-1)g2 cos2 θi+(2ty-1)g2.
nˆ=1fx2+fy2+11/2 -fxxˆ-fyyˆ+1zˆ.
nˆ×E0=nˆ×E1,nˆ×H0=nˆ×H1
0nˆ·E0=1nˆ·E1,μ0nˆ·H0=μ1nˆ·H1
nˆ·Ei(r)=nˆ·E(r)2-nˆ·nˆ×H(r)iωμ0g0dS+P[(nˆ×E(r)×g0)+g0nˆ·E(r)]dS,
nˆ×Hi(r)=nˆ×H(r)2-nˆ×-iωnˆ×E(r)0g0dS+P[nˆ×H(r)×g0+nˆ·H(r)g0]dS,
-nˆ×Ebs(r)=-nˆ×E(r)2-nˆ×iωnˆ×H(r)μ1g1dS+P[nˆ×E(r)×g1]+[nˆ·E(r) 10g1]dS,
-nˆ·Hbs(r)=-nˆ·H(r)2-nˆ·-nˆ×E(r)iω1g1dS+P{[nˆ×H(r)×g1]+g1nˆ·H(r)}dS,
g0,1=exp(ik0,1R)4πR.
R={(x-x)2+(y-y)2+[f(x, y)-f(x, y)]2}1/2.
nˆb×Hbe(r)=Jb(r)2-nˆb×SbJb(r)×g1dS,
nˆb×Hbe(r)=-nˆb×Sr{-nˆ×E(r)iω1g1+[nˆ×H(r)×g1]+g1nˆ·H(r)}dS.
Hbs(r)=SbJb(r)×g1dS,
Ebs(r)=-iω1×SbJb(r)×g1dS.
J1(r)=n×Er(r)·xˆ,
J2(r)=n×Er(r)·yˆ,
J3(r)=n·Er(r),
J4(r)=n×Hr(r)·xˆ,
J5(r)=n×Hr(r)·yˆ,
J6(r)=n·Hr(r).
Z¯¯J¯=b¯i+b¯b,
Jb1(r)=nˆb×Hb(r)·xˆ,
Jb2(r)=nˆb×Hb(r)·yˆ,
Jb3(r)=nˆb×Hb(r)·zˆ,
b¯b=Z¯¯rbJ¯b=Z¯¯rbZ¯¯b-1Jbe¯=Z¯¯rbZ¯¯b-1Z¯¯brJ¯.
(Z¯¯-Z¯¯rbZ¯¯b-1Z¯¯br)J¯=b¯i.
(Z¯¯FS+Z¯¯S-Z¯¯rbZ¯¯b-1Z¯¯br)J¯=b¯i-Z¯¯WJ¯.
(Z¯¯FS+Z¯¯S)J¯=b¯i+Z¯¯rbZ¯¯b-1Z¯¯brJ¯-Z¯¯WJ¯.
Fhα=ik4π2ηPαi dSdxdy×exp(ikγ)J1(x, y)cos θs cos ϕs+J2(x, y)cos θs sin θs-J1(x, y)f(x, y)x sin θs-J2(x, y) f(x, y)y sin θs-η[J4(x, y)sin ϕs-J5(x, y)cos ϕs]
Fvα=ik4π2ηPαi dSdxdy×exp(-ikγ)[J1(x, y)sin ϕs-J2(x, y)cos ϕs]+ηJ4(x, y)cos θs cos θs+J5 cos θs sin ϕs-J4(x, y)f(x, y)x sin θs-J5(x, y)f(x, y)y sin θs,
Pαi=2π2η kρ<kdkxdky|Eiα(kx, ky)|2 kzk.
σβα(θs, θi)=1Nϕ n=1Nϕ|Fβα(θs, ϕsn; θi, ϕin)|2,
Γβα(θs2, θi2; θs1, θi1)=1Nϕ n=1NϕFβα(θs2, ϕs2n; θi2, ϕi2n)×Fβα*(θs1, ϕs1n; θi1, ϕi1n),
Γβ1α1β2α2(θs1, θi1; θs2, θi2)=1Nϕ n=1NϕFβ1α1(θs1, ϕs1n; θi1, ϕi1n)×Fβ2α2*(θs2, ϕs2n; θi2, ϕi2n).

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