Abstract

We present experimental measurements of light backscattered from double-scale randomly rough surfaces (oceanlike surfaces) with different statistical parameters illuminated at small and large angles of incidence. The surfaces are composed of a small-scale roughness superimposed on a slowly (large-scale) varying surface. The large-scale surfaces are diamond-machined periodic surfaces made on aluminum substrates and have either a sinusoidal or a Stokes wave profile. The small-scale roughness is added with lithographic techniques, and the surfaces are then gold coated. For a linearly polarized incident beam, it is found that the backscattered light is strongly depolarized mainly at small angles of incidence and strong shadowing effects are present for large angles of incidence (θinc>60°).

© 2012 Optical Society of America

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  1. D. A. Zimnyakov and V. V. Tuchin, “Optical tomography of tissues,” Quantum Electron. 32, 849–867 (2002).
    [CrossRef]
  2. J. B. Campbell, Introduction to Remote Sensing (Guilford Press, 2006).
  3. G. R. Valenzuela, “Theories for the interaction of electromagnetic and oceanic waves—a review,” Boundary-Layer Meteorol. 13, 61–85 (1978).
    [CrossRef]
  4. Y. Inouye and S. Kawata, “Near-field scanning optical microscope with a metallic probe tip,” Opt. Lett. 19, 159–161 (1994).
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  5. J. F. Aguilar and E. R. Méndez, “Imaging optically thick objects in scanning microscopy: perfectly conducting surfaces,” J. Opt. Soc. Am. A 11, 155–167 (1994).
    [CrossRef]
  6. J. M. Bennett and L. Mattsson, Introduction to Surface Roughness and Scattering (Optical Society of America, 1999).
  7. N. J. Elton, “A two-scale roughness model for the gloss of coated paper,” J. Opt. A 10, 085002 (2008).
    [CrossRef]
  8. E. R. Méndez and K. A. O’Donnell, “Observation of depolarization and backscattering enhancement in light scattering from Gaussian random surfaces,” Opt. Commun. 61, 91–95 (1987).
    [CrossRef]
  9. K. A. O’Donnell and E. R. Méndez, “Experimental study of scattering from characterized random surfaces,” J. Opt. Soc. Am. A 4, 1194–1205 (1987).
    [CrossRef]
  10. P. Beckmann and A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, 1963).
  11. J. A. Ogilvy, Theory of Wave Scattering from Random Rough Surfaces (Hilger, 1991).
  12. S. O. Rice, “Reflection of electromagnetic waves from slightly rough surfaces,” Commun. Pure Appl. Math. 4, 351–378 (1951).
    [CrossRef]
  13. A. A. Maradudin, T. Michel, A. R. McGurn, and E. R. Méndez, “Enhanced backscattering of light from a random grating,” Ann. Phys. 203, 255–307 (1990).
    [CrossRef]
  14. A. Mendoza and E. Méndez, “Light scattering by a reentrant fractal surface,” Appl. Opt. 36, 3521–3531 (1997).
    [CrossRef]
  15. M. J. Kim, J. C. Dainty, A. T. Friberg, and A. J. Sant, “Experimental study of enhanced backscattering from one and two dimensional random rough surfaces,” J. Opt. Soc. Am. A 7, 569–577 (1990).
    [CrossRef]
  16. M. E. Knotts, “Experimental studies of multiple scattering by rough surfaces,” Ph.D. thesis (Georgia Institute of Technology, 1994).
  17. A. J. Sant, “Enhanced backscattering of light from randomly rough diffusers,” Ph.D. thesis (Imperial College, University of London, 1990).
  18. J. A. DeSanto, “Theoretical methods in ocean acoustics,” in Ocean Acoustics, J. A. DeSanto, ed. (Springer-Verlag, 1979).
  19. M. Y. Ayari, A. Khenchaf, and A. Coatanhay, “Simulations of the bistatic scattering using two-scale model and the unified sea spectrum,” J. Appl. Remote Sens. 1, 013532 (2007).
    [CrossRef]
  20. J. T. Johnson, R. T. Shin, J. A. Kong, L. Tsang, and K. Pak, “A numerical study of the composite surface model for ocean backscattering,” IEEE Trans. Geosci. Remote Sens. 36, 72–83 (1998).
    [CrossRef]
  21. H. D. Mouche and V. Kudryavtsev, “Radar scattering of the ocean surface and sea-roughness properties: a combined analysis from dual-polarizations airborne radar observations and models in C band,” J. Geophys. Res. Oceans 111, C09004 (2006).
    [CrossRef]
  22. W. J. Plant, “A stochastic, multiscale model of microwave backscatter from the ocean,” J. Geophys. Res. 107, 3120(2002).
    [CrossRef]
  23. G. Soriano and C.-A. Guérin, “A cutoff invariant two-scale model in electromagnetic scattering from sea surfaces,” IEEE Geosci. Remote Sens. Lett. 5, 199–203 (2008).
    [CrossRef]
  24. M. Zhang, D. Nie, and H.-C. Yin, “A versatile composite surface model for electromagnetic backscattering from seas,” Waves Random Complex Media 21, 348–361 (2011).
  25. B. Kinsman, Wind Waves: Their Generation and Propagation on the Ocean Surface (Prentice-Hall, 1965).
  26. A. Fung and H. L. Chan, “Backscattering of waves by composite rough surfaces,” IEEE Trans. Antennas Propag. AP-17, 590–597 (1976).
  27. A. Voronovich and V. U. Zavorotny, “Theoretical model for scattering of radar signals in Ku—and C-bands from a rough sea surface with breaking waves,” Waves Random Media 11, 247–269 (2001).
  28. M. J. Kim, “Light scattering from characterised random rough surfaces,” Ph.D. thesis (Imperial College, University of London, 1989).
  29. J. Renau and J. A. Collinson, “Measurements of electromagnetic backscattering from known rough surfaces,” Bell Syst. Tech. J. 44, 2203–2226 (1965).
  30. J. Renau, P. K. Cheo, and H. G. Cooper, “Depolarisation of linearly polarised electromagnetic waves backscattered from rough metals and inhomogeneous dielectrics,” J. Opt. Soc. Am. 57, 459–467 (1967).
    [CrossRef]
  31. D. L. Jordan, “Experimental measurements of optical backscattering from surfaces of roughness comparable to the wavelength and their application to radar sea scattering,” Waves Random Media 5, 41–54 (1995).
    [CrossRef]
  32. P. A. Le Blond and L. A. Mysak, Waves in the Ocean (Elsevier, 1978).
  33. I. S. Robinson, J. O. Thomas, K. Ouchi, and Y. C. Robertson, Study of the Sea Surface, Ocean Waves and Dynamics with Special Reference to Synthetic Aperture Radar (SAR) Imagery (Oxford Computer Services, 1981).
  34. P. F. Gray, “A method of forming optical diffusers of simple known statistical properties,” Opt. Acta 25, 765–775 (1978).
    [CrossRef]
  35. K. A. O’Donnell and M. E. Knotss, “Polarization-dependence of scattering from one-dimensional rough surfaces,” J. Opt. Soc. Am. A 8, 1126–1131 (1991).
    [CrossRef]
  36. V. A. Ruiz-Cortés and J. C. Dainty, “Experimental light-scattering measurements from large-scale composite randomly rough surfaces,” J. Opt. Soc. Am. A 19, 2043–2052 (2002).
    [CrossRef]
  37. A. Stogryn, “Equations for calculating the dielectric constant of saline water,” IEEE Trans. Microwave Theory Tech. 19, 733–736 (1971).
    [CrossRef]
  38. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
    [CrossRef]
  39. J. C. Dainty, M. J. Kim, and A. J. Sant, “Measurements of angular scattering by randomly rough metal and dielectric surfaces,” in Scattering in Volumes and Surfaces, M. Nieto-Vesperinas and J. C. Dainty, eds. (Elsevier Science, 1990).
  40. D. E. Barrick and W. H. Peake, “A review of scattering from surfaces with different roughness scales,” Radio Sci. 3, 865–868 (1968).
  41. A. K. Fung, “Surface scattering effects at different spectral regions,” in Spectral Signatures of Objects in Remote Sensing, G. Guyot and M. Verbrugghe, eds. (INRA, 1984) pp. 693–707.

2011 (1)

M. Zhang, D. Nie, and H.-C. Yin, “A versatile composite surface model for electromagnetic backscattering from seas,” Waves Random Complex Media 21, 348–361 (2011).

2008 (2)

N. J. Elton, “A two-scale roughness model for the gloss of coated paper,” J. Opt. A 10, 085002 (2008).
[CrossRef]

G. Soriano and C.-A. Guérin, “A cutoff invariant two-scale model in electromagnetic scattering from sea surfaces,” IEEE Geosci. Remote Sens. Lett. 5, 199–203 (2008).
[CrossRef]

2007 (1)

M. Y. Ayari, A. Khenchaf, and A. Coatanhay, “Simulations of the bistatic scattering using two-scale model and the unified sea spectrum,” J. Appl. Remote Sens. 1, 013532 (2007).
[CrossRef]

2006 (1)

H. D. Mouche and V. Kudryavtsev, “Radar scattering of the ocean surface and sea-roughness properties: a combined analysis from dual-polarizations airborne radar observations and models in C band,” J. Geophys. Res. Oceans 111, C09004 (2006).
[CrossRef]

2002 (3)

W. J. Plant, “A stochastic, multiscale model of microwave backscatter from the ocean,” J. Geophys. Res. 107, 3120(2002).
[CrossRef]

D. A. Zimnyakov and V. V. Tuchin, “Optical tomography of tissues,” Quantum Electron. 32, 849–867 (2002).
[CrossRef]

V. A. Ruiz-Cortés and J. C. Dainty, “Experimental light-scattering measurements from large-scale composite randomly rough surfaces,” J. Opt. Soc. Am. A 19, 2043–2052 (2002).
[CrossRef]

2001 (1)

A. Voronovich and V. U. Zavorotny, “Theoretical model for scattering of radar signals in Ku—and C-bands from a rough sea surface with breaking waves,” Waves Random Media 11, 247–269 (2001).

1998 (1)

J. T. Johnson, R. T. Shin, J. A. Kong, L. Tsang, and K. Pak, “A numerical study of the composite surface model for ocean backscattering,” IEEE Trans. Geosci. Remote Sens. 36, 72–83 (1998).
[CrossRef]

1997 (1)

1995 (1)

D. L. Jordan, “Experimental measurements of optical backscattering from surfaces of roughness comparable to the wavelength and their application to radar sea scattering,” Waves Random Media 5, 41–54 (1995).
[CrossRef]

1994 (2)

1991 (1)

1990 (2)

M. J. Kim, J. C. Dainty, A. T. Friberg, and A. J. Sant, “Experimental study of enhanced backscattering from one and two dimensional random rough surfaces,” J. Opt. Soc. Am. A 7, 569–577 (1990).
[CrossRef]

A. A. Maradudin, T. Michel, A. R. McGurn, and E. R. Méndez, “Enhanced backscattering of light from a random grating,” Ann. Phys. 203, 255–307 (1990).
[CrossRef]

1987 (2)

E. R. Méndez and K. A. O’Donnell, “Observation of depolarization and backscattering enhancement in light scattering from Gaussian random surfaces,” Opt. Commun. 61, 91–95 (1987).
[CrossRef]

K. A. O’Donnell and E. R. Méndez, “Experimental study of scattering from characterized random surfaces,” J. Opt. Soc. Am. A 4, 1194–1205 (1987).
[CrossRef]

1978 (2)

G. R. Valenzuela, “Theories for the interaction of electromagnetic and oceanic waves—a review,” Boundary-Layer Meteorol. 13, 61–85 (1978).
[CrossRef]

P. F. Gray, “A method of forming optical diffusers of simple known statistical properties,” Opt. Acta 25, 765–775 (1978).
[CrossRef]

1976 (1)

A. Fung and H. L. Chan, “Backscattering of waves by composite rough surfaces,” IEEE Trans. Antennas Propag. AP-17, 590–597 (1976).

1972 (1)

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[CrossRef]

1971 (1)

A. Stogryn, “Equations for calculating the dielectric constant of saline water,” IEEE Trans. Microwave Theory Tech. 19, 733–736 (1971).
[CrossRef]

1968 (1)

D. E. Barrick and W. H. Peake, “A review of scattering from surfaces with different roughness scales,” Radio Sci. 3, 865–868 (1968).

1967 (1)

1965 (1)

J. Renau and J. A. Collinson, “Measurements of electromagnetic backscattering from known rough surfaces,” Bell Syst. Tech. J. 44, 2203–2226 (1965).

1951 (1)

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

Aguilar, J. F.

Ayari, M. Y.

M. Y. Ayari, A. Khenchaf, and A. Coatanhay, “Simulations of the bistatic scattering using two-scale model and the unified sea spectrum,” J. Appl. Remote Sens. 1, 013532 (2007).
[CrossRef]

Barrick, D. E.

D. E. Barrick and W. H. Peake, “A review of scattering from surfaces with different roughness scales,” Radio Sci. 3, 865–868 (1968).

Beckmann, P.

P. Beckmann and A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, 1963).

Bennett, J. M.

J. M. Bennett and L. Mattsson, Introduction to Surface Roughness and Scattering (Optical Society of America, 1999).

Campbell, J. B.

J. B. Campbell, Introduction to Remote Sensing (Guilford Press, 2006).

Chan, H. L.

A. Fung and H. L. Chan, “Backscattering of waves by composite rough surfaces,” IEEE Trans. Antennas Propag. AP-17, 590–597 (1976).

Cheo, P. K.

Christy, R. W.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[CrossRef]

Coatanhay, A.

M. Y. Ayari, A. Khenchaf, and A. Coatanhay, “Simulations of the bistatic scattering using two-scale model and the unified sea spectrum,” J. Appl. Remote Sens. 1, 013532 (2007).
[CrossRef]

Collinson, J. A.

J. Renau and J. A. Collinson, “Measurements of electromagnetic backscattering from known rough surfaces,” Bell Syst. Tech. J. 44, 2203–2226 (1965).

Cooper, H. G.

Dainty, J. C.

DeSanto, J. A.

J. A. DeSanto, “Theoretical methods in ocean acoustics,” in Ocean Acoustics, J. A. DeSanto, ed. (Springer-Verlag, 1979).

Elton, N. J.

N. J. Elton, “A two-scale roughness model for the gloss of coated paper,” J. Opt. A 10, 085002 (2008).
[CrossRef]

Friberg, A. T.

Fung, A.

A. Fung and H. L. Chan, “Backscattering of waves by composite rough surfaces,” IEEE Trans. Antennas Propag. AP-17, 590–597 (1976).

Fung, A. K.

A. K. Fung, “Surface scattering effects at different spectral regions,” in Spectral Signatures of Objects in Remote Sensing, G. Guyot and M. Verbrugghe, eds. (INRA, 1984) pp. 693–707.

Gray, P. F.

P. F. Gray, “A method of forming optical diffusers of simple known statistical properties,” Opt. Acta 25, 765–775 (1978).
[CrossRef]

Guérin, C.-A.

G. Soriano and C.-A. Guérin, “A cutoff invariant two-scale model in electromagnetic scattering from sea surfaces,” IEEE Geosci. Remote Sens. Lett. 5, 199–203 (2008).
[CrossRef]

Inouye, Y.

Johnson, J. T.

J. T. Johnson, R. T. Shin, J. A. Kong, L. Tsang, and K. Pak, “A numerical study of the composite surface model for ocean backscattering,” IEEE Trans. Geosci. Remote Sens. 36, 72–83 (1998).
[CrossRef]

Johnson, P. B.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[CrossRef]

Jordan, D. L.

D. L. Jordan, “Experimental measurements of optical backscattering from surfaces of roughness comparable to the wavelength and their application to radar sea scattering,” Waves Random Media 5, 41–54 (1995).
[CrossRef]

Kawata, S.

Khenchaf, A.

M. Y. Ayari, A. Khenchaf, and A. Coatanhay, “Simulations of the bistatic scattering using two-scale model and the unified sea spectrum,” J. Appl. Remote Sens. 1, 013532 (2007).
[CrossRef]

Kim, M. J.

M. J. Kim, J. C. Dainty, A. T. Friberg, and A. J. Sant, “Experimental study of enhanced backscattering from one and two dimensional random rough surfaces,” J. Opt. Soc. Am. A 7, 569–577 (1990).
[CrossRef]

M. J. Kim, “Light scattering from characterised random rough surfaces,” Ph.D. thesis (Imperial College, University of London, 1989).

J. C. Dainty, M. J. Kim, and A. J. Sant, “Measurements of angular scattering by randomly rough metal and dielectric surfaces,” in Scattering in Volumes and Surfaces, M. Nieto-Vesperinas and J. C. Dainty, eds. (Elsevier Science, 1990).

Kinsman, B.

B. Kinsman, Wind Waves: Their Generation and Propagation on the Ocean Surface (Prentice-Hall, 1965).

Knotss, M. E.

Knotts, M. E.

M. E. Knotts, “Experimental studies of multiple scattering by rough surfaces,” Ph.D. thesis (Georgia Institute of Technology, 1994).

Kong, J. A.

J. T. Johnson, R. T. Shin, J. A. Kong, L. Tsang, and K. Pak, “A numerical study of the composite surface model for ocean backscattering,” IEEE Trans. Geosci. Remote Sens. 36, 72–83 (1998).
[CrossRef]

Kudryavtsev, V.

H. D. Mouche and V. Kudryavtsev, “Radar scattering of the ocean surface and sea-roughness properties: a combined analysis from dual-polarizations airborne radar observations and models in C band,” J. Geophys. Res. Oceans 111, C09004 (2006).
[CrossRef]

Le Blond, P. A.

P. A. Le Blond and L. A. Mysak, Waves in the Ocean (Elsevier, 1978).

Maradudin, A. A.

A. A. Maradudin, T. Michel, A. R. McGurn, and E. R. Méndez, “Enhanced backscattering of light from a random grating,” Ann. Phys. 203, 255–307 (1990).
[CrossRef]

Mattsson, L.

J. M. Bennett and L. Mattsson, Introduction to Surface Roughness and Scattering (Optical Society of America, 1999).

McGurn, A. R.

A. A. Maradudin, T. Michel, A. R. McGurn, and E. R. Méndez, “Enhanced backscattering of light from a random grating,” Ann. Phys. 203, 255–307 (1990).
[CrossRef]

Méndez, E.

Méndez, E. R.

J. F. Aguilar and E. R. Méndez, “Imaging optically thick objects in scanning microscopy: perfectly conducting surfaces,” J. Opt. Soc. Am. A 11, 155–167 (1994).
[CrossRef]

A. A. Maradudin, T. Michel, A. R. McGurn, and E. R. Méndez, “Enhanced backscattering of light from a random grating,” Ann. Phys. 203, 255–307 (1990).
[CrossRef]

K. A. O’Donnell and E. R. Méndez, “Experimental study of scattering from characterized random surfaces,” J. Opt. Soc. Am. A 4, 1194–1205 (1987).
[CrossRef]

E. R. Méndez and K. A. O’Donnell, “Observation of depolarization and backscattering enhancement in light scattering from Gaussian random surfaces,” Opt. Commun. 61, 91–95 (1987).
[CrossRef]

Mendoza, A.

Michel, T.

A. A. Maradudin, T. Michel, A. R. McGurn, and E. R. Méndez, “Enhanced backscattering of light from a random grating,” Ann. Phys. 203, 255–307 (1990).
[CrossRef]

Mouche, H. D.

H. D. Mouche and V. Kudryavtsev, “Radar scattering of the ocean surface and sea-roughness properties: a combined analysis from dual-polarizations airborne radar observations and models in C band,” J. Geophys. Res. Oceans 111, C09004 (2006).
[CrossRef]

Mysak, L. A.

P. A. Le Blond and L. A. Mysak, Waves in the Ocean (Elsevier, 1978).

Nie, D.

M. Zhang, D. Nie, and H.-C. Yin, “A versatile composite surface model for electromagnetic backscattering from seas,” Waves Random Complex Media 21, 348–361 (2011).

O’Donnell, K. A.

Ogilvy, J. A.

J. A. Ogilvy, Theory of Wave Scattering from Random Rough Surfaces (Hilger, 1991).

Ouchi, K.

I. S. Robinson, J. O. Thomas, K. Ouchi, and Y. C. Robertson, Study of the Sea Surface, Ocean Waves and Dynamics with Special Reference to Synthetic Aperture Radar (SAR) Imagery (Oxford Computer Services, 1981).

Pak, K.

J. T. Johnson, R. T. Shin, J. A. Kong, L. Tsang, and K. Pak, “A numerical study of the composite surface model for ocean backscattering,” IEEE Trans. Geosci. Remote Sens. 36, 72–83 (1998).
[CrossRef]

Peake, W. H.

D. E. Barrick and W. H. Peake, “A review of scattering from surfaces with different roughness scales,” Radio Sci. 3, 865–868 (1968).

Plant, W. J.

W. J. Plant, “A stochastic, multiscale model of microwave backscatter from the ocean,” J. Geophys. Res. 107, 3120(2002).
[CrossRef]

Renau, J.

J. Renau, P. K. Cheo, and H. G. Cooper, “Depolarisation of linearly polarised electromagnetic waves backscattered from rough metals and inhomogeneous dielectrics,” J. Opt. Soc. Am. 57, 459–467 (1967).
[CrossRef]

J. Renau and J. A. Collinson, “Measurements of electromagnetic backscattering from known rough surfaces,” Bell Syst. Tech. J. 44, 2203–2226 (1965).

Rice, S. O.

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

Robertson, Y. C.

I. S. Robinson, J. O. Thomas, K. Ouchi, and Y. C. Robertson, Study of the Sea Surface, Ocean Waves and Dynamics with Special Reference to Synthetic Aperture Radar (SAR) Imagery (Oxford Computer Services, 1981).

Robinson, I. S.

I. S. Robinson, J. O. Thomas, K. Ouchi, and Y. C. Robertson, Study of the Sea Surface, Ocean Waves and Dynamics with Special Reference to Synthetic Aperture Radar (SAR) Imagery (Oxford Computer Services, 1981).

Ruiz-Cortés, V. A.

Sant, A. J.

M. J. Kim, J. C. Dainty, A. T. Friberg, and A. J. Sant, “Experimental study of enhanced backscattering from one and two dimensional random rough surfaces,” J. Opt. Soc. Am. A 7, 569–577 (1990).
[CrossRef]

A. J. Sant, “Enhanced backscattering of light from randomly rough diffusers,” Ph.D. thesis (Imperial College, University of London, 1990).

J. C. Dainty, M. J. Kim, and A. J. Sant, “Measurements of angular scattering by randomly rough metal and dielectric surfaces,” in Scattering in Volumes and Surfaces, M. Nieto-Vesperinas and J. C. Dainty, eds. (Elsevier Science, 1990).

Shin, R. T.

J. T. Johnson, R. T. Shin, J. A. Kong, L. Tsang, and K. Pak, “A numerical study of the composite surface model for ocean backscattering,” IEEE Trans. Geosci. Remote Sens. 36, 72–83 (1998).
[CrossRef]

Soriano, G.

G. Soriano and C.-A. Guérin, “A cutoff invariant two-scale model in electromagnetic scattering from sea surfaces,” IEEE Geosci. Remote Sens. Lett. 5, 199–203 (2008).
[CrossRef]

Spizzichino, A.

P. Beckmann and A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, 1963).

Stogryn, A.

A. Stogryn, “Equations for calculating the dielectric constant of saline water,” IEEE Trans. Microwave Theory Tech. 19, 733–736 (1971).
[CrossRef]

Thomas, J. O.

I. S. Robinson, J. O. Thomas, K. Ouchi, and Y. C. Robertson, Study of the Sea Surface, Ocean Waves and Dynamics with Special Reference to Synthetic Aperture Radar (SAR) Imagery (Oxford Computer Services, 1981).

Tsang, L.

J. T. Johnson, R. T. Shin, J. A. Kong, L. Tsang, and K. Pak, “A numerical study of the composite surface model for ocean backscattering,” IEEE Trans. Geosci. Remote Sens. 36, 72–83 (1998).
[CrossRef]

Tuchin, V. V.

D. A. Zimnyakov and V. V. Tuchin, “Optical tomography of tissues,” Quantum Electron. 32, 849–867 (2002).
[CrossRef]

Valenzuela, G. R.

G. R. Valenzuela, “Theories for the interaction of electromagnetic and oceanic waves—a review,” Boundary-Layer Meteorol. 13, 61–85 (1978).
[CrossRef]

Voronovich, A.

A. Voronovich and V. U. Zavorotny, “Theoretical model for scattering of radar signals in Ku—and C-bands from a rough sea surface with breaking waves,” Waves Random Media 11, 247–269 (2001).

Yin, H.-C.

M. Zhang, D. Nie, and H.-C. Yin, “A versatile composite surface model for electromagnetic backscattering from seas,” Waves Random Complex Media 21, 348–361 (2011).

Zavorotny, V. U.

A. Voronovich and V. U. Zavorotny, “Theoretical model for scattering of radar signals in Ku—and C-bands from a rough sea surface with breaking waves,” Waves Random Media 11, 247–269 (2001).

Zhang, M.

M. Zhang, D. Nie, and H.-C. Yin, “A versatile composite surface model for electromagnetic backscattering from seas,” Waves Random Complex Media 21, 348–361 (2011).

Zimnyakov, D. A.

D. A. Zimnyakov and V. V. Tuchin, “Optical tomography of tissues,” Quantum Electron. 32, 849–867 (2002).
[CrossRef]

Ann. Phys. (1)

A. A. Maradudin, T. Michel, A. R. McGurn, and E. R. Méndez, “Enhanced backscattering of light from a random grating,” Ann. Phys. 203, 255–307 (1990).
[CrossRef]

Appl. Opt. (1)

Bell Syst. Tech. J. (1)

J. Renau and J. A. Collinson, “Measurements of electromagnetic backscattering from known rough surfaces,” Bell Syst. Tech. J. 44, 2203–2226 (1965).

Boundary-Layer Meteorol. (1)

G. R. Valenzuela, “Theories for the interaction of electromagnetic and oceanic waves—a review,” Boundary-Layer Meteorol. 13, 61–85 (1978).
[CrossRef]

Commun. Pure Appl. Math. (1)

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

IEEE Geosci. Remote Sens. Lett. (1)

G. Soriano and C.-A. Guérin, “A cutoff invariant two-scale model in electromagnetic scattering from sea surfaces,” IEEE Geosci. Remote Sens. Lett. 5, 199–203 (2008).
[CrossRef]

IEEE Trans. Antennas Propag. (1)

A. Fung and H. L. Chan, “Backscattering of waves by composite rough surfaces,” IEEE Trans. Antennas Propag. AP-17, 590–597 (1976).

IEEE Trans. Geosci. Remote Sens. (1)

J. T. Johnson, R. T. Shin, J. A. Kong, L. Tsang, and K. Pak, “A numerical study of the composite surface model for ocean backscattering,” IEEE Trans. Geosci. Remote Sens. 36, 72–83 (1998).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

A. Stogryn, “Equations for calculating the dielectric constant of saline water,” IEEE Trans. Microwave Theory Tech. 19, 733–736 (1971).
[CrossRef]

J. Appl. Remote Sens. (1)

M. Y. Ayari, A. Khenchaf, and A. Coatanhay, “Simulations of the bistatic scattering using two-scale model and the unified sea spectrum,” J. Appl. Remote Sens. 1, 013532 (2007).
[CrossRef]

J. Geophys. Res. (1)

W. J. Plant, “A stochastic, multiscale model of microwave backscatter from the ocean,” J. Geophys. Res. 107, 3120(2002).
[CrossRef]

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Figures (9)

Fig. 1.
Fig. 1.

TalyStep profile traces taken from double-scale surfaces with sinusoidal profile. Upper plot (a), surface SIN01 with a standard deviation of heights of σζ=1.0μm and a 1/e autocorrelation width of a=3.70μm for the small-scale component. Lower plot (b), surface SIN02 with a standard deviation of heights of σζ=0.56μm and a 1/e autocorrelation width of a=2.17μm for the small-scale component.

Fig. 2.
Fig. 2.

TalyStep profile traces taken from double-scale surfaces with Stokes wave profile. Upper plot (a), surface STOKES01 with a standard deviation of heights of σζ=0.56μm and a 1/e autocorrelation width of a=2.49μm for the small-scale component. Lower plot (b), surface STOKES02 with a standard deviation of heights of σζ=0.73μm and a 1/e autocorrelation width of a=2.22μm for the small-scale component.

Fig. 3.
Fig. 3.

Schematic representation of the apparatus used for experimental backscattering measurements.

Fig. 4.
Fig. 4.

Experimental measurements of the angular distribution of the normalized backscattered intensity from surface SIN01. In circles (○) the ss component, diamonds (⋄) the sp component, triangles (Δ) the pp component, and asterisks (∗) the ps component.

Fig. 5.
Fig. 5.

Experimental measurements of the angular distribution of the normalized backscattered intensity from surface SIN02. In circles (○) the ss component, diamonds (⋄) the sp component, triangles (Δ) the pp component, and asterisks (∗) the ps component.

Fig. 6.
Fig. 6.

Experimental measurements of the angular distribution of the normalized backscattered intensity from surface STOKES01. In circles (○) the ss component, diamonds (⋄) the sp component, triangles (Δ) the pp component, and asterisks (∗) the ps component.

Fig. 7.
Fig. 7.

Experimental measurements of the angular distribution of the normalized backscattered intensity from surface STOKES02. In circles (○) the ss component, diamonds (⋄) the sp component, triangles (Δ) the pp component, and asterisks (∗) the ps component.

Fig. 8.
Fig. 8.

Normalized backscattered intensity of the polarized and depolarized components. Dotted line: the polarized component. Dashed line: the depolarized component. Circles: the copolarized (ss) component.

Fig. 9.
Fig. 9.

Normalized backscattered intensity of the polarized and random polarized components. Dotted line: the polarized component. Dashed line: the depolarized component. Circles: the copolarized (ss) component.

Tables (1)

Tables Icon

Table 1. Surface Parameters for the Large and Small Component of the Double-Scale Randomly Rough Surfaces

Equations (5)

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ζ(x)=Apsin(Kx),
ζ(x)=Apcos(Kx)+(12KAp2+1724K3Ap4)cos(2Kx)38K2Ap3cos(3Kx)+13K3Ap4cos(4Kx).
Inbs=Ibs(θinc)Ibs(0),
Inbs-pol=Ibs-ss(θinc)Ibs-sp(θinc)Ibs-ss(0),
Inbs-dpol=2Ibs-sp(θinc)Ibs-ss(0),

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