Abstract

Measurements of enhanced backscattering are presented from a range of characterized metallic surfaces of differing roughnesses by use of both visible and infrared laser radiation. The surfaces are isotropic and exhibit fractal behavior over a wide range of scale sizes with an estimated fractal index close to the marginal value of 2. Unlike previously reported results from work that used smoothly varying single-scale surfaces, these results obtained with the use of multiscale surfaces exhibit enhanced backscattering, even close to grazing incidence in both the copolarized and the cross-depolarized scattered components. The magnitude of the backscattered enhancement and the ratio of cross-depolarized to copolarized backscattered radiation show similar variations with the measured surface roughness, suggesting that both may possibly be due to the same mechanism, namely, multiple scattering.

© 1993 Optical Society of America

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  1. Y. Kuga, A. Ishimaru, “Retroreflectance from a dense distribution of spherical particles,” J. Opt. Soc. Am. A 1, 831–835 (1984).
    [CrossRef]
  2. M. P. Albada, A. Lagendijk, “Observation of weak localization of light in a random medium,” Phys. Rev. Lett. 55, 2692–2695 (1985).
    [CrossRef] [PubMed]
  3. Y. Kuga, L. Tsang, A. Ishimaru, “Depolarization effects of the enhanced retroreflectance from a dense distribution of spherical particles,” J. Opt. Soc. Am. A 2, 616–618 (1985).
    [CrossRef]
  4. A. Ishimaru, L. Tsang, “Backscattering enhancement of random discrete scatterers of moderate sizes,” J. Opt. Soc. Am. A 5, 228–236 (1988).
    [CrossRef]
  5. J. C. Dainty, D. N. Qu, S. Xu, “Statistical properties of enhanced backscattering produced by dense collections of latex spheres,” in Statistical Optics, G. M. Morris, ed., Proc. Soc. Photo-Opt. Instrum. Eng.976, 178–184 (1988).
    [CrossRef]
  6. D. N. Qu, J. C. Dainty, “Polarization dependence of dynamic light scattering by dense disordered media,” Opt. Lett. 13, 1066–1068 (1988).
    [CrossRef] [PubMed]
  7. E. R. Mendez, K. A. O’Donnell, “Observation of depolarization and backscattering enhancement in light scattering from Gaussian rough surfaces,” Opt. Commun. 61, 91–95 (1987).
    [CrossRef]
  8. K. A. O’Donnell, E. R. Mendez, “Experimental study of scattering from characterized random surfaces,” J. Opt. Soc. Am. A 4, 1194–1205 (1987).
    [CrossRef]
  9. M. J. Kim, J. C. Dainty, A. T. Friberg, 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]
  10. A. A. Maradudin, T. Michel, A. R. McGurn, E. R. Mendez, “Enhanced backscattering of light from a random grating,” Ann. Phys. 203, 255–307 (1990).
    [CrossRef]
  11. M. Nieto-Vesperinas, J. M. Soto-Crespo, “Monte Carlo simulations for scattering of electromagnetic waves from perfectly conductive random rough surfaces,” Opt. Lett. 12, 979–981 (1987).
    [CrossRef] [PubMed]
  12. N. C. Bruce, J. C. Dainty, “Multiple scattering from random rough surfaces using the Kirchhoff approximation,” J. Mod. Opt. 38, 579–590 (1991).
    [CrossRef]
  13. A. Ishimaru, J. S. Chen, “Scattering from very rough surfaces based on the modified second-order Kirchhoff approximation with angular and propagation shadowing,”J. Acoust. Soc. Am. 88, 1877–1883 (1990).
    [CrossRef]
  14. P. E. Wolf, G. Maret, “Weak localization and coherent backscattering of photons in disordered media,” Phys. Rev. Lett. 55, 2696–2699 (1985).
    [CrossRef] [PubMed]
  15. A. A. Maradudin, E. R. Mendez, T. Michel, “Backscattering effects in the elastic scattering of p-polarized light from a large amplitude random grating,” in Scattering in Volumes and Surfaces, M. Nieto-Vesperinas, J. C. Dainty, eds. (North-Holland, Amsterdam, 1990), pp. 157–174.
  16. E. Jakeman, “Enhanced backscattering through a deep random phase screen,” J. Opt. Soc. Am. A 5, 1638–1648 (1988).
    [CrossRef]
  17. E. Jakeman, P. R. Tapster, A. R. Weeks, “Enhanced backscattering through a deep random phase screen,”J. Phys. D 21, 532–536 (1988).
    [CrossRef]
  18. C. Macaskill, B. J. Kachoyan, “Numerical evaluation of the statistics of acoustic scattering from a rough surface,”J. Acoust. Soc. Am. 84, 1826–1835 (1988).
    [CrossRef]
  19. W. J. Pierson, L. Moskowitz, “A proposed spectral form for fully developed wind seas based on the unitarity theory of S. A. Kitaigorodskii,”J. Geophys. Res. 69, 5181–5190 (1964).
    [CrossRef]
  20. T. Michel, A. A. Maradudin, E. R. Méndez, “Enhanced backscattering of light from a non-Gaussian random metal surface,” J. Opt. Soc. Am. B 6, 2438–2446 (1989).
    [CrossRef]
  21. A. A. Maradudin, T. Michel, “The role of the surface height autocorrelation function in the enhanced backscattering of light from random metallic surfaces,” in Wave Propagation and Scattering in Varied Media II, V. K. Varadan, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1558, 233–250 (1991).
    [CrossRef]
  22. R. S. Sayles, T. R. Thomas, “Surface topography as a non-stationary random process,” Nature 271, 431–434 (1978).
    [CrossRef]
  23. R. E. Glazman, P. B. Weichman, “Statistical geometry of a small surface patch in a developed sea,”J. Geophys. Res. 94, 4998–5010 (1989).
    [CrossRef]
  24. G. R. Valenzuela, “Theories for the interaction of electromagnetic and oceanic waves—a review,” Boundary-Layer Meteorol. 13, 61–85 (1978).
    [CrossRef]
  25. B. B. Mandelbrot, Fractals (Freeman, San Francisco, Calif., 1977).
  26. M. V. Berry, “Diffractals,”J. Phys. A 12, 781–797 (1979).
    [CrossRef]
  27. D. L. Jordan, R. C. Hollins, E. Jakeman, “Experimental measurements of non-Gaussian scattering by a fractal diffuser,” Appl. Phys. B 31, 179–186 (1983).
    [CrossRef]
  28. E. L. Church, “Fractal surface finish,” Appl. Opt. 27, 1518–1526 (1988).
    [CrossRef] [PubMed]
  29. J. Renau, 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, H. G. Cooper, “Depolarization of linearly polarized EM waves backscattered from rough metals and inhomogeneous dielectrics,”J. Opt. Soc. Am. 57, 459–466 (1967).
    [CrossRef] [PubMed]
  31. P. K. Cheo, J. Renau, “Wavelength dependence of total and depolarized backscattered laser light from rough metallic surfaces,”J. Opt. Soc. Am. 59, 821–826 (1969).
    [CrossRef]

1991 (1)

N. C. Bruce, J. C. Dainty, “Multiple scattering from random rough surfaces using the Kirchhoff approximation,” J. Mod. Opt. 38, 579–590 (1991).
[CrossRef]

1990 (3)

A. Ishimaru, J. S. Chen, “Scattering from very rough surfaces based on the modified second-order Kirchhoff approximation with angular and propagation shadowing,”J. Acoust. Soc. Am. 88, 1877–1883 (1990).
[CrossRef]

M. J. Kim, J. C. Dainty, A. T. Friberg, 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, E. R. Mendez, “Enhanced backscattering of light from a random grating,” Ann. Phys. 203, 255–307 (1990).
[CrossRef]

1989 (2)

T. Michel, A. A. Maradudin, E. R. Méndez, “Enhanced backscattering of light from a non-Gaussian random metal surface,” J. Opt. Soc. Am. B 6, 2438–2446 (1989).
[CrossRef]

R. E. Glazman, P. B. Weichman, “Statistical geometry of a small surface patch in a developed sea,”J. Geophys. Res. 94, 4998–5010 (1989).
[CrossRef]

1988 (6)

1987 (3)

1985 (3)

M. P. Albada, A. Lagendijk, “Observation of weak localization of light in a random medium,” Phys. Rev. Lett. 55, 2692–2695 (1985).
[CrossRef] [PubMed]

Y. Kuga, L. Tsang, A. Ishimaru, “Depolarization effects of the enhanced retroreflectance from a dense distribution of spherical particles,” J. Opt. Soc. Am. A 2, 616–618 (1985).
[CrossRef]

P. E. Wolf, G. Maret, “Weak localization and coherent backscattering of photons in disordered media,” Phys. Rev. Lett. 55, 2696–2699 (1985).
[CrossRef] [PubMed]

1984 (1)

1983 (1)

D. L. Jordan, R. C. Hollins, E. Jakeman, “Experimental measurements of non-Gaussian scattering by a fractal diffuser,” Appl. Phys. B 31, 179–186 (1983).
[CrossRef]

1979 (1)

M. V. Berry, “Diffractals,”J. Phys. A 12, 781–797 (1979).
[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]

R. S. Sayles, T. R. Thomas, “Surface topography as a non-stationary random process,” Nature 271, 431–434 (1978).
[CrossRef]

1969 (1)

1967 (1)

1965 (1)

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

1964 (1)

W. J. Pierson, L. Moskowitz, “A proposed spectral form for fully developed wind seas based on the unitarity theory of S. A. Kitaigorodskii,”J. Geophys. Res. 69, 5181–5190 (1964).
[CrossRef]

Albada, M. P.

M. P. Albada, A. Lagendijk, “Observation of weak localization of light in a random medium,” Phys. Rev. Lett. 55, 2692–2695 (1985).
[CrossRef] [PubMed]

Berry, M. V.

M. V. Berry, “Diffractals,”J. Phys. A 12, 781–797 (1979).
[CrossRef]

Bruce, N. C.

N. C. Bruce, J. C. Dainty, “Multiple scattering from random rough surfaces using the Kirchhoff approximation,” J. Mod. Opt. 38, 579–590 (1991).
[CrossRef]

Chen, J. S.

A. Ishimaru, J. S. Chen, “Scattering from very rough surfaces based on the modified second-order Kirchhoff approximation with angular and propagation shadowing,”J. Acoust. Soc. Am. 88, 1877–1883 (1990).
[CrossRef]

Cheo, P. K.

Church, E. L.

Collinson, J. A.

J. Renau, 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.

N. C. Bruce, J. C. Dainty, “Multiple scattering from random rough surfaces using the Kirchhoff approximation,” J. Mod. Opt. 38, 579–590 (1991).
[CrossRef]

M. J. Kim, J. C. Dainty, A. T. Friberg, 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]

D. N. Qu, J. C. Dainty, “Polarization dependence of dynamic light scattering by dense disordered media,” Opt. Lett. 13, 1066–1068 (1988).
[CrossRef] [PubMed]

J. C. Dainty, D. N. Qu, S. Xu, “Statistical properties of enhanced backscattering produced by dense collections of latex spheres,” in Statistical Optics, G. M. Morris, ed., Proc. Soc. Photo-Opt. Instrum. Eng.976, 178–184 (1988).
[CrossRef]

Friberg, A. T.

Glazman, R. E.

R. E. Glazman, P. B. Weichman, “Statistical geometry of a small surface patch in a developed sea,”J. Geophys. Res. 94, 4998–5010 (1989).
[CrossRef]

Hollins, R. C.

D. L. Jordan, R. C. Hollins, E. Jakeman, “Experimental measurements of non-Gaussian scattering by a fractal diffuser,” Appl. Phys. B 31, 179–186 (1983).
[CrossRef]

Ishimaru, A.

Jakeman, E.

E. Jakeman, “Enhanced backscattering through a deep random phase screen,” J. Opt. Soc. Am. A 5, 1638–1648 (1988).
[CrossRef]

E. Jakeman, P. R. Tapster, A. R. Weeks, “Enhanced backscattering through a deep random phase screen,”J. Phys. D 21, 532–536 (1988).
[CrossRef]

D. L. Jordan, R. C. Hollins, E. Jakeman, “Experimental measurements of non-Gaussian scattering by a fractal diffuser,” Appl. Phys. B 31, 179–186 (1983).
[CrossRef]

Jordan, D. L.

D. L. Jordan, R. C. Hollins, E. Jakeman, “Experimental measurements of non-Gaussian scattering by a fractal diffuser,” Appl. Phys. B 31, 179–186 (1983).
[CrossRef]

Kachoyan, B. J.

C. Macaskill, B. J. Kachoyan, “Numerical evaluation of the statistics of acoustic scattering from a rough surface,”J. Acoust. Soc. Am. 84, 1826–1835 (1988).
[CrossRef]

Kim, M. J.

Kuga, Y.

Lagendijk, A.

M. P. Albada, A. Lagendijk, “Observation of weak localization of light in a random medium,” Phys. Rev. Lett. 55, 2692–2695 (1985).
[CrossRef] [PubMed]

Macaskill, C.

C. Macaskill, B. J. Kachoyan, “Numerical evaluation of the statistics of acoustic scattering from a rough surface,”J. Acoust. Soc. Am. 84, 1826–1835 (1988).
[CrossRef]

Mandelbrot, B. B.

B. B. Mandelbrot, Fractals (Freeman, San Francisco, Calif., 1977).

Maradudin, A. A.

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

T. Michel, A. A. Maradudin, E. R. Méndez, “Enhanced backscattering of light from a non-Gaussian random metal surface,” J. Opt. Soc. Am. B 6, 2438–2446 (1989).
[CrossRef]

A. A. Maradudin, T. Michel, “The role of the surface height autocorrelation function in the enhanced backscattering of light from random metallic surfaces,” in Wave Propagation and Scattering in Varied Media II, V. K. Varadan, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1558, 233–250 (1991).
[CrossRef]

A. A. Maradudin, E. R. Mendez, T. Michel, “Backscattering effects in the elastic scattering of p-polarized light from a large amplitude random grating,” in Scattering in Volumes and Surfaces, M. Nieto-Vesperinas, J. C. Dainty, eds. (North-Holland, Amsterdam, 1990), pp. 157–174.

Maret, G.

P. E. Wolf, G. Maret, “Weak localization and coherent backscattering of photons in disordered media,” Phys. Rev. Lett. 55, 2696–2699 (1985).
[CrossRef] [PubMed]

McGurn, A. R.

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

Mendez, E. R.

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

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

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

A. A. Maradudin, E. R. Mendez, T. Michel, “Backscattering effects in the elastic scattering of p-polarized light from a large amplitude random grating,” in Scattering in Volumes and Surfaces, M. Nieto-Vesperinas, J. C. Dainty, eds. (North-Holland, Amsterdam, 1990), pp. 157–174.

Méndez, E. R.

Michel, T.

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

T. Michel, A. A. Maradudin, E. R. Méndez, “Enhanced backscattering of light from a non-Gaussian random metal surface,” J. Opt. Soc. Am. B 6, 2438–2446 (1989).
[CrossRef]

A. A. Maradudin, T. Michel, “The role of the surface height autocorrelation function in the enhanced backscattering of light from random metallic surfaces,” in Wave Propagation and Scattering in Varied Media II, V. K. Varadan, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1558, 233–250 (1991).
[CrossRef]

A. A. Maradudin, E. R. Mendez, T. Michel, “Backscattering effects in the elastic scattering of p-polarized light from a large amplitude random grating,” in Scattering in Volumes and Surfaces, M. Nieto-Vesperinas, J. C. Dainty, eds. (North-Holland, Amsterdam, 1990), pp. 157–174.

Moskowitz, L.

W. J. Pierson, L. Moskowitz, “A proposed spectral form for fully developed wind seas based on the unitarity theory of S. A. Kitaigorodskii,”J. Geophys. Res. 69, 5181–5190 (1964).
[CrossRef]

Nieto-Vesperinas, M.

O’Donnell, K. A.

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

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

Pierson, W. J.

W. J. Pierson, L. Moskowitz, “A proposed spectral form for fully developed wind seas based on the unitarity theory of S. A. Kitaigorodskii,”J. Geophys. Res. 69, 5181–5190 (1964).
[CrossRef]

Qu, D. N.

D. N. Qu, J. C. Dainty, “Polarization dependence of dynamic light scattering by dense disordered media,” Opt. Lett. 13, 1066–1068 (1988).
[CrossRef] [PubMed]

J. C. Dainty, D. N. Qu, S. Xu, “Statistical properties of enhanced backscattering produced by dense collections of latex spheres,” in Statistical Optics, G. M. Morris, ed., Proc. Soc. Photo-Opt. Instrum. Eng.976, 178–184 (1988).
[CrossRef]

Renau, J.

Sant, A. J.

Sayles, R. S.

R. S. Sayles, T. R. Thomas, “Surface topography as a non-stationary random process,” Nature 271, 431–434 (1978).
[CrossRef]

Soto-Crespo, J. M.

Tapster, P. R.

E. Jakeman, P. R. Tapster, A. R. Weeks, “Enhanced backscattering through a deep random phase screen,”J. Phys. D 21, 532–536 (1988).
[CrossRef]

Thomas, T. R.

R. S. Sayles, T. R. Thomas, “Surface topography as a non-stationary random process,” Nature 271, 431–434 (1978).
[CrossRef]

Tsang, L.

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]

Weeks, A. R.

E. Jakeman, P. R. Tapster, A. R. Weeks, “Enhanced backscattering through a deep random phase screen,”J. Phys. D 21, 532–536 (1988).
[CrossRef]

Weichman, P. B.

R. E. Glazman, P. B. Weichman, “Statistical geometry of a small surface patch in a developed sea,”J. Geophys. Res. 94, 4998–5010 (1989).
[CrossRef]

Wolf, P. E.

P. E. Wolf, G. Maret, “Weak localization and coherent backscattering of photons in disordered media,” Phys. Rev. Lett. 55, 2696–2699 (1985).
[CrossRef] [PubMed]

Xu, S.

J. C. Dainty, D. N. Qu, S. Xu, “Statistical properties of enhanced backscattering produced by dense collections of latex spheres,” in Statistical Optics, G. M. Morris, ed., Proc. Soc. Photo-Opt. Instrum. Eng.976, 178–184 (1988).
[CrossRef]

Ann. Phys. (1)

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

Appl. Opt. (1)

Appl. Phys. B (1)

D. L. Jordan, R. C. Hollins, E. Jakeman, “Experimental measurements of non-Gaussian scattering by a fractal diffuser,” Appl. Phys. B 31, 179–186 (1983).
[CrossRef]

Bell Syst. Tech. J. (1)

J. Renau, 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]

J. Acoust. Soc. Am. (2)

A. Ishimaru, J. S. Chen, “Scattering from very rough surfaces based on the modified second-order Kirchhoff approximation with angular and propagation shadowing,”J. Acoust. Soc. Am. 88, 1877–1883 (1990).
[CrossRef]

C. Macaskill, B. J. Kachoyan, “Numerical evaluation of the statistics of acoustic scattering from a rough surface,”J. Acoust. Soc. Am. 84, 1826–1835 (1988).
[CrossRef]

J. Geophys. Res. (2)

W. J. Pierson, L. Moskowitz, “A proposed spectral form for fully developed wind seas based on the unitarity theory of S. A. Kitaigorodskii,”J. Geophys. Res. 69, 5181–5190 (1964).
[CrossRef]

R. E. Glazman, P. B. Weichman, “Statistical geometry of a small surface patch in a developed sea,”J. Geophys. Res. 94, 4998–5010 (1989).
[CrossRef]

J. Mod. Opt. (1)

N. C. Bruce, J. C. Dainty, “Multiple scattering from random rough surfaces using the Kirchhoff approximation,” J. Mod. Opt. 38, 579–590 (1991).
[CrossRef]

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (6)

J. Opt. Soc. Am. B (1)

J. Phys. A (1)

M. V. Berry, “Diffractals,”J. Phys. A 12, 781–797 (1979).
[CrossRef]

J. Phys. D (1)

E. Jakeman, P. R. Tapster, A. R. Weeks, “Enhanced backscattering through a deep random phase screen,”J. Phys. D 21, 532–536 (1988).
[CrossRef]

Nature (1)

R. S. Sayles, T. R. Thomas, “Surface topography as a non-stationary random process,” Nature 271, 431–434 (1978).
[CrossRef]

Opt. Commun. (1)

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

Opt. Lett. (2)

Phys. Rev. Lett. (2)

M. P. Albada, A. Lagendijk, “Observation of weak localization of light in a random medium,” Phys. Rev. Lett. 55, 2692–2695 (1985).
[CrossRef] [PubMed]

P. E. Wolf, G. Maret, “Weak localization and coherent backscattering of photons in disordered media,” Phys. Rev. Lett. 55, 2696–2699 (1985).
[CrossRef] [PubMed]

Other (4)

A. A. Maradudin, E. R. Mendez, T. Michel, “Backscattering effects in the elastic scattering of p-polarized light from a large amplitude random grating,” in Scattering in Volumes and Surfaces, M. Nieto-Vesperinas, J. C. Dainty, eds. (North-Holland, Amsterdam, 1990), pp. 157–174.

A. A. Maradudin, T. Michel, “The role of the surface height autocorrelation function in the enhanced backscattering of light from random metallic surfaces,” in Wave Propagation and Scattering in Varied Media II, V. K. Varadan, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1558, 233–250 (1991).
[CrossRef]

J. C. Dainty, D. N. Qu, S. Xu, “Statistical properties of enhanced backscattering produced by dense collections of latex spheres,” in Statistical Optics, G. M. Morris, ed., Proc. Soc. Photo-Opt. Instrum. Eng.976, 178–184 (1988).
[CrossRef]

B. B. Mandelbrot, Fractals (Freeman, San Francisco, Calif., 1977).

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Figures (11)

Fig. 1
Fig. 1

Measured structure function of surface S6. The straight line is drawn to indicate the linear region.

Fig. 2
Fig. 2

Variation of measured rms roughness and slope with measurement length.

Fig. 3
Fig. 3

Probability-density distribution for target S6. The measured points were determined from 10 surface profiles. The solid curve shows a Gaussian probability function, with the standard deviation calculated from the experimental data.

Fig. 4
Fig. 4

Experimental arrangement for the visible wavelength measurements.

Fig. 5
Fig. 5

Variation of backscattered intensity with angular deviation from the backscattered direction for surface S3 and an angle of incidence of 5°. Laser wavelength, 0.633 μm.

Fig. 6
Fig. 6

Variation of backscattered intensity with angular deviation from the backscattered direction for surface S3 and an angle of incidence of 83°. Laser wavelength, 0.633 μm.

Fig. 7
Fig. 7

Variation of measured backscattered enhancement with angle of incidence for copolarized and cross-depolarized scattered radiation. Incident laser wavelength, 0.633 μm.

Fig. 8
Fig. 8

Variation of backscattered intensity with angular deviation from the backscattered direction for surface S3 measured by a CO2 laser (λ = 10.6 μm). Angle of incidence = 70°.

Fig. 9
Fig. 9

Variation of ratio of cross-depolarized to copolarized backscattered radiation with angle of incidence for three surfaces of differing roughnesses.

Fig. 10
Fig. 10

Variation of ratio of cross-depolarized to copolarized signal with measured surface roughness for three angles of incidence.

Fig. 11
Fig. 11

Variation of magnitude of backscattered enhancement with measured surface roughness for two angles of incidence.

Tables (1)

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Table 1 Measured Surface Parameters

Equations (2)

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

S ( δ ) = [ h ( x ) - h ( x + δ ) ] 2 ,
S ( δ ) = L 2 - ν δ ν - B δ 2 ,

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