Abstract

An experimental study of backscatter enhancement from rough surfaces is presented. The Stokes parameters of the average scattered light from two-dimensional rough surfaces show the presence of an unpolarized component, which lends support to the multiply scattering ray model. Experimental data from one-dimensional rough surfaces are compared with numerical calculation.

© 1990 Optical Society of America

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References

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  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]
  2. 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]
  3. A. V. Markov, “Les particularités dans la réflexion de la lumière par la surface de la lune,” Astron. Nachr. 221, 65–78 (1924).
    [CrossRef]
  4. P. Oetking, “Photometric studies of diffusely reflecting surfaces with applications to the brightness of the moon,” J. Geophys. Res. 71, 2505–2513 (1966).
    [CrossRef]
  5. W. G. Egan, T. Hilgeman, “Retroreflectance measurements of photometric standards and coatings,” Appl. Opt. 15, 1845–1849 (1976).
    [CrossRef] [PubMed]
  6. W. W. Montgomery, R. H. Kohl, “Opposition-effect experimentation,” Opt. Lett. 5, 546–548 (1980).
    [CrossRef] [PubMed]
  7. P. Beckmann, A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, New York, 1963).
  8. J. Shen, A. A. Maradudin, “Multiple scattering of waves from random rough surfaces,” Phys. Rev. B 22, 4234–4240 (1980).
    [CrossRef]
  9. M. Nieto-Vesperinas, N. Garcia, “A detailed study of the scattering of scalar waves from random rough surfaces,” Opt. Acta 28, 1651–1672 (1981).
    [CrossRef]
  10. D. P. Winebrenner, A. Ishimaru, “Application of the phase-perturbation technique to randomly rough surfaces,” J. Opt. Soc. Am. A 2, 2285–2294 (1985).
    [CrossRef]
  11. E. Bahar, M. A. Fitzwater, “Depolarization and backscatter enhancement in light scattering from random rough surface: comparison of full wave theory with experiment,” J. Opt. Soc. Am. A 6, 33–43 (1989).
    [CrossRef]
  12. R. R. Lentz, “A numerical study of electromagnetic scattering from ocean-like surfaces,” Radio Sci. 9, 1139–1146 (1974).
    [CrossRef]
  13. R. M. Axline, A. K. Fung, “Numerical calculation of scattering from a perfectly conducting rough surface,” IEEE Trans. Antennas Propag. AP-26, 482–488 (1978).
    [CrossRef]
  14. H. L. Chan, A. K. Fung, “A numerical study of the Kirchhoff approximation in horizontally polarized backscattering from a random surface,” Radio Sci. 13, 811–818 (1978).
    [CrossRef]
  15. 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]
  16. J. M. Soto-Crespo, M. Nieto-Vesperinas, “Electromagnetic scattering from very rough random surfaces and deep reflection gratings,” J. Opt. Soc. Am. A 6, 367–384 (1989).
    [CrossRef]
  17. E. I. Thorsos, “The validity of the Kirchhoff approximation for rough surface scattering using a Gaussian roughness spectrum,” J. Acoust. Soc. Am. 83, 78–92 (1987).
    [CrossRef]
  18. A. A. Maradudin, E. R. Mendez, T. Michel, “Backscattering effects in the elastic scattering of p-polarized light from a large-amplitude random metallic grating,” Opt. Lett. 14, 151–153 (1989).
    [CrossRef] [PubMed]
  19. Y. Kuga, A. Ishimaru, “Retroreflectance from a dense distribution of spherical particles,” J. Opt. Soc. Am. A 1, 831–835 (1984).
    [CrossRef]
  20. E. Jakeman, “Enhanced backscattering through a deep random phase screen,” J. Opt. Soc. Am. A 5, 1638–1648 (1988).
    [CrossRef]
  21. F. O. Bartell, E. L. Dereniak, W. L. Wolfe, “The theory and measurement of bidirectional reflectance distribution function (BRDF) and bidirectional transmittance distribution function (BRTF),” in Radiation Scattering in Optical Systems, G. H. Hunt, ed., Proc. Soc. Photo-Opt. Instrum. Eng.257, 154–160 (1980).
    [CrossRef]
  22. F. E. Nicodemus, “Directional reflectance and emissivity of an opaque surface,” Appl. Opt. 4, 767–773 (1965).
    [CrossRef]
  23. F. E. Nicodemus, “Reflectance nomenclature and directional reflectance and emissivity,” Appl. Opt. 9, 1474–1475 (1970).
    [CrossRef] [PubMed]
  24. F. Grum, G. W. Luckey, “Optical sphere paint and a working standard of reflectance,” Appl. Opt. 7, 2289–2294 (1968).
    [CrossRef] [PubMed]
  25. P. F. Gray, “A method of forming optical diffusers of simple known statistical properties,” Opt. Acta 25, 765–775 (1978).
    [CrossRef]
  26. Ref. 2, Figs. 12–14.
  27. Ref. 7, Chap. 6.

1989 (3)

1988 (1)

1987 (4)

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]

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]

E. I. Thorsos, “The validity of the Kirchhoff approximation for rough surface scattering using a Gaussian roughness spectrum,” J. Acoust. Soc. Am. 83, 78–92 (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]

1985 (1)

1984 (1)

1981 (1)

M. Nieto-Vesperinas, N. Garcia, “A detailed study of the scattering of scalar waves from random rough surfaces,” Opt. Acta 28, 1651–1672 (1981).
[CrossRef]

1980 (2)

J. Shen, A. A. Maradudin, “Multiple scattering of waves from random rough surfaces,” Phys. Rev. B 22, 4234–4240 (1980).
[CrossRef]

W. W. Montgomery, R. H. Kohl, “Opposition-effect experimentation,” Opt. Lett. 5, 546–548 (1980).
[CrossRef] [PubMed]

1978 (3)

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

R. M. Axline, A. K. Fung, “Numerical calculation of scattering from a perfectly conducting rough surface,” IEEE Trans. Antennas Propag. AP-26, 482–488 (1978).
[CrossRef]

H. L. Chan, A. K. Fung, “A numerical study of the Kirchhoff approximation in horizontally polarized backscattering from a random surface,” Radio Sci. 13, 811–818 (1978).
[CrossRef]

1976 (1)

1974 (1)

R. R. Lentz, “A numerical study of electromagnetic scattering from ocean-like surfaces,” Radio Sci. 9, 1139–1146 (1974).
[CrossRef]

1970 (1)

1968 (1)

1966 (1)

P. Oetking, “Photometric studies of diffusely reflecting surfaces with applications to the brightness of the moon,” J. Geophys. Res. 71, 2505–2513 (1966).
[CrossRef]

1965 (1)

1924 (1)

A. V. Markov, “Les particularités dans la réflexion de la lumière par la surface de la lune,” Astron. Nachr. 221, 65–78 (1924).
[CrossRef]

Axline, R. M.

R. M. Axline, A. K. Fung, “Numerical calculation of scattering from a perfectly conducting rough surface,” IEEE Trans. Antennas Propag. AP-26, 482–488 (1978).
[CrossRef]

Bahar, E.

Bartell, F. O.

F. O. Bartell, E. L. Dereniak, W. L. Wolfe, “The theory and measurement of bidirectional reflectance distribution function (BRDF) and bidirectional transmittance distribution function (BRTF),” in Radiation Scattering in Optical Systems, G. H. Hunt, ed., Proc. Soc. Photo-Opt. Instrum. Eng.257, 154–160 (1980).
[CrossRef]

Beckmann, P.

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

Chan, H. L.

H. L. Chan, A. K. Fung, “A numerical study of the Kirchhoff approximation in horizontally polarized backscattering from a random surface,” Radio Sci. 13, 811–818 (1978).
[CrossRef]

Dereniak, E. L.

F. O. Bartell, E. L. Dereniak, W. L. Wolfe, “The theory and measurement of bidirectional reflectance distribution function (BRDF) and bidirectional transmittance distribution function (BRTF),” in Radiation Scattering in Optical Systems, G. H. Hunt, ed., Proc. Soc. Photo-Opt. Instrum. Eng.257, 154–160 (1980).
[CrossRef]

Egan, W. G.

Fitzwater, M. A.

Fung, A. K.

R. M. Axline, A. K. Fung, “Numerical calculation of scattering from a perfectly conducting rough surface,” IEEE Trans. Antennas Propag. AP-26, 482–488 (1978).
[CrossRef]

H. L. Chan, A. K. Fung, “A numerical study of the Kirchhoff approximation in horizontally polarized backscattering from a random surface,” Radio Sci. 13, 811–818 (1978).
[CrossRef]

Garcia, N.

M. Nieto-Vesperinas, N. Garcia, “A detailed study of the scattering of scalar waves from random rough surfaces,” Opt. Acta 28, 1651–1672 (1981).
[CrossRef]

Gray, P. F.

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

Grum, F.

Hilgeman, T.

Ishimaru, A.

Jakeman, E.

Kohl, R. H.

Kuga, Y.

Lentz, R. R.

R. R. Lentz, “A numerical study of electromagnetic scattering from ocean-like surfaces,” Radio Sci. 9, 1139–1146 (1974).
[CrossRef]

Luckey, G. W.

Maradudin, A. A.

Markov, A. V.

A. V. Markov, “Les particularités dans la réflexion de la lumière par la surface de la lune,” Astron. Nachr. 221, 65–78 (1924).
[CrossRef]

Mendez, E. R.

Michel, T.

Montgomery, W. W.

Nicodemus, F. E.

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]

Oetking, P.

P. Oetking, “Photometric studies of diffusely reflecting surfaces with applications to the brightness of the moon,” J. Geophys. Res. 71, 2505–2513 (1966).
[CrossRef]

Shen, J.

J. Shen, A. A. Maradudin, “Multiple scattering of waves from random rough surfaces,” Phys. Rev. B 22, 4234–4240 (1980).
[CrossRef]

Soto-Crespo, J. M.

Spizzichino, A.

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

Thorsos, E. I.

E. I. Thorsos, “The validity of the Kirchhoff approximation for rough surface scattering using a Gaussian roughness spectrum,” J. Acoust. Soc. Am. 83, 78–92 (1987).
[CrossRef]

Winebrenner, D. P.

Wolfe, W. L.

F. O. Bartell, E. L. Dereniak, W. L. Wolfe, “The theory and measurement of bidirectional reflectance distribution function (BRDF) and bidirectional transmittance distribution function (BRTF),” in Radiation Scattering in Optical Systems, G. H. Hunt, ed., Proc. Soc. Photo-Opt. Instrum. Eng.257, 154–160 (1980).
[CrossRef]

Appl. Opt. (4)

Astron. Nachr. (1)

A. V. Markov, “Les particularités dans la réflexion de la lumière par la surface de la lune,” Astron. Nachr. 221, 65–78 (1924).
[CrossRef]

IEEE Trans. Antennas Propag. (1)

R. M. Axline, A. K. Fung, “Numerical calculation of scattering from a perfectly conducting rough surface,” IEEE Trans. Antennas Propag. AP-26, 482–488 (1978).
[CrossRef]

J. Acoust. Soc. Am. (1)

E. I. Thorsos, “The validity of the Kirchhoff approximation for rough surface scattering using a Gaussian roughness spectrum,” J. Acoust. Soc. Am. 83, 78–92 (1987).
[CrossRef]

J. Geophys. Res. (1)

P. Oetking, “Photometric studies of diffusely reflecting surfaces with applications to the brightness of the moon,” J. Geophys. Res. 71, 2505–2513 (1966).
[CrossRef]

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

Opt. Acta (2)

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

M. Nieto-Vesperinas, N. Garcia, “A detailed study of the scattering of scalar waves from random rough surfaces,” Opt. Acta 28, 1651–1672 (1981).
[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. (3)

Phys. Rev. B (1)

J. Shen, A. A. Maradudin, “Multiple scattering of waves from random rough surfaces,” Phys. Rev. B 22, 4234–4240 (1980).
[CrossRef]

Radio Sci. (2)

R. R. Lentz, “A numerical study of electromagnetic scattering from ocean-like surfaces,” Radio Sci. 9, 1139–1146 (1974).
[CrossRef]

H. L. Chan, A. K. Fung, “A numerical study of the Kirchhoff approximation in horizontally polarized backscattering from a random surface,” Radio Sci. 13, 811–818 (1978).
[CrossRef]

Other (4)

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

Ref. 2, Figs. 12–14.

Ref. 7, Chap. 6.

F. O. Bartell, E. L. Dereniak, W. L. Wolfe, “The theory and measurement of bidirectional reflectance distribution function (BRDF) and bidirectional transmittance distribution function (BRTF),” in Radiation Scattering in Optical Systems, G. H. Hunt, ed., Proc. Soc. Photo-Opt. Instrum. Eng.257, 154–160 (1980).
[CrossRef]

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Figures (14)

Fig. 1
Fig. 1

Schematic diagram of the scatterometer viewed from above. PMT, photomultiplier tube.

Fig. 2
Fig. 2

Scatter envelope from a MgO surface, s incident polarization (λ = 0.633 μm). Second curves from bottom denote Σss, curves immediately below these indicate Σsp, and topmost curves denote Σtot. θi is a, 0°; b, −30°, and c, −60°. The solid curves denote the case of a perfect Lambertian surface with a perfect scatterometer response.

Fig. 3
Fig. 3

Scatter envelope from MgO surface, p incident polarization (λ = 0.633 μm). Second curves from bottom denote Σpp, curves immediately below these indicate Σps, and topmost curves denote Σtot. θi is a, 0°;b, −30°, c, −60°. The solid curves denote the case of a perfect Lambertian surface with a perfect scatterometer response.

Fig. 4
Fig. 4

Plate #313, θi = 0°, λ = 0.633 μm. The copolarized and cross-polarized components Σss and Σsp are shown in a; the equivalent Σpol and Σunpol are shown in b. Solid curves denote Σss and Σunpol, and dotted lines denote Σsp and Σpol.

Fig. 5
Fig. 5

Plate #313, θi = −10°, λ = 0.633 μm. Labels as in Fig. 4.

Fig. 6
Fig. 6

Plate #313, θi = −20°, λ = 0.633 μm. Labels as in Fig. 4.

Fig. 7
Fig. 7

Plate #313, θi = −40°, λ = 0.633 μm. Labels as in Fig. 4.

Fig. 8
Fig. 8

Plate #440, s incident polarization (λ = 0.633 μm), for θi = a, 0°; b, −10°; c, −20°; d, −40°. The thicker curves denote experimental Σss; the thinner curves show the numerically calculated values. The measured cross-polarized component, denoted by the line almost coincident with the x axis, is shown only for the case of normal incidence.

Fig. 9
Fig. 9

Plate #440, p incident polarization (λ = 0.633 μm), for θi = a, 0°; b, −10°; c, −20°, d, −40°. The thicker curves denote experimental Σpp; the thinner curves show the numerically calculated values. The measured cross-polarized component, denoted by the line almost coincident with the x axis, is shown only for the case of normal incidence.

Fig. 10
Fig. 10

Plate #440, s incident polarization (λ = 10.6 μm), for θi = a, 0°; b, −30°; c, −50°. Labels as in Fig. 9.

Fig. 11
Fig. 11

Plate #440, p incident polarization (λ = 10.6 μm), for θi = a, 0°; b, −30°; c, −50°. Labels as in Fig. 9.

Fig. 12
Fig. 12

Plate #440 (λ = 10.6 μm); plot of the normalized coherent component power for s and p incident polarization obtained from calculation and experiment, shown as crosses and open circles, respectively. The physical-optics solutions for s and p polarizations and a one-dimensional rough surface are shown dashed and dotted.

Fig. 13
Fig. 13

Plate #436 (λ = 0.633 μm); plots of Σss (solid curves) and Σpp (dotted curves) for θi = a, 0°; b, −10°; c, −20°, d, −40°.

Fig. 14
Fig. 14

Plate #436 (λ = 0.633 μm); plot of Σss (open circles) and Σpp (crosses) for θi = a, 0°; b, −30°; and c, −50°.

Equations (7)

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R d = Δ Ω d Ω W ( Ω ) J ( Ω ) ,
R d = Δ Ω J ,
= J Φ i ,
= f r cos θ .
( θ i , θ ) = 1 π cos θ .
pol = s s s p
unpol = 2 s p .

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