Abstract

A facet model is used to predict the polarization states of light scattered from rough surfaces. The states are compared with experimentally determined elements from various types of rough substrates. The experimental data are found to be quite similar to what is predicted by the model.

© 1992 Optical Society of America

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References

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  8. V. Celli, A. A. Maradudin, A. M. Marvin, A. R. McGurn, “Some aspects of light scattering from a randomly rough metal surface,” J. Opt. Soc. Am. A 2, 2225–2239 (1985).
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  12. 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).
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  13. M. Saillard, D. Maystre, “Scattering from metallic and dielectric rough surfaces,” J. Opt. Soc. Am. A 7, 982–990 (1990).
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  14. V. J. Iafelice, W. S. Bickel, “Polarized light-scattering matrix elements for select perfect and perturbed optical surfaces,” Appl. Opt. 26, 2410–2415 (1987).
    [CrossRef]
  15. W. S. Bickel, R. R. Zito, V. J. Iafelice, “Polarized light scattering from metal surfaces,” J. Appl. Phys. 61, 5392–5398 (1987).
    [CrossRef]
  16. K. A. O’Donnell, M. E. Knotts, “Polarization dependence of scattering from one-dimensional rough surfaces,” J. Opt. Soc. Am. A 8, 1126–1131 (1991).
    [CrossRef]
  17. P. Beckmann, The Depolarization of Electromagnetic Waves (Golem, Boulder, Colo., 1968).
  18. J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1962).
  19. D. E. Grey, ed., American Institute of Physics Handbook (McGraw-Hill, New York, 1972).
  20. A. J. Hunt, D. R. Huffman, “A new polarization-modulated light scattering instrument,” Rev. Sci. Instrum. 44, 1753–1762 (1973).
    [CrossRef]
  21. R. J. Perry, A. J. Hunt, D. R. Huffman, “Experimental determinations of Mueller scattering matrices for nonspherical particles,” Appl. Opt. 17, 2700–2710 (1978).
    [CrossRef] [PubMed]
  22. W. S. Bickel, J. F. Davidson, D. R. Huffman, R. Kilkson, “Application of polarization effects in light scattering: a new biophysical tool,” Proc. Natl. Acad. Sci. USA 73, 486–490 (1976).
    [CrossRef] [PubMed]
  23. B. W. Bell, “Single fiber light scattering matrix: an experimental determination,” M.S. thesis (Optical Sciences Center, University of Arizona, Tucson, Ariz., 1981).
  24. V. J. Iafelice, “Polarized light scattering matrix elements for select perfect and perturbed surfaces,” M.S. thesis (Department of Physics, University of Arizona, Tucson, Ariz., 1985).

1991 (2)

1990 (2)

1989 (2)

1987 (3)

1985 (2)

1978 (1)

1976 (1)

W. S. Bickel, J. F. Davidson, D. R. Huffman, R. Kilkson, “Application of polarization effects in light scattering: a new biophysical tool,” Proc. Natl. Acad. Sci. USA 73, 486–490 (1976).
[CrossRef] [PubMed]

1973 (1)

A. J. Hunt, D. R. Huffman, “A new polarization-modulated light scattering instrument,” Rev. Sci. Instrum. 44, 1753–1762 (1973).
[CrossRef]

1965 (1)

Anderson, R.

Bahar, E.

Bailey, W. M.

W. S. Bickel, W. M. Bailey, “Stokes vectors, Mueller matrices, and polarized light,” Am. J. Phys. 53, 468–478 (1985).
[CrossRef]

Beckmann, P.

P. Beckmann, The Depolarization of Electromagnetic Waves (Golem, Boulder, Colo., 1968).

Bell, B. W.

B. W. Bell, “Single fiber light scattering matrix: an experimental determination,” M.S. thesis (Optical Sciences Center, University of Arizona, Tucson, Ariz., 1981).

Bickel, W. S.

W. S. Bickel, R. R. Zito, V. J. Iafelice, “Polarized light scattering from metal surfaces,” J. Appl. Phys. 61, 5392–5398 (1987).
[CrossRef]

V. J. Iafelice, W. S. Bickel, “Polarized light-scattering matrix elements for select perfect and perturbed optical surfaces,” Appl. Opt. 26, 2410–2415 (1987).
[CrossRef]

W. S. Bickel, W. M. Bailey, “Stokes vectors, Mueller matrices, and polarized light,” Am. J. Phys. 53, 468–478 (1985).
[CrossRef]

W. S. Bickel, J. F. Davidson, D. R. Huffman, R. Kilkson, “Application of polarization effects in light scattering: a new biophysical tool,” Proc. Natl. Acad. Sci. USA 73, 486–490 (1976).
[CrossRef] [PubMed]

Bohren, C.

C. Bohren, D. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

Celli, V.

Dainty, J. C.

Davidson, J. F.

W. S. Bickel, J. F. Davidson, D. R. Huffman, R. Kilkson, “Application of polarization effects in light scattering: a new biophysical tool,” Proc. Natl. Acad. Sci. USA 73, 486–490 (1976).
[CrossRef] [PubMed]

Fitzwater, M. A.

Friberg, A. T.

Huffman, D.

C. Bohren, D. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

Huffman, D. R.

R. J. Perry, A. J. Hunt, D. R. Huffman, “Experimental determinations of Mueller scattering matrices for nonspherical particles,” Appl. Opt. 17, 2700–2710 (1978).
[CrossRef] [PubMed]

W. S. Bickel, J. F. Davidson, D. R. Huffman, R. Kilkson, “Application of polarization effects in light scattering: a new biophysical tool,” Proc. Natl. Acad. Sci. USA 73, 486–490 (1976).
[CrossRef] [PubMed]

A. J. Hunt, D. R. Huffman, “A new polarization-modulated light scattering instrument,” Rev. Sci. Instrum. 44, 1753–1762 (1973).
[CrossRef]

Hunt, A. J.

R. J. Perry, A. J. Hunt, D. R. Huffman, “Experimental determinations of Mueller scattering matrices for nonspherical particles,” Appl. Opt. 17, 2700–2710 (1978).
[CrossRef] [PubMed]

A. J. Hunt, D. R. Huffman, “A new polarization-modulated light scattering instrument,” Rev. Sci. Instrum. 44, 1753–1762 (1973).
[CrossRef]

Iafelice, V. J.

W. S. Bickel, R. R. Zito, V. J. Iafelice, “Polarized light scattering from metal surfaces,” J. Appl. Phys. 61, 5392–5398 (1987).
[CrossRef]

V. J. Iafelice, W. S. Bickel, “Polarized light-scattering matrix elements for select perfect and perturbed optical surfaces,” Appl. Opt. 26, 2410–2415 (1987).
[CrossRef]

V. J. Iafelice, “Polarized light scattering matrix elements for select perfect and perturbed surfaces,” M.S. thesis (Department of Physics, University of Arizona, Tucson, Ariz., 1985).

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1962).

Kerker, M.

M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969).

Kilkson, R.

W. S. Bickel, J. F. Davidson, D. R. Huffman, R. Kilkson, “Application of polarization effects in light scattering: a new biophysical tool,” Proc. Natl. Acad. Sci. USA 73, 486–490 (1976).
[CrossRef] [PubMed]

Kim, M. J.

Knotts, M. E.

Maradudin, A. A.

Marvin, A. M.

Maystre, D.

McGurn, A. R.

Méndez, E. R.

Nicodemus, F. E.

Nieto-Vesperinas, M.

O’Donnell, K. A.

Perry, R. J.

Saillard, M.

Sant, A. J.

Soto-Crespo, J. M.

Stover, J. C.

J. C. Stover, Optical Scattering Measurement and Analysis (McGraw-Hill, New York, 1990).

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1976).

Zito, R. R.

W. S. Bickel, R. R. Zito, V. J. Iafelice, “Polarized light scattering from metal surfaces,” J. Appl. Phys. 61, 5392–5398 (1987).
[CrossRef]

Am. J. Phys. (1)

W. S. Bickel, W. M. Bailey, “Stokes vectors, Mueller matrices, and polarized light,” Am. J. Phys. 53, 468–478 (1985).
[CrossRef]

Appl. Opt. (4)

J. Appl. Phys. (1)

W. S. Bickel, R. R. Zito, V. J. Iafelice, “Polarized light scattering from metal surfaces,” J. Appl. Phys. 61, 5392–5398 (1987).
[CrossRef]

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

Proc. Natl. Acad. Sci. USA (1)

W. S. Bickel, J. F. Davidson, D. R. Huffman, R. Kilkson, “Application of polarization effects in light scattering: a new biophysical tool,” Proc. Natl. Acad. Sci. USA 73, 486–490 (1976).
[CrossRef] [PubMed]

Rev. Sci. Instrum. (1)

A. J. Hunt, D. R. Huffman, “A new polarization-modulated light scattering instrument,” Rev. Sci. Instrum. 44, 1753–1762 (1973).
[CrossRef]

Other (9)

J. C. Stover, Optical Scattering Measurement and Analysis (McGraw-Hill, New York, 1990).

B. W. Bell, “Single fiber light scattering matrix: an experimental determination,” M.S. thesis (Optical Sciences Center, University of Arizona, Tucson, Ariz., 1981).

V. J. Iafelice, “Polarized light scattering matrix elements for select perfect and perturbed surfaces,” M.S. thesis (Department of Physics, University of Arizona, Tucson, Ariz., 1985).

P. Beckmann, The Depolarization of Electromagnetic Waves (Golem, Boulder, Colo., 1968).

J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1962).

D. E. Grey, ed., American Institute of Physics Handbook (McGraw-Hill, New York, 1972).

C. Bohren, D. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1976).

M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969).

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Figures (10)

Fig. 1
Fig. 1

Geometry of the light scattering at a surface.

Fig. 2
Fig. 2

Geometry of the facet reflection of a rough surface.

Fig. 3
Fig. 3

Light-scattering Mueller matrix elements predicted by the facet model for a copper (n = 1.1 − 2.5i) substrate (×) and an aluminum (n = 0.5 − 5.0i) substrate (○) illuminated at ϑinc = 90° and λ = 0.4416 μm.

Fig. 4
Fig. 4

Experimental light-scattering Mueller matrix elements of a rough copper substrate illuminated at ϑinc = 0°, 15°, 30°, 45°, 60°, and 75° (λ = 0.4416 μm).

Fig. 5
Fig. 5

Experimental light-scattering Mueller matrix elements of a rough aluminum substrate illuminated at ϑinc = 0°, 15°, 30°, 45°, 60°, and 75° (λ = 0.4416 μm).

Fig. 6
Fig. 6

Micrograph of randomly sanded aluminum substrate.

Fig. 7
Fig. 7

Micrographs of three different substrates roughened by sandblasting.

Fig. 8
Fig. 8

Experimental light-scattering Mueller matrix elements of reference aluminum substrate 0 (mirror) illuminated at ϑinc = 15°, 30°, 45°, 60°, and 75° (λ = 0.4416 μm).

Fig. 9
Fig. 9

Experimental light-scattering Mueller matrix elements of substrate 4 (slightly roughened) illuminated at ϑinc = 15°, 30°, 45°, 60°, and 75° (λ = 0.4416 μm).

Fig. 10
Fig. 10

Experimental light-scattering Mueller matrix elements of roughened substrate 10 illuminated at ϑinc = 15°, 30°, 45°, 60°, and 75° (λ = 0.4416 μm).

Equations (13)

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R TE ( ϑ ) = n 1 cos ϑ - n 2 [ 1 - ( n 1 / n 2 ) 2 sin 2 ϑ ] 1 / 2 n 1 cos ϑ + n 2 [ 1 - ( n 1 / n 2 ) 2 sin 2 ϑ ] 1 / 2 ,
R TM ( ϑ ) = n 2 cos ϑ - n 1 [ 1 - ( n 1 / n 2 ) 2 sin 2 ϑ ] 1 / 2 n 2 cos ϑ + n 1 [ 1 - ( n 1 / n 2 ) 2 sin 2 ϑ ] 1 / 2 ,
ϑ = ( ϑ sca - π ) / 2.
E T * sca = E T * inc R T * ( ϑ ) A inc s k 1 · n ^ ( r ) k 1 × exp [ i ( k 2 - k 1 ) · r ] δ π , ( ϑ sca - 2 ϑ ) d s ,
[ E TM sca E TE sca ] = [ S 2 S 3 S 4 S 1 ] [ E TM inc E TE inc ]
S 11 = S 11 = ½ ( S 1 2 + S 2 2 ) ,
S 12 = S 12 / S 11 = ½ ( S 1 2 - S 2 2 ) / S 11 ,
S 33 = S 33 / S 11 = Re ( S 1 S 2 * ) / S 11 ,
S 34 = S 34 / S 11 = Im ( S 1 S 2 * ) / S 11 .
S 11 * = S 11 ,
S 12 * = S 12 / S 11 ,
S 33 * = ( S 13 + S 33 ) / ( S 11 + S 31 ) ,
S 34 * = ( S 14 + S 34 ) / ( S 11 + S 31 ) .

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