Abstract

The scattering of light from a slightly rough surface overlying a reflecting surface is investigated. It is shown that the long-scale component of the roughness spectrum plays a critical role in the scattering patterns obtained. The scattered interference patterns are critically dependent on small variation of the rms height of the long-scale component of the roughness. Conventional perturbation theory is found to be invalid in cases in which interference phenomena in the scattering are of importance. A model is proposed that quantitatively describes the measured angular intensity distributions.

© 1998 Optical Society of America

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References

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  1. T. Young, Philos. Trans. R. Soc. London Ser. A X, 41 (1802); G. Stokes, Trans. Cambridge Philos. Soc. 9, 147 (1851); C. V. Raman and G. L. Datta, Philos. Mag. Ser. 6 42, 826 (1921).
    [CrossRef]
  2. A. J. de Witte, Am. J. Phys. 35, 301 (1967).
    [CrossRef]
  3. M. Françon, Laser Speckle and Applications in Optics (Academic, San Diego, Calif., 1979).
  4. M. Françon, in Laser Speckle and Related PhenomenaJ. C. Dainty, ed. (Springer-Verlag, Berlin, 1984).
  5. J. Q. Lu, J. A. Sanchez-Gil, E. R. Mendez, Z.-H. Gu, and A. A. Maradudin, J. Opt. Soc. Am. A 15, 185 (1998).
    [CrossRef]
  6. V. Freilikher, M. Pustilnik, and I. Yurkevich, Opt. Lett. 19, 1382 (1994).
    [CrossRef] [PubMed]
  7. F. Bass and I. Fuks, Wave Scattering from a Statistically Rough Surface (Pergamon, New York, 1979).

1998 (1)

1994 (1)

1967 (1)

A. J. de Witte, Am. J. Phys. 35, 301 (1967).
[CrossRef]

1802 (1)

T. Young, Philos. Trans. R. Soc. London Ser. A X, 41 (1802); G. Stokes, Trans. Cambridge Philos. Soc. 9, 147 (1851); C. V. Raman and G. L. Datta, Philos. Mag. Ser. 6 42, 826 (1921).
[CrossRef]

Bass, F.

F. Bass and I. Fuks, Wave Scattering from a Statistically Rough Surface (Pergamon, New York, 1979).

de Witte, A. J.

A. J. de Witte, Am. J. Phys. 35, 301 (1967).
[CrossRef]

Françon, M.

M. Françon, Laser Speckle and Applications in Optics (Academic, San Diego, Calif., 1979).

M. Françon, in Laser Speckle and Related PhenomenaJ. C. Dainty, ed. (Springer-Verlag, Berlin, 1984).

Freilikher, V.

Fuks, I.

F. Bass and I. Fuks, Wave Scattering from a Statistically Rough Surface (Pergamon, New York, 1979).

Gu, Z.-H.

Lu, J. Q.

Maradudin, A. A.

Mendez, E. R.

Pustilnik, M.

Sanchez-Gil, J. A.

Young, T.

T. Young, Philos. Trans. R. Soc. London Ser. A X, 41 (1802); G. Stokes, Trans. Cambridge Philos. Soc. 9, 147 (1851); C. V. Raman and G. L. Datta, Philos. Mag. Ser. 6 42, 826 (1921).
[CrossRef]

Yurkevich, I.

Am. J. Phys. (1)

A. J. de Witte, Am. J. Phys. 35, 301 (1967).
[CrossRef]

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

Opt. Lett. (1)

Philos. Trans. R. Soc. London Ser. A (1)

T. Young, Philos. Trans. R. Soc. London Ser. A X, 41 (1802); G. Stokes, Trans. Cambridge Philos. Soc. 9, 147 (1851); C. V. Raman and G. L. Datta, Philos. Mag. Ser. 6 42, 826 (1921).
[CrossRef]

Other (3)

F. Bass and I. Fuks, Wave Scattering from a Statistically Rough Surface (Pergamon, New York, 1979).

M. Françon, Laser Speckle and Applications in Optics (Academic, San Diego, Calif., 1979).

M. Françon, in Laser Speckle and Related PhenomenaJ. C. Dainty, ed. (Springer-Verlag, Berlin, 1984).

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Figures (2)

Fig. 1
Fig. 1

Photographs of interference rings from (a, b) Fabry–Perot plates and (c, d) glass plates with LSR at various incident angles. a, θin=2.3°; b, 2.9°; c, 4°; d, 6°. We blocked points of reflection on the screen with a neutral-density filter to decrease their brightness. The incident beam can be seen emerging from a hole in the screen, and the visible line is produced by scattering of the beam by dust particles in the air. Note that for a Fabry–Perot plate the reflected beam can be on a, ring maxima or b, ring minima, as the incident angle is varied. For a plate with LSR, however, the reflected beam is locked to an interference maximum (c, d).

Fig. 2
Fig. 2

Intensity distribution of light scattered from a glass plate with LSR and comparison with the theory of Ref.  8 (dotted curve). In the calculation we used the following experimentally measured sample parameters: angle of incidence, 4°; plate thickness, 150 µm; rms height of SSR, 0.1 µm; coherence length of SSR, 9.5 µm; rms height of LSR, 0.06 µm; coherence length of LSR, 1.5  mm.

Equations (1)

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Iθin, θsI0gθingθsW˜q,

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