Abstract

Speckle patterns in the light field scattered from the rough surface of a cylindrical object are experimentally studied. The light speckles are elongated in the direction normal to the cylinder axis. A theoretical model explains the main features of the scattered light field. The dimensions of light speckles depend on both the surface roughness and the surface curvature.

© 1997 Optical Society of America

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References

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  1. J. M. Burch, J. M. J. Tokarski, “Production of multiple beam fringes from photographic scatterers,” Opt. Acta 15, 101–111 (1968).
  2. M. Françon, “Information processing using speckle patterns,” in Laser Speckle and Related Phenomena, J. C. Dainty, ed. Vol. 9 of Topics in Applied Physics (Springer-Verlag, Berlin, 1975), Chap. 5.
  3. A. E. Ennos, “Speckle interferometry,” in Laser Speckle and Related Phenomena, J. C. Dainty, ed., Vol. 9 of Topics in Applied Physics (Springer-Verlag, Berlin, 1975), Chap. 6.
  4. I. Yamaguchi, “Theory and applications of speckle displacement and decorrelation,” in Speckle Metrology, R. S. Sirohi, ed. (Marcel Dekker, New York, 1993), pp. 1–39.
  5. P. Beckmann, A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, Oxford, 1963).
  6. L. J. Goldfisher, “Autocorrelation function and power spectral density of a laser-produced speckle pattern,” J. Opt. Soc. Am. 55, 247–253 (1965).
    [Crossref]
  7. H. Fujii, T. Asakura, “Effect of surface roughness on the statistical distribution of image speckle intensity,” Opt. Commun. 11, 35–38 (1974).
    [Crossref]
  8. J. W. Goodman, “Statistical properties of laser speckle patterns,” in Laser Speckle and Related Phenomena, J. C. Dainty, ed., Vol. 9 of Topics in Applied Physics (Springer-Verlag, Berlin, 1975), Chap. 2.
  9. T. Asakura, “Surface roughness measurement,” in Speckle Metrology, R. K. Erf, ed. (Academic, New York, 1978), Chap. 3.
    [Crossref]
  10. J. M. Elson, J. M. Bennett, “Relation between the angular dependence of scattering and the statistical properties of optical surfaces,” J. Opt. Soc. Am. 69, 31–47 (1979).
    [Crossref]
  11. E. Marx, V. Vorburger, “Direct and inverse problems for light scattered by rough surfaces,” Appl. Opt. 29, 3613–3626 (1990).
    [Crossref] [PubMed]
  12. L. Cao, T. Vorburger, A. Lieberman, T. Lettieri, “Light-scattering measurement of the rms slopes of rough surfaces,” Appl. Opt. 30, 3221–3227 (1991).
    [Crossref] [PubMed]
  13. E. Marx, B. Leridon, T. Lettieri, J. Song, T. Vorburger, “Autocorrelation functions from optical scattering for one-dimensionally rough surfaces,” Appl. Opt. 32, 67–76 (1993).
    [Crossref] [PubMed]
  14. T. Vorburger, E. Marx, T. Lettieri, “Regimes of surface roughness measurable with light scattering,” Appl. Opt. 32, 3401–3408 (1993).
    [Crossref] [PubMed]
  15. M. A. Taubenblatt, “Light scattering from cylindrical structures on surfaces,” Opt. Lett. 15, 255–257 (1990).
    [Crossref] [PubMed]
  16. Y. Y. Fan, V. M. Huynh, “Light scattering from rough periodic cylindrical surfaces,” Appl. Opt. 32, 3452–3458 (1993).
    [Crossref] [PubMed]
  17. P. K. Rastogi, “Measurement of the derivatives of curved surfaces using speckle interferometry,” J. Mod. Opt. 41, 659–661 (1994).
    [Crossref]
  18. F. Kuik, J. F. de Haan, J. W. Hovenier, “Single scattering of light by circular cylinders,” Appl. Opt. 33, 4906–4918 (1994).
    [Crossref] [PubMed]
  19. I. Yamaguchi, T. Fujita, “Laser speckle rotary encoder,” Appl. Opt. 28, 4401–4406 (1989).
    [Crossref] [PubMed]
  20. M. Sjödahl, I. Yamaguchi, “Strain and torque measurements on cylindrical objects using the laser speckle strain gauge,” Opt. Eng. 35, 1179–1186 (1996).
    [Crossref]

1996 (1)

M. Sjödahl, I. Yamaguchi, “Strain and torque measurements on cylindrical objects using the laser speckle strain gauge,” Opt. Eng. 35, 1179–1186 (1996).
[Crossref]

1994 (2)

P. K. Rastogi, “Measurement of the derivatives of curved surfaces using speckle interferometry,” J. Mod. Opt. 41, 659–661 (1994).
[Crossref]

F. Kuik, J. F. de Haan, J. W. Hovenier, “Single scattering of light by circular cylinders,” Appl. Opt. 33, 4906–4918 (1994).
[Crossref] [PubMed]

1993 (3)

1991 (1)

1990 (2)

1989 (1)

1979 (1)

1974 (1)

H. Fujii, T. Asakura, “Effect of surface roughness on the statistical distribution of image speckle intensity,” Opt. Commun. 11, 35–38 (1974).
[Crossref]

1968 (1)

J. M. Burch, J. M. J. Tokarski, “Production of multiple beam fringes from photographic scatterers,” Opt. Acta 15, 101–111 (1968).

1965 (1)

Asakura, T.

H. Fujii, T. Asakura, “Effect of surface roughness on the statistical distribution of image speckle intensity,” Opt. Commun. 11, 35–38 (1974).
[Crossref]

T. Asakura, “Surface roughness measurement,” in Speckle Metrology, R. K. Erf, ed. (Academic, New York, 1978), Chap. 3.
[Crossref]

Beckmann, P.

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

Bennett, J. M.

Burch, J. M.

J. M. Burch, J. M. J. Tokarski, “Production of multiple beam fringes from photographic scatterers,” Opt. Acta 15, 101–111 (1968).

Cao, L.

de Haan, J. F.

Elson, J. M.

Ennos, A. E.

A. E. Ennos, “Speckle interferometry,” in Laser Speckle and Related Phenomena, J. C. Dainty, ed., Vol. 9 of Topics in Applied Physics (Springer-Verlag, Berlin, 1975), Chap. 6.

Fan, Y. Y.

Françon, M.

M. Françon, “Information processing using speckle patterns,” in Laser Speckle and Related Phenomena, J. C. Dainty, ed. Vol. 9 of Topics in Applied Physics (Springer-Verlag, Berlin, 1975), Chap. 5.

Fujii, H.

H. Fujii, T. Asakura, “Effect of surface roughness on the statistical distribution of image speckle intensity,” Opt. Commun. 11, 35–38 (1974).
[Crossref]

Fujita, T.

Goldfisher, L. J.

Goodman, J. W.

J. W. Goodman, “Statistical properties of laser speckle patterns,” in Laser Speckle and Related Phenomena, J. C. Dainty, ed., Vol. 9 of Topics in Applied Physics (Springer-Verlag, Berlin, 1975), Chap. 2.

Hovenier, J. W.

Huynh, V. M.

Kuik, F.

Leridon, B.

Lettieri, T.

Lieberman, A.

Marx, E.

Rastogi, P. K.

P. K. Rastogi, “Measurement of the derivatives of curved surfaces using speckle interferometry,” J. Mod. Opt. 41, 659–661 (1994).
[Crossref]

Sjödahl, M.

M. Sjödahl, I. Yamaguchi, “Strain and torque measurements on cylindrical objects using the laser speckle strain gauge,” Opt. Eng. 35, 1179–1186 (1996).
[Crossref]

Song, J.

Spizzichino, A.

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

Taubenblatt, M. A.

Tokarski, J. M. J.

J. M. Burch, J. M. J. Tokarski, “Production of multiple beam fringes from photographic scatterers,” Opt. Acta 15, 101–111 (1968).

Vorburger, T.

Vorburger, V.

Yamaguchi, I.

M. Sjödahl, I. Yamaguchi, “Strain and torque measurements on cylindrical objects using the laser speckle strain gauge,” Opt. Eng. 35, 1179–1186 (1996).
[Crossref]

I. Yamaguchi, T. Fujita, “Laser speckle rotary encoder,” Appl. Opt. 28, 4401–4406 (1989).
[Crossref] [PubMed]

I. Yamaguchi, “Theory and applications of speckle displacement and decorrelation,” in Speckle Metrology, R. S. Sirohi, ed. (Marcel Dekker, New York, 1993), pp. 1–39.

Appl. Opt. (7)

J. Mod. Opt. (1)

P. K. Rastogi, “Measurement of the derivatives of curved surfaces using speckle interferometry,” J. Mod. Opt. 41, 659–661 (1994).
[Crossref]

J. Opt. Soc. Am. (2)

Opt. Acta (1)

J. M. Burch, J. M. J. Tokarski, “Production of multiple beam fringes from photographic scatterers,” Opt. Acta 15, 101–111 (1968).

Opt. Commun. (1)

H. Fujii, T. Asakura, “Effect of surface roughness on the statistical distribution of image speckle intensity,” Opt. Commun. 11, 35–38 (1974).
[Crossref]

Opt. Eng. (1)

M. Sjödahl, I. Yamaguchi, “Strain and torque measurements on cylindrical objects using the laser speckle strain gauge,” Opt. Eng. 35, 1179–1186 (1996).
[Crossref]

Opt. Lett. (1)

Other (6)

J. W. Goodman, “Statistical properties of laser speckle patterns,” in Laser Speckle and Related Phenomena, J. C. Dainty, ed., Vol. 9 of Topics in Applied Physics (Springer-Verlag, Berlin, 1975), Chap. 2.

T. Asakura, “Surface roughness measurement,” in Speckle Metrology, R. K. Erf, ed. (Academic, New York, 1978), Chap. 3.
[Crossref]

M. Françon, “Information processing using speckle patterns,” in Laser Speckle and Related Phenomena, J. C. Dainty, ed. Vol. 9 of Topics in Applied Physics (Springer-Verlag, Berlin, 1975), Chap. 5.

A. E. Ennos, “Speckle interferometry,” in Laser Speckle and Related Phenomena, J. C. Dainty, ed., Vol. 9 of Topics in Applied Physics (Springer-Verlag, Berlin, 1975), Chap. 6.

I. Yamaguchi, “Theory and applications of speckle displacement and decorrelation,” in Speckle Metrology, R. S. Sirohi, ed. (Marcel Dekker, New York, 1993), pp. 1–39.

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

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Figures (6)

Fig. 1
Fig. 1

Rough surface of a flat substrate illuminated by a laser beam with diameter D. Points P, Q are the limits of the light spot. The scattered speckle pattern is studied at observation plane β placed at a distance L. Light is scattered from each surface point within an angle θ whose extension depends on the surface roughness. For large enough values of θ light rays that emerge from P, Q interfere at the observation plane. For smaller values of θ a maximum distance of d = L tan(θ/2) exists such that light rays issued from surface points C, C′ can interfere at point A of the observation plane. This maximum distance determines the length λL/d of the light speckles at plane β.

Fig. 2
Fig. 2

Rough cylindrical surface (center O, radius R) illuminated by a laser beam in the direction AO. The scattered speckle pattern is studied in the observation plane β, which is parallel to the cylinder axis and normal to the laser beam. Distance AO is referred to as L in the text. The light ray incident at point C is i. The light ray reflected if the cylinder surface is perfectly smooth is r. The normal to the surface at point C is n, whereas α is the incident and reflected angle. The reflected light is homogeneously scattered within an angle θ centered in ray r. If the distance between the scattering points is greater than the distance CC′ = d shown in this figure, the light rays scattered from them cannot interfere at point A. This maximum distance thus determines the dimension (λL/d) of the speckles along the observation plane.

Fig. 3
Fig. 3

Three-dimensional view of the experiment. The laser beam (a 4-mW He–Ne with a diameter of D = 2 mm) is normal to the cylinder axis a, a. Observation plane β is normal to the laser beam. The light speckles that appear in the observation plane are elongated in the direction normal to the laser beam. Their length and width are (g l , g w), respectively.

Fig. 4
Fig. 4

(a) Image of the surface of cylinder C 1 used in experiments 1 and 2 outlined in the text. The cylinder (which is part of a clip of the kind used to hold sheets of paper) was obtained by mechanical extrusion. As a result, grooves parallel to the cylinder axis appear on the cylinder surface. Numbers in the coordinate axis are pixels of the CCD camera. (b) Image of the surface of cylinder C 2 used in experiments 3 and 4 outlined in the text. The cylinder (which is a pole of the kind commonly used in optical setups) was obtained by turning and rectification with machine tools. As a result, grooves perpendicular to the cylinder axis appear on the cylinder surface. The vertical bright image corresponds to an optical fiber (125-µm diameter) that was used as a distance reference.

Fig. 5
Fig. 5

(a) Light field scattered from cylinder C 1 in the setup of Fig. 3. The scattered light field has the shape of a narrow strip elongated in the horizontal direction. The light speckles are also elongated in the horizontal direction. (b) Enlarged detail of a region of the light field in (a). (c) Light field scattered from cylinder C 1 concentrically covered with paper, which increases the surface roughness and destroys the anisotropy observed in Fig. 4(a). Note the difference with respect to (a) and (b). In this photograph the speckle dimensions are the same in all directions.

Fig. 6
Fig. 6

(a) Global photograph of the light field scattered from cylinder C 2. (b) Enlarged detail of a region of the light field in (a). As in Figs. 5(a) and 5(b), the light speckles are elongated in the horizontal direction. (c) Photograph of the light field scattered from cylinder C 2 concentrically covered with paper. Note the difference with respect to (a). As in Fig. 5(c) the speckle dimensions are the same in all directions.

Equations (8)

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

g=λL/D.
d=2L tanθ/2
gd=λL/d.
tanθ2-2α=d2L-R cos α,
sin α=d/2R,
sinθ/4 < D/2R.
gl=λLd=λL2R sinθ/4.
r=glgw=D2R sinθ/4,

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