Abstract

A new approach for determining the roughness of engineering surfaces that is applicable to industrial in-process measurements is introduced. Laser speckle patterns, arising from light scattered from rough surfaces that are illuminated by polychromatic laser light, are detected in the far-field region. The incoherent superposition of these light intensities and the angular dispersion cause the effect of speckle elongation. This is characterized by increasing speckle widths and leads to a radial structure of the speckle patterns. With increasing surface roughness, the elongation is replaced more and more by the decorrelation of the monochromatic speckle patterns for the different wavelengths. Such effects were detected with the CCD technique and analyzed by local autocorrelation functions of intensity fluctuations that were calculated for different areas of the speckle patterns. The results of surface-roughness determination by means of the speckle elongation effect are presented.

© 1997 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. T. V. Vorburger, E. C. Teague, “Optical techniques for on-line measurement of surface topography,” Precis. Eng. 3, 61–83 (1981).
    [CrossRef]
  2. J. M. Bennett, L. Mattsson, Introduction to Surface Roughness and Scattering (Optical Society of America, Washington, D.C., 1989), pp. 24–31
  3. R. Brodmann, G. Thurn, “Roughness measurement of ground, turned and shot-peened surfaces by the light scattering method,” Wear 109, 1–13 (1986).
    [CrossRef]
  4. U. Persson, “Roughness measurement by means of the speckle technique in the visible and infrared regions,” Opt. Eng. 32, 3327–3332 (1993).
    [CrossRef]
  5. L. Cuthbert, V. M. Huynh, “Statistical analysis of Fourier transform patterns for surface texture assessment,” Meas. Sci. Technol. 3, 740–745 (1992).
    [CrossRef]
  6. J. C. Dainty, “Introduction,” in Laser Speckle and Related Phenomena, J. C. Dainty, ed., Vol. 9 of Springer Series in Topics in Applied Physics (Springer-Verlag, Berlin, 1975), Chap. 1, pp. 1–7.
  7. G. Parry, “Some effects of surface roughness on the appearence of speckle in polychromatic light,” Opt. Commun. 12, 75–78 (1974).
    [CrossRef]
  8. G. Bitz, Verfahren zur Bestimmung von Rauheitskenngrössen durch Specklekorrelation (Fortschritt-Berichte VDI, VDI-Verlag, Düsseldorf, 1982), Series 8, Number 47, Chap. 4, 5, pp. 25–59.
  9. B. Ruffing, “Berührungslose Messung technischer Oberflächen mit Speckle-Korrelationsverfahren,” Ph.D. dissertation (Universität Karlsruhe, Karlsruhe, Germany, 1987), Chap. 3, pp. 44–59.
  10. P. Lehmann, Untersuchungen zur Lichtstreuung an technischen Oberflächen im Hinblick auf eine prozessgekoppelte laser-optische Rauheitsmessung (Fortschritt-Berichte VDI, VDI-Verlag, Düsseldorf, 1995), Series 8, Number 463, Chap. 7, pp. 103–108.
  11. C. T. Stansberg, “Surface roughness measurements by means of polychromatic speckle patterns,” Appl. Opt. 18, 4051–4060 (1979).
    [CrossRef] [PubMed]
  12. Ref. 10, Chap. 8, pp. 130–148.
  13. J. A. Ogilvy, Theory of Wave Scattering from Random Rough Surfaces (Hilger, Bristol, 1991), Chap. 4, pp. 100–117.
  14. Ref. 13, Chap. 4, pp. 74–85.
  15. P. Beckmann, A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, Oxford1963), Chap. 3, pp. 15–33.
  16. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), Chap. 5, pp. 77–89.
  17. Ref. 10, Chap. 2, pp. 8–31.
  18. A. Papoulis, Probability, Random Variables and Stochastic Processes (McGraw-Hill, New York, 1965), Chap. 8, pp. 263–264.
  19. Ref. 18, Chap. 8, pp. 266–267.
  20. J. W. Goodman, “Statistical properties of laser speckle,” in Laser Speckle and Related Phenomena, J. C. Dainty, ed., Vol. 9 of Springer Series in Topics in Applied Physics (Springer-Verlag, Berlin, 1975), Chap. 2, pp. 20–21.
  21. J. W. Goodman, Statistical Optics (Wiley, New York, 1985), Chap. 2, pp. 40–44.
  22. Ref. 18, Chap. 8, p. 254.
  23. Ref. 15, Chap. 5, p. 81.
  24. Ref. 13, Chap. 2, pp. 12–17.
  25. Ref. 8, Chap. 4, pp. 48–50.
  26. Ref. 10, Chap. 6, pp. 96–97.
  27. Ref. 10, Chap. 7, pp. 108–123.
  28. J. Peters, P. Lehmann, A. Schöne, “Specklekorrelation mit einem dichromatischen Fouriertransformationssystem,” in Laser in der Technik, W. Waidelich, ed. (Springer-Verlag, Berlin, 1994), pp. 184–189.
  29. Q. B. Li, F. P. Chiang, “Three-dimensional dimension of laser speckle,” Appl. Optics 31, 6287–6291 (1992).
    [CrossRef]
  30. Y. Tomita, K. Nakagawa, T. Asakura, “Fibrous radial structure of speckle patterns in polychromatic light,” Appl. Opt. 19, 3211–3218 (1980).
    [CrossRef] [PubMed]
  31. H. M. Pedersen, “Second order statistics of light diffracted from Gaussian, rough surfaces with applications to the roughness dependence of speckles,” Opt. Acta 22, 523–535 (1975).
    [CrossRef]
  32. Ref. 16, Chap. 4, pp. 59–61.
  33. Ref. 10, Chap. 2, pp. 28–29.
  34. J. Peklenik, “Neue statistische Verfahren zur topographischen Erfassung von Oberflächen. 2. Teil,” WT Z. Ind. Fertigung 59, 633–637 (1969).

1993

U. Persson, “Roughness measurement by means of the speckle technique in the visible and infrared regions,” Opt. Eng. 32, 3327–3332 (1993).
[CrossRef]

1992

L. Cuthbert, V. M. Huynh, “Statistical analysis of Fourier transform patterns for surface texture assessment,” Meas. Sci. Technol. 3, 740–745 (1992).
[CrossRef]

Q. B. Li, F. P. Chiang, “Three-dimensional dimension of laser speckle,” Appl. Optics 31, 6287–6291 (1992).
[CrossRef]

1986

R. Brodmann, G. Thurn, “Roughness measurement of ground, turned and shot-peened surfaces by the light scattering method,” Wear 109, 1–13 (1986).
[CrossRef]

1981

T. V. Vorburger, E. C. Teague, “Optical techniques for on-line measurement of surface topography,” Precis. Eng. 3, 61–83 (1981).
[CrossRef]

1980

1979

1975

H. M. Pedersen, “Second order statistics of light diffracted from Gaussian, rough surfaces with applications to the roughness dependence of speckles,” Opt. Acta 22, 523–535 (1975).
[CrossRef]

1974

G. Parry, “Some effects of surface roughness on the appearence of speckle in polychromatic light,” Opt. Commun. 12, 75–78 (1974).
[CrossRef]

1969

J. Peklenik, “Neue statistische Verfahren zur topographischen Erfassung von Oberflächen. 2. Teil,” WT Z. Ind. Fertigung 59, 633–637 (1969).

Asakura, T.

Beckmann, P.

P. Beckmann, A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, Oxford1963), Chap. 3, pp. 15–33.

Bennett, J. M.

J. M. Bennett, L. Mattsson, Introduction to Surface Roughness and Scattering (Optical Society of America, Washington, D.C., 1989), pp. 24–31

Bitz, G.

G. Bitz, Verfahren zur Bestimmung von Rauheitskenngrössen durch Specklekorrelation (Fortschritt-Berichte VDI, VDI-Verlag, Düsseldorf, 1982), Series 8, Number 47, Chap. 4, 5, pp. 25–59.

Brodmann, R.

R. Brodmann, G. Thurn, “Roughness measurement of ground, turned and shot-peened surfaces by the light scattering method,” Wear 109, 1–13 (1986).
[CrossRef]

Chiang, F. P.

Q. B. Li, F. P. Chiang, “Three-dimensional dimension of laser speckle,” Appl. Optics 31, 6287–6291 (1992).
[CrossRef]

Cuthbert, L.

L. Cuthbert, V. M. Huynh, “Statistical analysis of Fourier transform patterns for surface texture assessment,” Meas. Sci. Technol. 3, 740–745 (1992).
[CrossRef]

Dainty, J. C.

J. C. Dainty, “Introduction,” in Laser Speckle and Related Phenomena, J. C. Dainty, ed., Vol. 9 of Springer Series in Topics in Applied Physics (Springer-Verlag, Berlin, 1975), Chap. 1, pp. 1–7.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), Chap. 5, pp. 77–89.

J. W. Goodman, “Statistical properties of laser speckle,” in Laser Speckle and Related Phenomena, J. C. Dainty, ed., Vol. 9 of Springer Series in Topics in Applied Physics (Springer-Verlag, Berlin, 1975), Chap. 2, pp. 20–21.

J. W. Goodman, Statistical Optics (Wiley, New York, 1985), Chap. 2, pp. 40–44.

Huynh, V. M.

L. Cuthbert, V. M. Huynh, “Statistical analysis of Fourier transform patterns for surface texture assessment,” Meas. Sci. Technol. 3, 740–745 (1992).
[CrossRef]

Lehmann, P.

P. Lehmann, Untersuchungen zur Lichtstreuung an technischen Oberflächen im Hinblick auf eine prozessgekoppelte laser-optische Rauheitsmessung (Fortschritt-Berichte VDI, VDI-Verlag, Düsseldorf, 1995), Series 8, Number 463, Chap. 7, pp. 103–108.

J. Peters, P. Lehmann, A. Schöne, “Specklekorrelation mit einem dichromatischen Fouriertransformationssystem,” in Laser in der Technik, W. Waidelich, ed. (Springer-Verlag, Berlin, 1994), pp. 184–189.

Li, Q. B.

Q. B. Li, F. P. Chiang, “Three-dimensional dimension of laser speckle,” Appl. Optics 31, 6287–6291 (1992).
[CrossRef]

Mattsson, L.

J. M. Bennett, L. Mattsson, Introduction to Surface Roughness and Scattering (Optical Society of America, Washington, D.C., 1989), pp. 24–31

Nakagawa, K.

Ogilvy, J. A.

J. A. Ogilvy, Theory of Wave Scattering from Random Rough Surfaces (Hilger, Bristol, 1991), Chap. 4, pp. 100–117.

Papoulis, A.

A. Papoulis, Probability, Random Variables and Stochastic Processes (McGraw-Hill, New York, 1965), Chap. 8, pp. 263–264.

Parry, G.

G. Parry, “Some effects of surface roughness on the appearence of speckle in polychromatic light,” Opt. Commun. 12, 75–78 (1974).
[CrossRef]

Pedersen, H. M.

H. M. Pedersen, “Second order statistics of light diffracted from Gaussian, rough surfaces with applications to the roughness dependence of speckles,” Opt. Acta 22, 523–535 (1975).
[CrossRef]

Peklenik, J.

J. Peklenik, “Neue statistische Verfahren zur topographischen Erfassung von Oberflächen. 2. Teil,” WT Z. Ind. Fertigung 59, 633–637 (1969).

Persson, U.

U. Persson, “Roughness measurement by means of the speckle technique in the visible and infrared regions,” Opt. Eng. 32, 3327–3332 (1993).
[CrossRef]

Peters, J.

J. Peters, P. Lehmann, A. Schöne, “Specklekorrelation mit einem dichromatischen Fouriertransformationssystem,” in Laser in der Technik, W. Waidelich, ed. (Springer-Verlag, Berlin, 1994), pp. 184–189.

Ruffing, B.

B. Ruffing, “Berührungslose Messung technischer Oberflächen mit Speckle-Korrelationsverfahren,” Ph.D. dissertation (Universität Karlsruhe, Karlsruhe, Germany, 1987), Chap. 3, pp. 44–59.

Schöne, A.

J. Peters, P. Lehmann, A. Schöne, “Specklekorrelation mit einem dichromatischen Fouriertransformationssystem,” in Laser in der Technik, W. Waidelich, ed. (Springer-Verlag, Berlin, 1994), pp. 184–189.

Spizzichino, A.

P. Beckmann, A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, Oxford1963), Chap. 3, pp. 15–33.

Stansberg, C. T.

Teague, E. C.

T. V. Vorburger, E. C. Teague, “Optical techniques for on-line measurement of surface topography,” Precis. Eng. 3, 61–83 (1981).
[CrossRef]

Thurn, G.

R. Brodmann, G. Thurn, “Roughness measurement of ground, turned and shot-peened surfaces by the light scattering method,” Wear 109, 1–13 (1986).
[CrossRef]

Tomita, Y.

Vorburger, T. V.

T. V. Vorburger, E. C. Teague, “Optical techniques for on-line measurement of surface topography,” Precis. Eng. 3, 61–83 (1981).
[CrossRef]

Appl. Opt.

Appl. Optics

Q. B. Li, F. P. Chiang, “Three-dimensional dimension of laser speckle,” Appl. Optics 31, 6287–6291 (1992).
[CrossRef]

Meas. Sci. Technol.

L. Cuthbert, V. M. Huynh, “Statistical analysis of Fourier transform patterns for surface texture assessment,” Meas. Sci. Technol. 3, 740–745 (1992).
[CrossRef]

Opt. Acta

H. M. Pedersen, “Second order statistics of light diffracted from Gaussian, rough surfaces with applications to the roughness dependence of speckles,” Opt. Acta 22, 523–535 (1975).
[CrossRef]

Opt. Commun.

G. Parry, “Some effects of surface roughness on the appearence of speckle in polychromatic light,” Opt. Commun. 12, 75–78 (1974).
[CrossRef]

Opt. Eng.

U. Persson, “Roughness measurement by means of the speckle technique in the visible and infrared regions,” Opt. Eng. 32, 3327–3332 (1993).
[CrossRef]

Precis. Eng.

T. V. Vorburger, E. C. Teague, “Optical techniques for on-line measurement of surface topography,” Precis. Eng. 3, 61–83 (1981).
[CrossRef]

Wear

R. Brodmann, G. Thurn, “Roughness measurement of ground, turned and shot-peened surfaces by the light scattering method,” Wear 109, 1–13 (1986).
[CrossRef]

WT Z. Ind. Fertigung

J. Peklenik, “Neue statistische Verfahren zur topographischen Erfassung von Oberflächen. 2. Teil,” WT Z. Ind. Fertigung 59, 633–637 (1969).

Other

J. C. Dainty, “Introduction,” in Laser Speckle and Related Phenomena, J. C. Dainty, ed., Vol. 9 of Springer Series in Topics in Applied Physics (Springer-Verlag, Berlin, 1975), Chap. 1, pp. 1–7.

Ref. 16, Chap. 4, pp. 59–61.

Ref. 10, Chap. 2, pp. 28–29.

J. M. Bennett, L. Mattsson, Introduction to Surface Roughness and Scattering (Optical Society of America, Washington, D.C., 1989), pp. 24–31

G. Bitz, Verfahren zur Bestimmung von Rauheitskenngrössen durch Specklekorrelation (Fortschritt-Berichte VDI, VDI-Verlag, Düsseldorf, 1982), Series 8, Number 47, Chap. 4, 5, pp. 25–59.

B. Ruffing, “Berührungslose Messung technischer Oberflächen mit Speckle-Korrelationsverfahren,” Ph.D. dissertation (Universität Karlsruhe, Karlsruhe, Germany, 1987), Chap. 3, pp. 44–59.

P. Lehmann, Untersuchungen zur Lichtstreuung an technischen Oberflächen im Hinblick auf eine prozessgekoppelte laser-optische Rauheitsmessung (Fortschritt-Berichte VDI, VDI-Verlag, Düsseldorf, 1995), Series 8, Number 463, Chap. 7, pp. 103–108.

Ref. 10, Chap. 8, pp. 130–148.

J. A. Ogilvy, Theory of Wave Scattering from Random Rough Surfaces (Hilger, Bristol, 1991), Chap. 4, pp. 100–117.

Ref. 13, Chap. 4, pp. 74–85.

P. Beckmann, A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, Oxford1963), Chap. 3, pp. 15–33.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), Chap. 5, pp. 77–89.

Ref. 10, Chap. 2, pp. 8–31.

A. Papoulis, Probability, Random Variables and Stochastic Processes (McGraw-Hill, New York, 1965), Chap. 8, pp. 263–264.

Ref. 18, Chap. 8, pp. 266–267.

J. W. Goodman, “Statistical properties of laser speckle,” in Laser Speckle and Related Phenomena, J. C. Dainty, ed., Vol. 9 of Springer Series in Topics in Applied Physics (Springer-Verlag, Berlin, 1975), Chap. 2, pp. 20–21.

J. W. Goodman, Statistical Optics (Wiley, New York, 1985), Chap. 2, pp. 40–44.

Ref. 18, Chap. 8, p. 254.

Ref. 15, Chap. 5, p. 81.

Ref. 13, Chap. 2, pp. 12–17.

Ref. 8, Chap. 4, pp. 48–50.

Ref. 10, Chap. 6, pp. 96–97.

Ref. 10, Chap. 7, pp. 108–123.

J. Peters, P. Lehmann, A. Schöne, “Specklekorrelation mit einem dichromatischen Fouriertransformationssystem,” in Laser in der Technik, W. Waidelich, ed. (Springer-Verlag, Berlin, 1994), pp. 184–189.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (9)

Fig. 1
Fig. 1

Photograph of a dichromatic speckle pattern (wavelength combination 488 and 514 nm) produced by the scattering of light of an argon laser from a ground metallic surface of 0.5-µm rms roughness.

Fig. 2
Fig. 2

Scattering geometry with angle of incidence Θe, scattering angle Θs, and the corresponding wave vectors ke and ks.

Fig. 3
Fig. 3

Geometric arrangement with the Fourier-transform properties of a lens.

Fig. 4
Fig. 4

Simulated far-field speckle intensity curves for several wavelengths of laser light assuming 1-mm beam diameter, perpendicular incidence, and (a) 0.1-µm rms roughness or (b) 1.25-µm rms roughness.

Fig. 5
Fig. 5

Theoretical results of the normalized speckle elongation for different wavelength combinations, depending on the ξ coordinate in the focal plane of a Fourier-transform lens.

Fig. 6
Fig. 6

Optical setup for generating, detecting, and evaluating polychromatic speckle patterns.

Fig. 7
Fig. 7

Optical setup for coupling two beams of laser diodes emitting different light wavelengths (e.g., 650 and 670 nm).

Fig. 8
Fig. 8

(a) Dichromatic far-field speckle pattern (negative image) of a ground surface of 0.5-µm rms roughness (beam diameter 1.5 mm, lens focal length 150 mm, wavelength combination 650 and 670 nm), (b) autocorrelation widths belonging to the image segments indicated in (a).

Fig. 9
Fig. 9

Experimental results representing the roughness dependence of the mean autocorrelation width when an argon-ion laser is used for polychromatic surface illumination.

Tables (1)

Tables Icon

Table 1 Results of Rough Surface Classification (Sample: Rugotest 104)

Equations (23)

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

umξ, η=-RFΘecos Θs+cos Θe8LxLy cos Θe×-+-+wx, yexp-ivxmx+vymy+vzmhx, ydxdy,
wx, y=4/πexp-x2/Lx2+y2/Ly2,
vxm=kmsin Θs-sin Θe+ξfcos Θs,
vym=kmη/f,
vzm=kmcos Θs+cos Θe.
umξ=-RFΘeπLx-+exp-x2/Lx2exp-ivxmx+vzmhxdx.
ρ12=I1-I1I2-I2I1-I12I2-I221/2=I1I2-I1I2I12-I121/2I22-I221/2,
I1I2=u1u2*2+u1u1*u2u2*, Im2=2Im2, m 1, 2.
ρ12=u1u2*2u1u1*u2u2*.
umun*=RF2πLx2-+exp-xm2+xn2/Lx2×exp-ivxmxm-vxnxn×exp-ivzmhm-vznhndxmdxn.
exp-ivzmhm-vznhn=exp-12σh2vzm2-2vzmvznρhxm-xn+vzn2=exp-12σh2vzm-vzn2exp-σh2vzmvzn1-ρhxm-xn,
ρhΔxexp-Δx/Λk21-ΔxΛk2 for ΔxΛk.
umun*=RF2exp-12σh2vzm-vzn2πLx2-+×exp-xm2+xn2Lx2exp-ivxmxm-vxnxn×exp-σh2vzmvznxm-xn2Λk2dxmdxn=RF2 exp[-12σh2vzm-vzn21+2σh2vzmvznLx2/Λk21/2×exp-vxm-vxn2Lx28×exp-vxm+vxn2Lx281+2vxmvxnσhLx/Λk2.
1+2σh2vzmvznLx2/Λk21/2σhLxΛk2vzmvzn1/2.
ρmnexp-σh2vzm-vzn2exp-vxm-vxn2Lx24, m, n 1, 2.
σh=-ln ρ121/2vz1-vz2.
ρΔIξ1, ξ2=ΔIξ1ΔIξ2ΔI2ξ1ΔI2ξ21/2.
ρmn=ρmnξ1, ξ2; km, kn=umξ1; kmun*ξ2; kn2umξ1; km2unξ2; kn2,
Iξ=j=1NkIξ, kj=j=1Nkujξ, kj2
ρΔIξ1, ξ2=m=1Nkn=1NkSmSnρmnξ1, ξ2; km, knm=1Nkn=1NkSmSnρmnξ1, ξ1; km, kn1/2m=1Nkn=1NkSmSnρmnξ2, ξ2; km, kn1/2
Sm=Iξ, km/Iξ, Sn=Iξ, kn/Iξ,
ρmnξ1, ξ2; km, kn=exp-σh24 cos2 Θekm-kn2×exp-Lx2 cos2 Θe4f2kmξ1-knξ22.
ρΔIξ1, ξ2=m=1Nkn=1NkSmSn exp-σh24 cos2 Θekm-kn2exp-Lx2 cos2 Θe4f2kmξ1-knξ22j=12m=1Nkn=1NkSmSn exp-σh24 cos2 Θekm-kn2exp-Lx2 cos2 Θe4f2ξj2km-kn21/2.

Metrics