Abstract

Here polychromatic speckle patterns generated either by a polychromatic light source that emits at discrete frequencies or by a light source showing a continuous narrow-band spectral distribution are studied. The purpose here is the application of polychromatic speckle-pattern analysis to an in-process surface roughness characterization. To compare the coherence properties of the different polychromatic light sources, first a modified definition of the coherence length is introduced. Furthermore, the relevant optical phenomena, namely, the speckle elongation caused by the angular dispersion and the roughness-dependent speckle decorrelation, are summarized. It is shown that light sources with a continuous spectral distribution have essential advantages in comparison with discrete wavelength sources. The theoretical results are confirmed by experimental investigations based on a digital algorithm for the evaluation of CCD images of polychromatic speckle patterns, which are recorded in the Fourier plane of a Fourier-transforming lens.

© 2002 Optical Society of America

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References

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  1. J. M. Bennett, L. Mattson, Introduction to Surface Roughness and Scattering, 2nd ed. (Optical Society of America, Washington, D.C., 1999), Chap. 3.
  2. T. V. Vorburger, E. C. Teague, “Optical techniques for an on-line measurement of surface topography,” Proc. Eng. 3, 61–83 (1981).
    [CrossRef]
  3. J. C. Dainty, “The statistics of speckle patterns,” Prog. Opt. 14, 1–46 (1974).
  4. G. Parry, “Some effects of surface roughness on the appearance of speckle in polychromatic light,” Opt. Commun. 12, 75–80 (1974).
    [CrossRef]
  5. H. M. Pedersen, “Second order statistics of light diffracted from gaussian, rough surfaces with application to the roughness dependence of speckles,” Opt. Acta 22, 523–535 (1975).
    [CrossRef]
  6. P. Lehmann, S. Patzelt, A. Schoene, “Surface roughness measurement by means of polychromatic speckle elongation,” Appl. Opt. 36, 2188–2197 (1997).
    [CrossRef] [PubMed]
  7. P. Lehmann, S. Patzelt, A. Ciossek, “In-process Charakterisierug von Mikrotopographien technischer Oberflaechen durch polychromatische Speckle-Autokorrelation,” Tech. Messen 66, 269–276 (1999).
  8. Y. Tomita, K. Nakagawa, T. Asakura, “Fibrous radial structure of speckle patterns in polychromatic light,” Appl. Opt. 19, 3211–3218 (1980).
    [CrossRef] [PubMed]
  9. J. Peters, “Messung des Mittenrauhwerts zylindrischer Teile waehrend des Schleifens,” VDI-Berichte 90, 27–31 (1965).
  10. R. Brodmann, T. Gast, G. Thurn, “An optical instrument for measuring the surface roughness in production control,” CIRP Ann. 33, 403–406 (1984).
    [CrossRef]
  11. R. Brodmann, O. Gersdorfer, G. Thurn, “Optical roughness measuring instrument for fine-machined surfaces,” Opt. Eng. 24, 408–413 (1985).
    [CrossRef]
  12. C. S. Lee, S. W. Kim, D. Y. Yim, “An in-process measurement technique using laser for non-contact monitoring of surface roughness and form accuracy,” CIRP Ann. 36, 425–428 (1987).
    [CrossRef]
  13. P. Lehmann, G. Goch, “Comparison of conventional light scattering and speckle techniques concerning an in-process characterisation of surface topography,” CIRP Ann. 48, 419–422 (1999).
  14. J. Peters, P. Vanherck, M. Sastrodinoto, “Assessment of surface typology analysis techniques,” CIRP Ann. 28, 539–554 (1979).
  15. M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge University, New York, 1999), p. 606.
  16. L. Mandel, “Fluctuations of light beams,”Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam1963), Vol. 2, pp. 181–247.
    [CrossRef]
  17. G. Parry, “Speckle patterns in partially coherent light,” in Laser Speckle and Related Phenomena, J. C. Dainty, ed. (Springer-Verlag, Berlin, 1975), pp. 78–122.

1999

P. Lehmann, G. Goch, “Comparison of conventional light scattering and speckle techniques concerning an in-process characterisation of surface topography,” CIRP Ann. 48, 419–422 (1999).

P. Lehmann, S. Patzelt, A. Ciossek, “In-process Charakterisierug von Mikrotopographien technischer Oberflaechen durch polychromatische Speckle-Autokorrelation,” Tech. Messen 66, 269–276 (1999).

1997

1987

C. S. Lee, S. W. Kim, D. Y. Yim, “An in-process measurement technique using laser for non-contact monitoring of surface roughness and form accuracy,” CIRP Ann. 36, 425–428 (1987).
[CrossRef]

1985

R. Brodmann, O. Gersdorfer, G. Thurn, “Optical roughness measuring instrument for fine-machined surfaces,” Opt. Eng. 24, 408–413 (1985).
[CrossRef]

1984

R. Brodmann, T. Gast, G. Thurn, “An optical instrument for measuring the surface roughness in production control,” CIRP Ann. 33, 403–406 (1984).
[CrossRef]

1981

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

1980

1979

J. Peters, P. Vanherck, M. Sastrodinoto, “Assessment of surface typology analysis techniques,” CIRP Ann. 28, 539–554 (1979).

1975

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

1974

J. C. Dainty, “The statistics of speckle patterns,” Prog. Opt. 14, 1–46 (1974).

G. Parry, “Some effects of surface roughness on the appearance of speckle in polychromatic light,” Opt. Commun. 12, 75–80 (1974).
[CrossRef]

1965

J. Peters, “Messung des Mittenrauhwerts zylindrischer Teile waehrend des Schleifens,” VDI-Berichte 90, 27–31 (1965).

Asakura, T.

Bennett, J. M.

J. M. Bennett, L. Mattson, Introduction to Surface Roughness and Scattering, 2nd ed. (Optical Society of America, Washington, D.C., 1999), Chap. 3.

Born, M.

M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge University, New York, 1999), p. 606.

Brodmann, R.

R. Brodmann, O. Gersdorfer, G. Thurn, “Optical roughness measuring instrument for fine-machined surfaces,” Opt. Eng. 24, 408–413 (1985).
[CrossRef]

R. Brodmann, T. Gast, G. Thurn, “An optical instrument for measuring the surface roughness in production control,” CIRP Ann. 33, 403–406 (1984).
[CrossRef]

Ciossek, A.

P. Lehmann, S. Patzelt, A. Ciossek, “In-process Charakterisierug von Mikrotopographien technischer Oberflaechen durch polychromatische Speckle-Autokorrelation,” Tech. Messen 66, 269–276 (1999).

Dainty, J. C.

J. C. Dainty, “The statistics of speckle patterns,” Prog. Opt. 14, 1–46 (1974).

Gast, T.

R. Brodmann, T. Gast, G. Thurn, “An optical instrument for measuring the surface roughness in production control,” CIRP Ann. 33, 403–406 (1984).
[CrossRef]

Gersdorfer, O.

R. Brodmann, O. Gersdorfer, G. Thurn, “Optical roughness measuring instrument for fine-machined surfaces,” Opt. Eng. 24, 408–413 (1985).
[CrossRef]

Goch, G.

P. Lehmann, G. Goch, “Comparison of conventional light scattering and speckle techniques concerning an in-process characterisation of surface topography,” CIRP Ann. 48, 419–422 (1999).

Kim, S. W.

C. S. Lee, S. W. Kim, D. Y. Yim, “An in-process measurement technique using laser for non-contact monitoring of surface roughness and form accuracy,” CIRP Ann. 36, 425–428 (1987).
[CrossRef]

Lee, C. S.

C. S. Lee, S. W. Kim, D. Y. Yim, “An in-process measurement technique using laser for non-contact monitoring of surface roughness and form accuracy,” CIRP Ann. 36, 425–428 (1987).
[CrossRef]

Lehmann, P.

P. Lehmann, G. Goch, “Comparison of conventional light scattering and speckle techniques concerning an in-process characterisation of surface topography,” CIRP Ann. 48, 419–422 (1999).

P. Lehmann, S. Patzelt, A. Ciossek, “In-process Charakterisierug von Mikrotopographien technischer Oberflaechen durch polychromatische Speckle-Autokorrelation,” Tech. Messen 66, 269–276 (1999).

P. Lehmann, S. Patzelt, A. Schoene, “Surface roughness measurement by means of polychromatic speckle elongation,” Appl. Opt. 36, 2188–2197 (1997).
[CrossRef] [PubMed]

Mandel, L.

L. Mandel, “Fluctuations of light beams,”Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam1963), Vol. 2, pp. 181–247.
[CrossRef]

Mattson, L.

J. M. Bennett, L. Mattson, Introduction to Surface Roughness and Scattering, 2nd ed. (Optical Society of America, Washington, D.C., 1999), Chap. 3.

Nakagawa, K.

Parry, G.

G. Parry, “Some effects of surface roughness on the appearance of speckle in polychromatic light,” Opt. Commun. 12, 75–80 (1974).
[CrossRef]

G. Parry, “Speckle patterns in partially coherent light,” in Laser Speckle and Related Phenomena, J. C. Dainty, ed. (Springer-Verlag, Berlin, 1975), pp. 78–122.

Patzelt, S.

P. Lehmann, S. Patzelt, A. Ciossek, “In-process Charakterisierug von Mikrotopographien technischer Oberflaechen durch polychromatische Speckle-Autokorrelation,” Tech. Messen 66, 269–276 (1999).

P. Lehmann, S. Patzelt, A. Schoene, “Surface roughness measurement by means of polychromatic speckle elongation,” Appl. Opt. 36, 2188–2197 (1997).
[CrossRef] [PubMed]

Pedersen, H. M.

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

Peters, J.

J. Peters, P. Vanherck, M. Sastrodinoto, “Assessment of surface typology analysis techniques,” CIRP Ann. 28, 539–554 (1979).

J. Peters, “Messung des Mittenrauhwerts zylindrischer Teile waehrend des Schleifens,” VDI-Berichte 90, 27–31 (1965).

Sastrodinoto, M.

J. Peters, P. Vanherck, M. Sastrodinoto, “Assessment of surface typology analysis techniques,” CIRP Ann. 28, 539–554 (1979).

Schoene, A.

Teague, E. C.

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

Thurn, G.

R. Brodmann, O. Gersdorfer, G. Thurn, “Optical roughness measuring instrument for fine-machined surfaces,” Opt. Eng. 24, 408–413 (1985).
[CrossRef]

R. Brodmann, T. Gast, G. Thurn, “An optical instrument for measuring the surface roughness in production control,” CIRP Ann. 33, 403–406 (1984).
[CrossRef]

Tomita, Y.

Vanherck, P.

J. Peters, P. Vanherck, M. Sastrodinoto, “Assessment of surface typology analysis techniques,” CIRP Ann. 28, 539–554 (1979).

Vorburger, T. V.

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

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge University, New York, 1999), p. 606.

Yim, D. Y.

C. S. Lee, S. W. Kim, D. Y. Yim, “An in-process measurement technique using laser for non-contact monitoring of surface roughness and form accuracy,” CIRP Ann. 36, 425–428 (1987).
[CrossRef]

Appl. Opt.

CIRP Ann.

C. S. Lee, S. W. Kim, D. Y. Yim, “An in-process measurement technique using laser for non-contact monitoring of surface roughness and form accuracy,” CIRP Ann. 36, 425–428 (1987).
[CrossRef]

P. Lehmann, G. Goch, “Comparison of conventional light scattering and speckle techniques concerning an in-process characterisation of surface topography,” CIRP Ann. 48, 419–422 (1999).

J. Peters, P. Vanherck, M. Sastrodinoto, “Assessment of surface typology analysis techniques,” CIRP Ann. 28, 539–554 (1979).

R. Brodmann, T. Gast, G. Thurn, “An optical instrument for measuring the surface roughness in production control,” CIRP Ann. 33, 403–406 (1984).
[CrossRef]

Opt. Acta

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

Opt. Commun.

G. Parry, “Some effects of surface roughness on the appearance of speckle in polychromatic light,” Opt. Commun. 12, 75–80 (1974).
[CrossRef]

Opt. Eng.

R. Brodmann, O. Gersdorfer, G. Thurn, “Optical roughness measuring instrument for fine-machined surfaces,” Opt. Eng. 24, 408–413 (1985).
[CrossRef]

Proc. Eng.

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

Prog. Opt.

J. C. Dainty, “The statistics of speckle patterns,” Prog. Opt. 14, 1–46 (1974).

Tech. Messen

P. Lehmann, S. Patzelt, A. Ciossek, “In-process Charakterisierug von Mikrotopographien technischer Oberflaechen durch polychromatische Speckle-Autokorrelation,” Tech. Messen 66, 269–276 (1999).

VDI-Berichte

J. Peters, “Messung des Mittenrauhwerts zylindrischer Teile waehrend des Schleifens,” VDI-Berichte 90, 27–31 (1965).

Other

M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge University, New York, 1999), p. 606.

L. Mandel, “Fluctuations of light beams,”Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam1963), Vol. 2, pp. 181–247.
[CrossRef]

G. Parry, “Speckle patterns in partially coherent light,” in Laser Speckle and Related Phenomena, J. C. Dainty, ed. (Springer-Verlag, Berlin, 1975), pp. 78–122.

J. M. Bennett, L. Mattson, Introduction to Surface Roughness and Scattering, 2nd ed. (Optical Society of America, Washington, D.C., 1999), Chap. 3.

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Figures (9)

Fig. 1
Fig. 1

Experimental arrangement for the generation and evaluation of polychromatic speckle patterns.

Fig. 2
Fig. 2

(a) Spectral intensity distribution of a trichromatic laser source. (b) Spectral intensity distribution of a SLD operated at a total optical output power P of 0.5 and 0.1 mW.

Fig. 3
Fig. 3

Theoretical results showing the roughness dependence of the speckle elongation effect, assuming λ̅ = 810 nm, Δl = 6 µm, beam diameter 2L x = 2L y = 2 mm. (a) Trichromatic light source. (b) Light source with Gaussian spectral distribution.

Fig. 4
Fig. 4

(a) Trichromatic speckle pattern (768 × 576 pixels) obtained from an EDM surface with Ra = 0.4 µm recorded by a CCD array in the Fourier plane of an f = 50 mm double convex lens. (b) Polychromatic speckle pattern obtained from the same surface by use of a SLD showing a continuous narrow-band spectral distribution.

Fig. 5
Fig. 5

Subareas (128 × 128 pixels) of the speckle pattern shown in Fig. 4(b): In area A the speckles are nearly circular, in area B1 the speckle elongation occurs in the x direction, and in area B2 the speckle elongation occurs in the y direction.

Fig. 6
Fig. 6

Contour plots of two-dimensional autocorrelation functions for the speckle intensities according to Fig. 5: (a) area A, (b) area B1, (c) area B2.

Fig. 7
Fig. 7

Dependence of the squared aspect ratio of speckle diameters on the position of the area under evaluation for the two speckle patterns (a) of Fig. 4(a) and (b) of Fig. 4(b).

Fig. 8
Fig. 8

(a) Polychromatic speckle pattern obtained under the same conditions as Fig. 4(b) but from a rougher surface (Ra = 6.4 µm). (b) Corresponding dependence of the squared aspect ratio of speckle diameters on the position of the area under evaluation.

Fig. 9
Fig. 9

Experimental results of the roughness characterization of EDM samples (Rugotest 107) obtained by use of (a) a trichromatic light source (λ1 = 672 nm, λ2 = 678 nm, λ3 = 689 nm) and (b) a SLD at different coherence lengths depending on the output power P (the error bars represent the standard deviation of five measurements at different areas of the same sample).

Equations (26)

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

Δτ2=-+ τ2|Γτ|2dτ-+ |Γτ|2dτ,
Γτ=UtU*t+τ=-+ Sνexpi2πντdν.
Sν=exp-ν-ν¯22σν2
Δτ=12π2σν.
Sν=n=1Nk snδν-νn,n=1Nk sn=1,
ΓτΓ*τ=n=1Nk sn expi2πνnτ×n=1Nk sn exp-i2πνnτ.
ΓτΓ*τ=1+cos2πτν1-ν2+cos2πτν1-ν3+cos2πτν2-ν3
Δτ-2=2τ2γτ2τ=0.
Δτ=38π2ν1-ν22+8π2ν1-ν32+8π2ν2-ν32-1/2
Δl=λ¯2ln21/2πΔλ,
Δl=λ¯232πΔλ,
γΔIξ1, ξ2=ΔI ξ1ΔI ξ2ΔI2ξ1 ΔI2ξ21/2,
ΓΔIξ1, ξ2=ΔI ξ1ΔI ξ2Iξ1 Iξ2=γΔIξ1, ξ2ΔI2ξ11/2Iξ1ΔI2ξ21/2Iξ2
=γΔIξ1, ξ2ΓΔIξ1, ξ11/2ΓΔIξ2, ξ21/2,
ΔIξ1ΔI ξ2= 00 SkmS kn× ΔIξ1, kmΔI ξ2, kn dkmdkn.
ΓΔIv, d=ΓΔIv, 0exp-k¯2vx2 ×1+4σk2vz21+4σk2v2dx2vx2 +dy2vy2,
v= vx0vz= Lxξ/2f02σh,d= dxdy0= LxΔξ/2fLxΔη/2f0.
ΓΔIv, dx=ΓΔIv, 0exp-k¯2vx21+4σk2vz21+4σk2v2Δξ02ξ2.
ΓΔIv, dy=ΓΔIv, 0exp-k¯2vx2Δη02ξ2
ΔξspΔηsp =1-exp-k¯2vx2Δξ02/ξ21-exp-k¯2vx21+4σk2vz21+4σk2v2 Δξ02/ξ2.
Iξ=j=1Nk Iξ, kj,
ΓΔIξ1, ξ2=m=1Nkn=1Nk smsnγmnξ1, ξ2; km, kn
=m=1Nkn=1Nk smsn exp- kmv1-knv22
sm= I ξ, km/ I ξ,sn= I ξ, kn/ Iξ.
Δv1= LxΔξ0/2f00, Δv2=0LxΔξ0/2f0,
ΔξspΔηsp=1-γΔIv, v+Δv21-γΔIv, v+Δv1.

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