Abstract

The changes in the microtopography of a metal surface during a corrosion process are measured by decorrelation of the scattered speckle fields under coherent illumination. For that purpose a quantitative relation between the decorrelation of the scattered light fields and the rate of corrosion is established in a theoretical model, based on the statistics of phase and reflectivity changes of point scatterers at the surface. The speckle fields are recorded by a CCD camera and processed numerically in a computer, yielding the standard deviation of the topography changes with nanometer sensitivity. From the analysis of a series of images taken at equal time intervals during the corrosion process, the degree of interrelation among subsequent topography changes is calculated.

© 1999 Optical Society of America

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References

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  1. W. H. Cubberly, ed., Corrosion, Vol. 13 of Metals Handbook, 9th ed. (American Society for Metals, Metals Park, Ohio, 1987).
  2. F. Jin, F. P. Chiang, “A new technique using digital speckle correlation for nondestructive testing of corrosion,” Mater. Eval. 55, 813–816 (1997).
  3. R. A. Ashton, D. Slovin, H. J. Gerritsen, “Interferometric holography applied to elastic stress and surface corrosion,” Appl. Opt. 10, 440–441 (1971).
    [CrossRef] [PubMed]
  4. K. N. Petrov, Yu. P. Presnyakov, “Holographic interferometry of the corrosion process,” Opt. Spectrosc. (USSR) 44, 309–311 (1978).
  5. Yu. I. Ostrovsky, V. P. Shchepinov, “Correlation holographic and speckle interferometry,” Prog. Opt. 30, 87–135 (1992).
    [CrossRef]
  6. C. S. Vikram, K. Vedam, “Holographic interferometry of corrosion,” Optik (Stuttgart) 55, 407–414 (1980).
  7. D. Coburn, J. Slevin, “Digital correlation system for nondestructive testing of thermally stressed ceramics,” Appl. Opt. 34, 5977–5586 (1995).
    [CrossRef] [PubMed]
  8. J. Steckenrider, J. W. Wagner, “Computed speckle decorrelation (CSD) for the study of fatigue damage,” Opt. Lasers Eng. 22, 3–15 (1995).
    [CrossRef]
  9. T. Fricke-Begemann, F. Beyrau, G. Gülker, K. D. Hinsch, P. Jäschke, K. Wolff, “Analysis of microstructure changes and dynamic processes at rough surfaces using speckle correlation,” in Scattering and Surface Roughness II, Z. Gu, A. Maradudin, eds., Proc. SPIE3426, 113–123 (1998).
    [CrossRef]
  10. M. Sjödahl, L. R. Benckert, “Electronic speckle photography: analysis of an algorithm giving the displacement with subpixel accuracy,” Appl. Opt. 32, 2278–2284 (1993).
    [CrossRef] [PubMed]
  11. J. W. Goodman, “Statistical properties of laser speckle patterns,” in Laser Speckle and Related Phenomena, J. C. Dainty, ed. (Springer-Verlag, Berlin, 1975), pp. 9–75.
  12. D. Leger, E. Mathieu, J. C. Perrin, “Optical surface roughness determination using speckle correlation techniques,” Appl. Opt. 14, 872–877 (1975).
    [CrossRef]
  13. A. Papoulis, Probability, Random Variables and Stochastic Processes (McGraw-Hill, New York, 1991).

1997

F. Jin, F. P. Chiang, “A new technique using digital speckle correlation for nondestructive testing of corrosion,” Mater. Eval. 55, 813–816 (1997).

1995

D. Coburn, J. Slevin, “Digital correlation system for nondestructive testing of thermally stressed ceramics,” Appl. Opt. 34, 5977–5586 (1995).
[CrossRef] [PubMed]

J. Steckenrider, J. W. Wagner, “Computed speckle decorrelation (CSD) for the study of fatigue damage,” Opt. Lasers Eng. 22, 3–15 (1995).
[CrossRef]

1993

1992

Yu. I. Ostrovsky, V. P. Shchepinov, “Correlation holographic and speckle interferometry,” Prog. Opt. 30, 87–135 (1992).
[CrossRef]

1980

C. S. Vikram, K. Vedam, “Holographic interferometry of corrosion,” Optik (Stuttgart) 55, 407–414 (1980).

1978

K. N. Petrov, Yu. P. Presnyakov, “Holographic interferometry of the corrosion process,” Opt. Spectrosc. (USSR) 44, 309–311 (1978).

1975

1971

Ashton, R. A.

Benckert, L. R.

Beyrau, F.

T. Fricke-Begemann, F. Beyrau, G. Gülker, K. D. Hinsch, P. Jäschke, K. Wolff, “Analysis of microstructure changes and dynamic processes at rough surfaces using speckle correlation,” in Scattering and Surface Roughness II, Z. Gu, A. Maradudin, eds., Proc. SPIE3426, 113–123 (1998).
[CrossRef]

Chiang, F. P.

F. Jin, F. P. Chiang, “A new technique using digital speckle correlation for nondestructive testing of corrosion,” Mater. Eval. 55, 813–816 (1997).

Coburn, D.

Fricke-Begemann, T.

T. Fricke-Begemann, F. Beyrau, G. Gülker, K. D. Hinsch, P. Jäschke, K. Wolff, “Analysis of microstructure changes and dynamic processes at rough surfaces using speckle correlation,” in Scattering and Surface Roughness II, Z. Gu, A. Maradudin, eds., Proc. SPIE3426, 113–123 (1998).
[CrossRef]

Gerritsen, H. J.

Goodman, J. W.

J. W. Goodman, “Statistical properties of laser speckle patterns,” in Laser Speckle and Related Phenomena, J. C. Dainty, ed. (Springer-Verlag, Berlin, 1975), pp. 9–75.

Gülker, G.

T. Fricke-Begemann, F. Beyrau, G. Gülker, K. D. Hinsch, P. Jäschke, K. Wolff, “Analysis of microstructure changes and dynamic processes at rough surfaces using speckle correlation,” in Scattering and Surface Roughness II, Z. Gu, A. Maradudin, eds., Proc. SPIE3426, 113–123 (1998).
[CrossRef]

Hinsch, K. D.

T. Fricke-Begemann, F. Beyrau, G. Gülker, K. D. Hinsch, P. Jäschke, K. Wolff, “Analysis of microstructure changes and dynamic processes at rough surfaces using speckle correlation,” in Scattering and Surface Roughness II, Z. Gu, A. Maradudin, eds., Proc. SPIE3426, 113–123 (1998).
[CrossRef]

Jäschke, P.

T. Fricke-Begemann, F. Beyrau, G. Gülker, K. D. Hinsch, P. Jäschke, K. Wolff, “Analysis of microstructure changes and dynamic processes at rough surfaces using speckle correlation,” in Scattering and Surface Roughness II, Z. Gu, A. Maradudin, eds., Proc. SPIE3426, 113–123 (1998).
[CrossRef]

Jin, F.

F. Jin, F. P. Chiang, “A new technique using digital speckle correlation for nondestructive testing of corrosion,” Mater. Eval. 55, 813–816 (1997).

Leger, D.

Mathieu, E.

Ostrovsky, Yu. I.

Yu. I. Ostrovsky, V. P. Shchepinov, “Correlation holographic and speckle interferometry,” Prog. Opt. 30, 87–135 (1992).
[CrossRef]

Papoulis, A.

A. Papoulis, Probability, Random Variables and Stochastic Processes (McGraw-Hill, New York, 1991).

Perrin, J. C.

Petrov, K. N.

K. N. Petrov, Yu. P. Presnyakov, “Holographic interferometry of the corrosion process,” Opt. Spectrosc. (USSR) 44, 309–311 (1978).

Presnyakov, Yu. P.

K. N. Petrov, Yu. P. Presnyakov, “Holographic interferometry of the corrosion process,” Opt. Spectrosc. (USSR) 44, 309–311 (1978).

Shchepinov, V. P.

Yu. I. Ostrovsky, V. P. Shchepinov, “Correlation holographic and speckle interferometry,” Prog. Opt. 30, 87–135 (1992).
[CrossRef]

Sjödahl, M.

Slevin, J.

Slovin, D.

Steckenrider, J.

J. Steckenrider, J. W. Wagner, “Computed speckle decorrelation (CSD) for the study of fatigue damage,” Opt. Lasers Eng. 22, 3–15 (1995).
[CrossRef]

Vedam, K.

C. S. Vikram, K. Vedam, “Holographic interferometry of corrosion,” Optik (Stuttgart) 55, 407–414 (1980).

Vikram, C. S.

C. S. Vikram, K. Vedam, “Holographic interferometry of corrosion,” Optik (Stuttgart) 55, 407–414 (1980).

Wagner, J. W.

J. Steckenrider, J. W. Wagner, “Computed speckle decorrelation (CSD) for the study of fatigue damage,” Opt. Lasers Eng. 22, 3–15 (1995).
[CrossRef]

Wolff, K.

T. Fricke-Begemann, F. Beyrau, G. Gülker, K. D. Hinsch, P. Jäschke, K. Wolff, “Analysis of microstructure changes and dynamic processes at rough surfaces using speckle correlation,” in Scattering and Surface Roughness II, Z. Gu, A. Maradudin, eds., Proc. SPIE3426, 113–123 (1998).
[CrossRef]

Appl. Opt.

Mater. Eval.

F. Jin, F. P. Chiang, “A new technique using digital speckle correlation for nondestructive testing of corrosion,” Mater. Eval. 55, 813–816 (1997).

Opt. Lasers Eng.

J. Steckenrider, J. W. Wagner, “Computed speckle decorrelation (CSD) for the study of fatigue damage,” Opt. Lasers Eng. 22, 3–15 (1995).
[CrossRef]

Opt. Spectrosc. (USSR)

K. N. Petrov, Yu. P. Presnyakov, “Holographic interferometry of the corrosion process,” Opt. Spectrosc. (USSR) 44, 309–311 (1978).

Optik (Stuttgart)

C. S. Vikram, K. Vedam, “Holographic interferometry of corrosion,” Optik (Stuttgart) 55, 407–414 (1980).

Prog. Opt.

Yu. I. Ostrovsky, V. P. Shchepinov, “Correlation holographic and speckle interferometry,” Prog. Opt. 30, 87–135 (1992).
[CrossRef]

Other

W. H. Cubberly, ed., Corrosion, Vol. 13 of Metals Handbook, 9th ed. (American Society for Metals, Metals Park, Ohio, 1987).

T. Fricke-Begemann, F. Beyrau, G. Gülker, K. D. Hinsch, P. Jäschke, K. Wolff, “Analysis of microstructure changes and dynamic processes at rough surfaces using speckle correlation,” in Scattering and Surface Roughness II, Z. Gu, A. Maradudin, eds., Proc. SPIE3426, 113–123 (1998).
[CrossRef]

J. W. Goodman, “Statistical properties of laser speckle patterns,” in Laser Speckle and Related Phenomena, J. C. Dainty, ed. (Springer-Verlag, Berlin, 1975), pp. 9–75.

A. Papoulis, Probability, Random Variables and Stochastic Processes (McGraw-Hill, New York, 1991).

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Figures (12)

Fig. 1
Fig. 1

Experimental setup for digital speckle correlation.

Fig. 2
Fig. 2

Correlation coefficient versus time for two different types of steel in a humid acid atmosphere.

Fig. 3
Fig. 3

Correlation coefficient of the light scattered from two sample surfaces versus normalized standard deviation of their difference in height following different probability densities. The squares show results from a Monte Carlo simulation.

Fig. 4
Fig. 4

Correlation coefficient versus normalized standard deviation in reflectivity difference. Parameters are the standard deviation of difference in optical phase, σΔφ, and the correlation ρ between changes in phase and reflectivity.

Fig. 5
Fig. 5

Course of the correlation in the scattered light for corrosion of a pure-iron surface. Each state of the process is compared with all subsequent ones.

Fig. 6
Fig. 6

Averaged standard deviation of the topography changes on a sample of pure iron of 0.5-µm surface roughness versus corrosion time. Also shown are the theoretical values if the changes were completely correlated (r j j+ N = 1) or uncorrelated (r j j+ N = 0).

Fig. 7
Fig. 7

Correlation between topography changes versus time difference for the corrosion of a pure-iron surface of roughness 0.5 µm rms.

Fig. 8
Fig. 8

Standard deviation of the topography changes versus corrosion time for 11 different samples.

Fig. 9
Fig. 9

Iron sample with three different roughnesses as seen by the camera in the experimental setup.

Fig. 10
Fig. 10

Correlation between topography changes versus time difference for 11 different samples.

Fig. 11
Fig. 11

Topography changes versus corrosion time, calculated for the same sample as in Fig. 6 with different variances of the alterations in reflectivity.

Fig. 12
Fig. 12

Correlation between topography changes versus time difference, calculated for the same sample as in Fig. 7 with different variances of the alterations in reflectivity.

Equations (19)

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cI1I2=I1I2-I1I2I12-I12I22-I221/2.
A1=k ak expiφk,
Δφk=2π/λ1+cos θΔhk,
A2=k bkak expiφk-Δφk.
A2A2*=k bk2ak2=b2A1A1*,
A1A2*=k ak2bk expiΔφk=b expiΔφ k ak2,
cI1I2=|A1A2*|2A1A1*A2A2*.
cI1I2=|b expiΔφ|2b2.
pΔφ, b=12πσΔφσb1-ρ2exp-121-ρ2×Δφ-ΔφσΔφ2+b-bσb2-2ρ Δφ-Δφb-bσΔφσb,
cI1I2=exp-σΔφ21-1-ρ2σΔφ2σb2b2.
cI1I2=exp-4π21+cos θ2λ2 σΔh2,
cI1I2=1-σb2b2.
σ1N2=j,k=1N rjkσjσk,
σ1N=Nσk.
σ1N=Nσk.
r12=σ122-σ12-σ222σ1σ2.
σb,0N2b0N2=1-b0N2b0N2<1-b0N2,
1-σb,0N2b0N2=1-σb2b2N,
σb2b2<1-b0N21/N.

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