Abstract

We present a detailed investigation of digital speckle correlation to measure small changes in the microstructure of random rough surfaces. The corresponding alterations in the scattered-light field are recorded by an electronic camera with subsequent numerical correlation. Among the classical theoretical approaches to describe the scattering at random rough surfaces, the composite-roughness model is advanced to calculate the speckle correlation in terms of parameters of the changes in surface microstructure. For an experimental verification, surfaces with similar microstructure are fabricated with a photolithographic technique. They are employed for comparative measurements with high-resolution scanning force microscopy and for correlation measurements under variation of experimental parameters. A good agreement between theoretically predicted and experimental correlation data can be observed. The results allow a quantitative whole-field monitoring of surface processes by remote optical means.

© 2004 Optical Society of America

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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  5. J. A. Mendez, M. Roblin, “Contraste de franges d’interférence produits par l’enregistrement photographique de deux speckles en présence d’un dépointage longitudinal entre les deux poses,” Nouv. Rev. Optique 7, 105–112 (1976).
  6. Y. I. Ostrovsky, V. P. Shchepinov, “Correlation speckle interferometry in the mechanics of contact interaction,” in Speckle Metrology, R. S. Sirohi, ed. (Marcel Dekker, New York, 1993), Chap. 11.
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    [Crossref] [PubMed]
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  9. G. Gülker, K. D. Hinsch, “Detection of surface microstructure changes by electronic speckle pattern interferometry,” Opt. Lasers Eng. 26, 165–178 (1997).
    [Crossref]
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  11. T. Fricke-Begemann, “Three-dimensional deformation field measurement with digital speckle correlation,” Appl. Opt. (to be published).
  12. J. W. Wagner, “Detecting nonuniformity in small welds and solder seams using optical correlation and electronic processing,” Appl. Opt. 20, 3605–3611 (1981).
    [Crossref] [PubMed]
  13. P. Zanetta, M. Facchini, “Local correlation of laser speckle applied to the study of salt efflorescence on stone surfaces,” Opt. Commun. 104, 35–38 (1993).
    [Crossref]
  14. D. Coburn, J. Slevin, “Digital correlation system for nondestructive testing of thermally stressed ceramics,” Appl. Opt. 34, 5977–5986 (1995).
    [Crossref] [PubMed]
  15. G. V. Dreiden, I. V. Semenova, “Correlation holographic interferometry applied for studies of laser-induced erosion,” Opt. Commun. 118, 21–24 (1995).
    [Crossref]
  16. J. S. Steckenrider, J. W. Wagner, “Computed speckle decorrelation (CSD) for the study of fatigue damage,” Opt. Lasers Eng. 22, 3–15 (1995).
    [Crossref]
  17. J. A. Ogilvy, Theory of Wave Scattering from Random Rough Surfaces (Hilger, IOP, Bristol, UK, 1991).
  18. M. Nieto-Vesperinas, Scattering and Diffraction in Physical Optics (Wiley, New York, 1991).
  19. A. G. Voronovich, Wave Scattering from Rough Surfaces, 2nd ed. (Springer-Verlag, Berlin, 1999).
  20. A. Papoulis, Probability, Random Variables, and Stochastic Processes, 3rd ed. (McGraw-Hill, New York, 1991).
  21. 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]
  22. M. Sjödahl, “Some recent advances in electronic speckle photography,” Opt. Lasers Eng. 29, 125–144 (1998).
    [Crossref]
  23. J. W. Goodman, Statistical Optics (Wiley, New York, 1985).
  24. T. Fricke-Begemann, G. Gülker, K. D. Hinsch, K. Wolff, “Corrosion monitoring with speckle correlation,” Appl. Opt. 38, 5948–5955 (1999).
    [Crossref]
  25. K. N. Petrov, Y. P. Presnyakov, “Holographic interferometry of the corrosion process,” Opt. Spektrosk. 44, 309–311 (1978).
  26. 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. A. Maradudin, eds., Proc. SPIE3426, 113–123 (1998).
    [Crossref]
  27. P. Beckmann, A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, Oxford, UK, 1963).
  28. B. F. Kur’yanov, “The scattering of sound at rough surfaces with two types of irregularity,” Sov. Phys. Acoust. 8, 252–257 (1963).
  29. G. S. Brown, “Backscattering from a gaussian-distributed perfectly conducting rough surface,” IEEE Trans. Antennas Propag. AP-26, 472–482 (1978).
    [Crossref]
  30. S. T. McDaniel, A. D. Gorman, “An examination of the composite-roughness scattering model,” J. Acoust. Soc. Am. 73, 1476–1486 (1983).
    [Crossref]
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    [Crossref]
  34. A. Stogryn, “Electromagnetic scattering from rough, finitely conducting surfaces,” Radio Sci. 2, 415–428 (1967).
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    [Crossref]
  36. E. Rodrı́guez, “Beyond the Kirchhoff approximation,” Radio Sci. 24, 681–693 (1989).
    [Crossref]
  37. P. F. Gray, “A method of forming optical diffusers of simple known statistical properties,” Opt. Acta 25, 765–775 (1978).
    [Crossref]
  38. K. A. O’Donnell, “Experimental study of scattering from characterized random surfaces,” J. Opt. Soc. Am. A 4, 1194–1205 (1987).
    [Crossref]
  39. A. J. Sant, J. C. Dainty, M. J. Kim, “Comparison of surface scattering between identical, randomly rough metal and dielectric diffusers,” Opt. Lett. 14, 1183–1185 (1989).
    [Crossref] [PubMed]
  40. K. D. Hinsch, T. Fricke-Begemann, G. Gülker, K. Wolff, “Speckle correlation for the analysis of random processes at rough surfaces,” Opt. Lasers Eng. 33, 87–105 (2000).
    [Crossref]

2002 (1)

2000 (1)

K. D. Hinsch, T. Fricke-Begemann, G. Gülker, K. Wolff, “Speckle correlation for the analysis of random processes at rough surfaces,” Opt. Lasers Eng. 33, 87–105 (2000).
[Crossref]

1999 (1)

1998 (1)

M. Sjödahl, “Some recent advances in electronic speckle photography,” Opt. Lasers Eng. 29, 125–144 (1998).
[Crossref]

1997 (1)

G. Gülker, K. D. Hinsch, “Detection of surface microstructure changes by electronic speckle pattern interferometry,” Opt. Lasers Eng. 26, 165–178 (1997).
[Crossref]

1995 (3)

D. Coburn, J. Slevin, “Digital correlation system for nondestructive testing of thermally stressed ceramics,” Appl. Opt. 34, 5977–5986 (1995).
[Crossref] [PubMed]

G. V. Dreiden, I. V. Semenova, “Correlation holographic interferometry applied for studies of laser-induced erosion,” Opt. Commun. 118, 21–24 (1995).
[Crossref]

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

1993 (2)

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]

P. Zanetta, M. Facchini, “Local correlation of laser speckle applied to the study of salt efflorescence on stone surfaces,” Opt. Commun. 104, 35–38 (1993).
[Crossref]

1992 (1)

1989 (2)

1987 (1)

1985 (2)

1983 (1)

S. T. McDaniel, A. D. Gorman, “An examination of the composite-roughness scattering model,” J. Acoust. Soc. Am. 73, 1476–1486 (1983).
[Crossref]

1981 (1)

1978 (3)

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

G. S. Brown, “Backscattering from a gaussian-distributed perfectly conducting rough surface,” IEEE Trans. Antennas Propag. AP-26, 472–482 (1978).
[Crossref]

P. F. Gray, “A method of forming optical diffusers of simple known statistical properties,” Opt. Acta 25, 765–775 (1978).
[Crossref]

1976 (1)

J. A. Mendez, M. Roblin, “Contraste de franges d’interférence produits par l’enregistrement photographique de deux speckles en présence d’un dépointage longitudinal entre les deux poses,” Nouv. Rev. Optique 7, 105–112 (1976).

1971 (1)

1970 (1)

1967 (2)

M. L. Burrows, “A reformulated boundary perturbation theory in electromagnetism and its application to a sphere,” Can. J. Phys. 45, 1729–1743 (1967).
[Crossref]

A. Stogryn, “Electromagnetic scattering from rough, finitely conducting surfaces,” Radio Sci. 2, 415–428 (1967).

1963 (1)

B. F. Kur’yanov, “The scattering of sound at rough surfaces with two types of irregularity,” Sov. Phys. Acoust. 8, 252–257 (1963).

Ashton, R. A.

Bahar, E.

Beckmann, P.

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

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. A. Maradudin, eds., Proc. SPIE3426, 113–123 (1998).
[Crossref]

Brown, G. S.

G. S. Brown, “Backscattering from a gaussian-distributed perfectly conducting rough surface,” IEEE Trans. Antennas Propag. AP-26, 472–482 (1978).
[Crossref]

Burrows, M. L.

M. L. Burrows, “A reformulated boundary perturbation theory in electromagnetism and its application to a sphere,” Can. J. Phys. 45, 1729–1743 (1967).
[Crossref]

Chen, M. F.

Coburn, D.

Dainty, J. C.

Dreiden, G. V.

G. V. Dreiden, I. V. Semenova, “Correlation holographic interferometry applied for studies of laser-induced erosion,” Opt. Commun. 118, 21–24 (1995).
[Crossref]

Facchini, M.

P. Zanetta, M. Facchini, “Local correlation of laser speckle applied to the study of salt efflorescence on stone surfaces,” Opt. Commun. 104, 35–38 (1993).
[Crossref]

Fitzwater, M. A.

Fricke-Begemann, T.

K. D. Hinsch, T. Fricke-Begemann, G. Gülker, K. Wolff, “Speckle correlation for the analysis of random processes at rough surfaces,” Opt. Lasers Eng. 33, 87–105 (2000).
[Crossref]

T. Fricke-Begemann, G. Gülker, K. D. Hinsch, K. Wolff, “Corrosion monitoring with speckle correlation,” Appl. Opt. 38, 5948–5955 (1999).
[Crossref]

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. A. Maradudin, eds., Proc. SPIE3426, 113–123 (1998).
[Crossref]

T. Fricke-Begemann, Optical Measurement of Deformation Fields and Surface Processes with Digital Speckle Correlation, Ph.D. dissertation (Carl von Ossietzky Universität Oldenburg, Oldenburg, Germany, 2002).

T. Fricke-Begemann, “Three-dimensional deformation field measurement with digital speckle correlation,” Appl. Opt. (to be published).

Fung, A. K.

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).

J. W. Goodman, Statistical Optics (Wiley, New York, 1985).

Gorman, A. D.

S. T. McDaniel, A. D. Gorman, “An examination of the composite-roughness scattering model,” J. Acoust. Soc. Am. 73, 1476–1486 (1983).
[Crossref]

Gray, P. F.

P. F. Gray, “A method of forming optical diffusers of simple known statistical properties,” Opt. Acta 25, 765–775 (1978).
[Crossref]

Gülker, G.

K. D. Hinsch, T. Fricke-Begemann, G. Gülker, K. Wolff, “Speckle correlation for the analysis of random processes at rough surfaces,” Opt. Lasers Eng. 33, 87–105 (2000).
[Crossref]

T. Fricke-Begemann, G. Gülker, K. D. Hinsch, K. Wolff, “Corrosion monitoring with speckle correlation,” Appl. Opt. 38, 5948–5955 (1999).
[Crossref]

G. Gülker, K. D. Hinsch, “Detection of surface microstructure changes by electronic speckle pattern interferometry,” Opt. Lasers Eng. 26, 165–178 (1997).
[Crossref]

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. A. Maradudin, eds., Proc. SPIE3426, 113–123 (1998).
[Crossref]

Hinsch, K. D.

K. D. Hinsch, T. Fricke-Begemann, G. Gülker, K. Wolff, “Speckle correlation for the analysis of random processes at rough surfaces,” Opt. Lasers Eng. 33, 87–105 (2000).
[Crossref]

T. Fricke-Begemann, G. Gülker, K. D. Hinsch, K. Wolff, “Corrosion monitoring with speckle correlation,” Appl. Opt. 38, 5948–5955 (1999).
[Crossref]

G. Gülker, K. D. Hinsch, “Detection of surface microstructure changes by electronic speckle pattern interferometry,” Opt. Lasers Eng. 26, 165–178 (1997).
[Crossref]

K. D. Hinsch, F. McLysaght, K. Wolff, “Tilt-compensated real-time holographic speckle correlation,” Appl. Opt. 31, 5937–5939 (1992).
[Crossref] [PubMed]

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. 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. A. Maradudin, eds., Proc. SPIE3426, 113–123 (1998).
[Crossref]

Kim, M. J.

Kur’yanov, B. F.

B. F. Kur’yanov, “The scattering of sound at rough surfaces with two types of irregularity,” Sov. Phys. Acoust. 8, 252–257 (1963).

Marom, E.

E. Marom, “Real-time strain measurement by optical correlation,” Appl. Opt. 9, 1385–1391 (1970).
[Crossref] [PubMed]

E. Marom, “Holographic correlation,” in Holographic Non-destructive Testing, R. K. Erf, ed. (Academic, London, 1974), Chap. 6.

McDaniel, S. T.

S. T. McDaniel, A. D. Gorman, “An examination of the composite-roughness scattering model,” J. Acoust. Soc. Am. 73, 1476–1486 (1983).
[Crossref]

McLysaght, F.

Mendez, J. A.

J. A. Mendez, M. Roblin, “Contraste de franges d’interférence produits par l’enregistrement photographique de deux speckles en présence d’un dépointage longitudinal entre les deux poses,” Nouv. Rev. Optique 7, 105–112 (1976).

Nieto-Vesperinas, M.

M. Nieto-Vesperinas, Scattering and Diffraction in Physical Optics (Wiley, New York, 1991).

O’Donnell, K. A.

Ogilvy, J. A.

J. A. Ogilvy, Theory of Wave Scattering from Random Rough Surfaces (Hilger, IOP, Bristol, UK, 1991).

Ostrovsky, Y. I.

Y. I. Ostrovsky, V. P. Shchepinov, “Correlation speckle interferometry in the mechanics of contact interaction,” in Speckle Metrology, R. S. Sirohi, ed. (Marcel Dekker, New York, 1993), Chap. 11.

Y. I. Ostrovsky, V. P. Shchepinov, “Correlation holographic and speckle interferometry,” in Progress in Optics, Vol. XXX, E. Wolf, ed. (Elsevier, Amsterdam, 1992), pp. 87–135.

Papoulis, A.

A. Papoulis, Probability, Random Variables, and Stochastic Processes, 3rd ed. (McGraw-Hill, New York, 1991).

Petrov, K. N.

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

Presnyakov, Y. P.

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

Roblin, M.

J. A. Mendez, M. Roblin, “Contraste de franges d’interférence produits par l’enregistrement photographique de deux speckles en présence d’un dépointage longitudinal entre les deux poses,” Nouv. Rev. Optique 7, 105–112 (1976).

Rodri´guez, E.

E. Rodrı́guez, “Beyond the Kirchhoff approximation,” Radio Sci. 24, 681–693 (1989).
[Crossref]

Ruiz-Cortés, V. A.

Sant, A. J.

Semenova, I. V.

G. V. Dreiden, I. V. Semenova, “Correlation holographic interferometry applied for studies of laser-induced erosion,” Opt. Commun. 118, 21–24 (1995).
[Crossref]

Shchepinov, V. P.

Y. I. Ostrovsky, V. P. Shchepinov, “Correlation speckle interferometry in the mechanics of contact interaction,” in Speckle Metrology, R. S. Sirohi, ed. (Marcel Dekker, New York, 1993), Chap. 11.

Y. I. Ostrovsky, V. P. Shchepinov, “Correlation holographic and speckle interferometry,” in Progress in Optics, Vol. XXX, E. Wolf, ed. (Elsevier, Amsterdam, 1992), pp. 87–135.

Sjödahl, M.

Slevin, J.

Slovin, D.

Spizzichino, A.

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

Steckenrider, J. S.

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

Stogryn, A.

A. Stogryn, “Electromagnetic scattering from rough, finitely conducting surfaces,” Radio Sci. 2, 415–428 (1967).

Voronovich, A. G.

A. G. Voronovich, Wave Scattering from Rough Surfaces, 2nd ed. (Springer-Verlag, Berlin, 1999).

Wagner, J. W.

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

J. W. Wagner, “Detecting nonuniformity in small welds and solder seams using optical correlation and electronic processing,” Appl. Opt. 20, 3605–3611 (1981).
[Crossref] [PubMed]

Wolff, K.

K. D. Hinsch, T. Fricke-Begemann, G. Gülker, K. Wolff, “Speckle correlation for the analysis of random processes at rough surfaces,” Opt. Lasers Eng. 33, 87–105 (2000).
[Crossref]

T. Fricke-Begemann, G. Gülker, K. D. Hinsch, K. Wolff, “Corrosion monitoring with speckle correlation,” Appl. Opt. 38, 5948–5955 (1999).
[Crossref]

K. D. Hinsch, F. McLysaght, K. Wolff, “Tilt-compensated real-time holographic speckle correlation,” Appl. Opt. 31, 5937–5939 (1992).
[Crossref] [PubMed]

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. A. Maradudin, eds., Proc. SPIE3426, 113–123 (1998).
[Crossref]

Zanetta, P.

P. Zanetta, M. Facchini, “Local correlation of laser speckle applied to the study of salt efflorescence on stone surfaces,” Opt. Commun. 104, 35–38 (1993).
[Crossref]

Appl. Opt. (7)

Can. J. Phys. (1)

M. L. Burrows, “A reformulated boundary perturbation theory in electromagnetism and its application to a sphere,” Can. J. Phys. 45, 1729–1743 (1967).
[Crossref]

IEEE Trans. Antennas Propag. (1)

G. S. Brown, “Backscattering from a gaussian-distributed perfectly conducting rough surface,” IEEE Trans. Antennas Propag. AP-26, 472–482 (1978).
[Crossref]

J. Acoust. Soc. Am. (1)

S. T. McDaniel, A. D. Gorman, “An examination of the composite-roughness scattering model,” J. Acoust. Soc. Am. 73, 1476–1486 (1983).
[Crossref]

J. Opt. Soc. Am. A (4)

Nouv. Rev. Optique (1)

J. A. Mendez, M. Roblin, “Contraste de franges d’interférence produits par l’enregistrement photographique de deux speckles en présence d’un dépointage longitudinal entre les deux poses,” Nouv. Rev. Optique 7, 105–112 (1976).

Opt. Acta (1)

P. F. Gray, “A method of forming optical diffusers of simple known statistical properties,” Opt. Acta 25, 765–775 (1978).
[Crossref]

Opt. Commun. (2)

P. Zanetta, M. Facchini, “Local correlation of laser speckle applied to the study of salt efflorescence on stone surfaces,” Opt. Commun. 104, 35–38 (1993).
[Crossref]

G. V. Dreiden, I. V. Semenova, “Correlation holographic interferometry applied for studies of laser-induced erosion,” Opt. Commun. 118, 21–24 (1995).
[Crossref]

Opt. Lasers Eng. (4)

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

M. Sjödahl, “Some recent advances in electronic speckle photography,” Opt. Lasers Eng. 29, 125–144 (1998).
[Crossref]

G. Gülker, K. D. Hinsch, “Detection of surface microstructure changes by electronic speckle pattern interferometry,” Opt. Lasers Eng. 26, 165–178 (1997).
[Crossref]

K. D. Hinsch, T. Fricke-Begemann, G. Gülker, K. Wolff, “Speckle correlation for the analysis of random processes at rough surfaces,” Opt. Lasers Eng. 33, 87–105 (2000).
[Crossref]

Opt. Lett. (1)

Opt. Spektrosk. (1)

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

Radio Sci. (2)

E. Rodrı́guez, “Beyond the Kirchhoff approximation,” Radio Sci. 24, 681–693 (1989).
[Crossref]

A. Stogryn, “Electromagnetic scattering from rough, finitely conducting surfaces,” Radio Sci. 2, 415–428 (1967).

Sov. Phys. Acoust. (1)

B. F. Kur’yanov, “The scattering of sound at rough surfaces with two types of irregularity,” Sov. Phys. Acoust. 8, 252–257 (1963).

Other (13)

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

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. A. Maradudin, eds., Proc. SPIE3426, 113–123 (1998).
[Crossref]

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

T. Fricke-Begemann, Optical Measurement of Deformation Fields and Surface Processes with Digital Speckle Correlation, Ph.D. dissertation (Carl von Ossietzky Universität Oldenburg, Oldenburg, Germany, 2002).

T. Fricke-Begemann, “Three-dimensional deformation field measurement with digital speckle correlation,” Appl. Opt. (to be published).

Y. I. Ostrovsky, V. P. Shchepinov, “Correlation holographic and speckle interferometry,” in Progress in Optics, Vol. XXX, E. Wolf, ed. (Elsevier, Amsterdam, 1992), pp. 87–135.

Y. I. Ostrovsky, V. P. Shchepinov, “Correlation speckle interferometry in the mechanics of contact interaction,” in Speckle Metrology, R. S. Sirohi, ed. (Marcel Dekker, New York, 1993), Chap. 11.

E. Marom, “Holographic correlation,” in Holographic Non-destructive Testing, R. K. Erf, ed. (Academic, London, 1974), Chap. 6.

J. W. Goodman, Statistical Optics (Wiley, New York, 1985).

J. A. Ogilvy, Theory of Wave Scattering from Random Rough Surfaces (Hilger, IOP, Bristol, UK, 1991).

M. Nieto-Vesperinas, Scattering and Diffraction in Physical Optics (Wiley, New York, 1991).

A. G. Voronovich, Wave Scattering from Rough Surfaces, 2nd ed. (Springer-Verlag, Berlin, 1999).

A. Papoulis, Probability, Random Variables, and Stochastic Processes, 3rd ed. (McGraw-Hill, New York, 1991).

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Figures (9)

Fig. 1
Fig. 1

Experimental setup for DSC.

Fig. 2
Fig. 2

Illustration of the scattering geometry.

Fig. 3
Fig. 3

Model of a surface with two scales of roughness.

Fig. 4
Fig. 4

Experimental setup for the production of rough surfaces with similar microstructure in photoresist.

Fig. 5
Fig. 5

SFM measurement on photoresist samples. Depicted is (a) one surface profile and (b) the difference between two identically produced surface profiles in gray-scale coding. The size of the scan is 73.6×73.6 μm2.

Fig. 6
Fig. 6

Power spectrum of (a) the surface profile and (b) the profile difference of two surface realizations of a photoresist sample. Depicted are the horizontal (dashed curves) and vertical (dotted curves) cross sections in a logarithmic scale. The solid curve shows the PSD of a surface model with two Gaussian scales.

Fig. 7
Fig. 7

Speckle correlation versus angle of illumination for various wavelengths (as indicated) and two states of polarization (solid symbols and solid curves, s polarization; long separate dashes and dashed curves, p polarization).

Fig. 8
Fig. 8

Comparison of experimental correlation values and the prediction by the two-scale model. For four different wavelengths, the solid and the dashed curves depict the theoretical prediction for s and p polarization, respectively. The experimental results are shown by the same symbols as in Fig. 7.

Fig. 9
Fig. 9

Scattered intensity versus angle of illumination. Comparison of experimental data (symbols) and prediction by the two-scale model (curves) for two wavelengths and two states of polarization.

Equations (19)

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cii˜(Δr)=i(r)i˜(r+Δr)-ii˜[(i2-i2)(i˜2-i˜2)]1/2,
ccii˜=|a*a˜|2|a|2|a˜|2=|ccaa˜|2.
ccii˜=exp[-k2(cos θ+cos θ2)2σΔh2],
ccaa˜=Phh˜(Δκ)[Ph(Δκ)Ph˜(Δκ)]1/2,
a*a˜αβ=Aill4πr2k2Fαβ2π-χhh˜(-Δkz, Δkz; Δρ)×exp(iΔκΔρ)d2Δρ,
Fαβ=Δkz-1eˆβ[(kˆinc×eˆα)×(kinc-ksc)]
χhh˜(-Δkz, Δkz; Δρ)=exp{-Δkz2σhσh˜[1-chh˜(Δρ)]}.
a*a˜αβ=Aill4πr22k2Fαβ2Δkz2σh2|chh˜(0)|×exp{-[1-chh˜(0)]Δkz2σh2}×exp-|Δκ|22Δkz2σh2|chh˜(0)|,
ccii˜=σh4(σh2-12σΔh2)2 exp(-Δkz2σΔh2)×exp-|Δκ|24Δkz2l2σΔh2σh2(σh2-12σΔh2).
E(1)(r)·eˆβ=k2 exp(ikr)4π0rSl[0E(r)E(r)+μ0H(r)H(r)]hs(r)dSl,
E(1)(r)·eˆβ=k2 exp(ikr)π0rSl[0(nˆ·Einc)(nˆ·Einc)+μ0(nˆ×Hinc)(nˆ×Hinc)]hs(r)dSl.
a(1)=k2 exp(ikr)πrSMΓαβ(xhl, yhl)hs(ρ)×exp(i[Δkzhl(ρ)+Δκρ])d2ρ,
Γαβ(xhl, yhl)={(nˆ·eˆα)(nˆ·eˆβ)-[nˆ×(kˆinc×eˆα)]·[nˆ×(kˆsc×eˆβ)]}(xhl2+yhl2+1)-1/2
a(1)*a˜(1)αβ=Aillk4π2r2-Γαβ(xhl, yhl)Γαβ(xh˜l, yh˜l)×exp{iΔkz[h˜l(ρ+Δρ)-hl(ρ)]}×σhsσh˜schsh˜s(Δρ)exp(iΔκΔρ)d2Δρ.
a(1)*a˜(1)αβ=Aill4πr22k4-Γαβ2Δκ-κΔkz×F[χhlh˜l](Δκ-κ)Phsh˜s(κ)d2κ,
Phsh˜s(Δκ)=(σhs2-σΔhs2/2)ls2/2 exp(-|Δκ|2ls2/4),
a*a˜αβ=Aill4πr2exp{-[1-chlh˜l(0)]Δkz2σhl2}×4Fαβ2γexp-|Δκ|2γk2+16Γαβ2(0)×k4(σhs2-12σΔhs2)2ls24+γk2ls2exp-ls2|Δκ|24+γk2ls2,
h(ρ)h(ρ+Δρ)=σhl2exp(-Δρ2/ll2)+σhs2exp(-Δρ2/ls2),
Ph=F[hh]=πσhl2ll2exp(-π2ll2|ν|2)+πσhs2ls2exp(-π2ls2|ν|2).

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