Abstract

A method for characterizing the microroughness of samples in optical coating technology is developed. Measurements over different spatial-frequency ranges are composed into a single power spectral density (PSD) covering a large bandwidth. This is followed by the extraction of characteristic parameters through fitting of the PSD to a suitable combination of theoretical models. The method allows us to combine microroughness measurements performed with different techniques, and the fitting procedure can be adapted to any behavior of a combined PSD. The method has been applied to a set of ion-beam-sputtered fluoride vacuum-UV coatings with increasing number of alternative low- and high-index layers. Conclusions about roughness development and microstructural growth are drawn.

© 2001 Optical Society of America

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    [CrossRef]
  2. D. Ristau, W. Arens, S. Bosch, A. Duparré, E. Masetti, D. Jacob, G. Kiriakidis, F. Peiro, E. Quesnel, A. V. Tikhonravov, “UV-optical and microstructural properties of MgF2 coatings deposited by IBS and PVD processes,” in Advances in Optical Interference Coatings, C. Amra, H. A. Macleod, eds., Proc. SPIE3738, 436–445 (1999).
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  14. E. Quesnel, M. Berger, J. Cigna, D. Duca, C. Pellé, F. Pierre, “Near-UV to IR optical characterization of YF3 thin films deposited by evaporation and ion beam processes,” in Developments in Optical Component Coatings, I. Reid, ed., Proc. SPIE2776, 366–372 (1996).
    [CrossRef]
  15. J. Dijon, E. Quesnel, B. Rolland, P. Garrec, C. Pellé, J. Hue, “High damage threshold fluoride UV mirrors made by ion beam sputtering,” in Laser-Induced Damage in Optical Materials Symposium, Boulder, 1997, G. J. Exharos, A. H. Guenther, M. R. Kozlowski, M. J. Soileau, eds., Proc. SPIE3244, 406–416 (1998).
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  19. A. Duparré, G. Notni, “Multi-type surface and thin film characterization using light scattering, scanning force microscopy and white light interferometry,” in Optical Metrology, G. A. Al-Jumailiy, ed., Vol. CR72 of SPIE Critical Review Papers (Society for Photo-Optical Instrumentation Engineers, Bellingham, Wa., 1999), pp. 213–231.
  20. A. Duparré, “Light scattering of thin dielectric films,” in Thin Films for Optical Coatings, R. E. Hummel, K. H. Günter, eds., Vol. 1 of Handbook of Optical Properties Series (CRC, Boca Raton, Fla., 1995), pp. 273–304.
  21. D. Rönnow, “Elastic light scattering by thin films, spectroscopic measurements and analysis,” Ph.D. dissertation (Acta Universitatis Upsaliensis, Uppsala, Sweden, 1996).
  22. E. L. Church, P. Z. Tackacs, T. A. Leonard, “The prediction of BRDFs from surface profile measurements,” in Scatter from Optical Components, J. C. Stover, ed. Proc. SPIE1165, 136–150 (1989).
    [CrossRef]
  23. E. Quesnel, A. Petit Dit Dariel, A. Duparré, J. Ferré-Borrull, J. Steinert, “DUV light scattering and morphology of ion beam sputtered fluoride coatings,” in Advances in Optical Interference Coatings, C. Amra, H. A. Macleod, eds., Proc. SPIE3738, 410–416 (1999).
    [CrossRef]
  24. J. Ferré-Borrull, A. Duparré, E. Quesnel, “Roughness and light scattering of ion-beam-sputtered fluoride coatings for 193 nm,” Appl. Opt. 39, 5854–5864 (2000).
    [CrossRef]
  25. G. Rasigni, F. Varnier, M. Rasigni, J. Palmari, A. Llebaria, “Roughness spectrum and surface plasmons for surfaces of silver, copper, gold, and magnesium deposits,” Phys. Rev. B 27, 819–830 (1983).
    [CrossRef]
  26. W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge U. Press, Cambridge, 1992).
  27. D. Rönnow, “Interface roughness statistics of thin films from angle-resolved light scattering at three wavelengths,” Opt. Eng. 37, 696–704 (1998).
    [CrossRef]
  28. S. Bosch, J. Ferré-Borrull, N. Leinfellner, A. Canillas, “Effective dielectric function of mixtures of three or more materials: a numerical procedure for computations,” Surface Sci. 453, 9–17 (2000).
    [CrossRef]
  29. A. Duparré, R. Dohle, H. Müller, “Relation between light scattering and morphology of columnar structured optical thin films,” J. Mod. Opt. 37, 1383–1390 (1990).
    [CrossRef]

2000 (2)

J. Ferré-Borrull, A. Duparré, E. Quesnel, “Roughness and light scattering of ion-beam-sputtered fluoride coatings for 193 nm,” Appl. Opt. 39, 5854–5864 (2000).
[CrossRef]

S. Bosch, J. Ferré-Borrull, N. Leinfellner, A. Canillas, “Effective dielectric function of mixtures of three or more materials: a numerical procedure for computations,” Surface Sci. 453, 9–17 (2000).
[CrossRef]

1998 (2)

D. Rönnow, “Interface roughness statistics of thin films from angle-resolved light scattering at three wavelengths,” Opt. Eng. 37, 696–704 (1998).
[CrossRef]

S. Jakobs, A. Duparré, H. Truckenbrodt, “Interfacial roughness and related scatter in ultraviolet optical coatings: a systematic experimental approach,” Appl. Opt. 37, 1180–1193 (1998).
[CrossRef]

1995 (1)

1992 (1)

1990 (1)

A. Duparré, R. Dohle, H. Müller, “Relation between light scattering and morphology of columnar structured optical thin films,” J. Mod. Opt. 37, 1383–1390 (1990).
[CrossRef]

1988 (1)

1984 (1)

J. M. Elson, “Theory of light scattering from a rough surface with an inhomogeneous dielectric permitivity,” Phys. Rev. B 30, 5460–5480 (1984).
[CrossRef]

1983 (2)

G. Rasigni, F. Varnier, M. Rasigni, J. Palmari, A. Llebaria, “Roughness spectrum and surface plasmons for surfaces of silver, copper, gold, and magnesium deposits,” Phys. Rev. B 27, 819–830 (1983).
[CrossRef]

J. M. Elson, J. P. Rahn, J. M. Bennett, “Relationship of the total integrated scattering from multilayer-coated optics to angle of incidence, polarization, correlation length, and roughness cross-correlation properties,” Appl. Opt. 22, 3207–3219 (1983).
[CrossRef] [PubMed]

1981 (1)

1980 (1)

1979 (1)

Amra, C.

C. Amra, J. H. Apfel, E. Pelletier, “Role of interface correlation in light scattering by a multilayer,” Appl. Opt. 31, 3134–3151 (1992).
[CrossRef] [PubMed]

C. Amra, P. Bousquet, “Scattering from surfaces and multilayer coatings: recent advances for a better investigation of experiment,” in Surface Measurement and Characterization, J. M. Bennett, ed., Proc. SPIE1009, 82–97 (1988).
[CrossRef]

Apfel, J. H.

Arens, W.

D. Ristau, W. Arens, S. Bosch, A. Duparré, E. Masetti, D. Jacob, G. Kiriakidis, F. Peiro, E. Quesnel, A. V. Tikhonravov, “UV-optical and microstructural properties of MgF2 coatings deposited by IBS and PVD processes,” in Advances in Optical Interference Coatings, C. Amra, H. A. Macleod, eds., Proc. SPIE3738, 436–445 (1999).
[CrossRef]

Basting, D.

U. Stamm, R. Paetzel, I. Bragin, J. Kleinschmidt, D. Basting, F. Voss, “Recent developments in industrial excimer laser technology,” in XI International Symposium on Gas Flow and Chemical Lasers and High-Power Laser Conference, D. R. Hall, H. J. Baker, eds., Proc. SPIE3092, 485–492 (1997).
[CrossRef]

Bennett, J. M.

Berger, M.

E. Quesnel, M. Berger, J. Cigna, D. Duca, C. Pellé, F. Pierre, “Near-UV to IR optical characterization of YF3 thin films deposited by evaporation and ion beam processes,” in Developments in Optical Component Coatings, I. Reid, ed., Proc. SPIE2776, 366–372 (1996).
[CrossRef]

Bosch, S.

S. Bosch, J. Ferré-Borrull, N. Leinfellner, A. Canillas, “Effective dielectric function of mixtures of three or more materials: a numerical procedure for computations,” Surface Sci. 453, 9–17 (2000).
[CrossRef]

D. Ristau, W. Arens, S. Bosch, A. Duparré, E. Masetti, D. Jacob, G. Kiriakidis, F. Peiro, E. Quesnel, A. V. Tikhonravov, “UV-optical and microstructural properties of MgF2 coatings deposited by IBS and PVD processes,” in Advances in Optical Interference Coatings, C. Amra, H. A. Macleod, eds., Proc. SPIE3738, 436–445 (1999).
[CrossRef]

Bousquet, P.

C. Amra, P. Bousquet, “Scattering from surfaces and multilayer coatings: recent advances for a better investigation of experiment,” in Surface Measurement and Characterization, J. M. Bennett, ed., Proc. SPIE1009, 82–97 (1988).
[CrossRef]

Bragin, I.

U. Stamm, R. Paetzel, I. Bragin, J. Kleinschmidt, D. Basting, F. Voss, “Recent developments in industrial excimer laser technology,” in XI International Symposium on Gas Flow and Chemical Lasers and High-Power Laser Conference, D. R. Hall, H. J. Baker, eds., Proc. SPIE3092, 485–492 (1997).
[CrossRef]

Canillas, A.

S. Bosch, J. Ferré-Borrull, N. Leinfellner, A. Canillas, “Effective dielectric function of mixtures of three or more materials: a numerical procedure for computations,” Surface Sci. 453, 9–17 (2000).
[CrossRef]

Church, E. L.

E. L. Church, “Fractal surface finish,” Appl. Opt. 27, 1518–1526 (1988).
[CrossRef] [PubMed]

E. L. Church, P. Z. Tackacs, T. A. Leonard, “The prediction of BRDFs from surface profile measurements,” in Scatter from Optical Components, J. C. Stover, ed. Proc. SPIE1165, 136–150 (1989).
[CrossRef]

Cigna, J.

E. Quesnel, M. Berger, J. Cigna, D. Duca, C. Pellé, F. Pierre, “Near-UV to IR optical characterization of YF3 thin films deposited by evaporation and ion beam processes,” in Developments in Optical Component Coatings, I. Reid, ed., Proc. SPIE2776, 366–372 (1996).
[CrossRef]

Dancy, J. H.

Dijon, J.

J. Dijon, E. Quesnel, B. Rolland, P. Garrec, C. Pellé, J. Hue, “High damage threshold fluoride UV mirrors made by ion beam sputtering,” in Laser-Induced Damage in Optical Materials Symposium, Boulder, 1997, G. J. Exharos, A. H. Guenther, M. R. Kozlowski, M. J. Soileau, eds., Proc. SPIE3244, 406–416 (1998).
[CrossRef]

Dohle, R.

A. Duparré, R. Dohle, H. Müller, “Relation between light scattering and morphology of columnar structured optical thin films,” J. Mod. Opt. 37, 1383–1390 (1990).
[CrossRef]

Duca, D.

E. Quesnel, M. Berger, J. Cigna, D. Duca, C. Pellé, F. Pierre, “Near-UV to IR optical characterization of YF3 thin films deposited by evaporation and ion beam processes,” in Developments in Optical Component Coatings, I. Reid, ed., Proc. SPIE2776, 366–372 (1996).
[CrossRef]

Duparré, A.

J. Ferré-Borrull, A. Duparré, E. Quesnel, “Roughness and light scattering of ion-beam-sputtered fluoride coatings for 193 nm,” Appl. Opt. 39, 5854–5864 (2000).
[CrossRef]

S. Jakobs, A. Duparré, H. Truckenbrodt, “Interfacial roughness and related scatter in ultraviolet optical coatings: a systematic experimental approach,” Appl. Opt. 37, 1180–1193 (1998).
[CrossRef]

A. Duparré, R. Dohle, H. Müller, “Relation between light scattering and morphology of columnar structured optical thin films,” J. Mod. Opt. 37, 1383–1390 (1990).
[CrossRef]

A. Duparré, G. Notni, “Multi-type surface and thin film characterization using light scattering, scanning force microscopy and white light interferometry,” in Optical Metrology, G. A. Al-Jumailiy, ed., Vol. CR72 of SPIE Critical Review Papers (Society for Photo-Optical Instrumentation Engineers, Bellingham, Wa., 1999), pp. 213–231.

E. Quesnel, A. Petit Dit Dariel, A. Duparré, J. Ferré-Borrull, J. Steinert, “DUV light scattering and morphology of ion beam sputtered fluoride coatings,” in Advances in Optical Interference Coatings, C. Amra, H. A. Macleod, eds., Proc. SPIE3738, 410–416 (1999).
[CrossRef]

A. Duparré, “Light scattering of thin dielectric films,” in Thin Films for Optical Coatings, R. E. Hummel, K. H. Günter, eds., Vol. 1 of Handbook of Optical Properties Series (CRC, Boca Raton, Fla., 1995), pp. 273–304.

D. Ristau, W. Arens, S. Bosch, A. Duparré, E. Masetti, D. Jacob, G. Kiriakidis, F. Peiro, E. Quesnel, A. V. Tikhonravov, “UV-optical and microstructural properties of MgF2 coatings deposited by IBS and PVD processes,” in Advances in Optical Interference Coatings, C. Amra, H. A. Macleod, eds., Proc. SPIE3738, 436–445 (1999).
[CrossRef]

Elson, J. M.

Ferré-Borrull, J.

J. Ferré-Borrull, A. Duparré, E. Quesnel, “Roughness and light scattering of ion-beam-sputtered fluoride coatings for 193 nm,” Appl. Opt. 39, 5854–5864 (2000).
[CrossRef]

S. Bosch, J. Ferré-Borrull, N. Leinfellner, A. Canillas, “Effective dielectric function of mixtures of three or more materials: a numerical procedure for computations,” Surface Sci. 453, 9–17 (2000).
[CrossRef]

E. Quesnel, A. Petit Dit Dariel, A. Duparré, J. Ferré-Borrull, J. Steinert, “DUV light scattering and morphology of ion beam sputtered fluoride coatings,” in Advances in Optical Interference Coatings, C. Amra, H. A. Macleod, eds., Proc. SPIE3738, 410–416 (1999).
[CrossRef]

Flannery, B. P.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge U. Press, Cambridge, 1992).

Garrec, P.

J. Dijon, E. Quesnel, B. Rolland, P. Garrec, C. Pellé, J. Hue, “High damage threshold fluoride UV mirrors made by ion beam sputtering,” in Laser-Induced Damage in Optical Materials Symposium, Boulder, 1997, G. J. Exharos, A. H. Guenther, M. R. Kozlowski, M. J. Soileau, eds., Proc. SPIE3244, 406–416 (1998).
[CrossRef]

Hue, J.

J. Dijon, E. Quesnel, B. Rolland, P. Garrec, C. Pellé, J. Hue, “High damage threshold fluoride UV mirrors made by ion beam sputtering,” in Laser-Induced Damage in Optical Materials Symposium, Boulder, 1997, G. J. Exharos, A. H. Guenther, M. R. Kozlowski, M. J. Soileau, eds., Proc. SPIE3244, 406–416 (1998).
[CrossRef]

Jacob, D.

D. Ristau, W. Arens, S. Bosch, A. Duparré, E. Masetti, D. Jacob, G. Kiriakidis, F. Peiro, E. Quesnel, A. V. Tikhonravov, “UV-optical and microstructural properties of MgF2 coatings deposited by IBS and PVD processes,” in Advances in Optical Interference Coatings, C. Amra, H. A. Macleod, eds., Proc. SPIE3738, 436–445 (1999).
[CrossRef]

Jakobs, S.

Kiriakidis, G.

D. Ristau, W. Arens, S. Bosch, A. Duparré, E. Masetti, D. Jacob, G. Kiriakidis, F. Peiro, E. Quesnel, A. V. Tikhonravov, “UV-optical and microstructural properties of MgF2 coatings deposited by IBS and PVD processes,” in Advances in Optical Interference Coatings, C. Amra, H. A. Macleod, eds., Proc. SPIE3738, 436–445 (1999).
[CrossRef]

Kleinschmidt, J.

U. Stamm, R. Paetzel, I. Bragin, J. Kleinschmidt, D. Basting, F. Voss, “Recent developments in industrial excimer laser technology,” in XI International Symposium on Gas Flow and Chemical Lasers and High-Power Laser Conference, D. R. Hall, H. J. Baker, eds., Proc. SPIE3092, 485–492 (1997).
[CrossRef]

Leinfellner, N.

S. Bosch, J. Ferré-Borrull, N. Leinfellner, A. Canillas, “Effective dielectric function of mixtures of three or more materials: a numerical procedure for computations,” Surface Sci. 453, 9–17 (2000).
[CrossRef]

Leonard, T. A.

E. L. Church, P. Z. Tackacs, T. A. Leonard, “The prediction of BRDFs from surface profile measurements,” in Scatter from Optical Components, J. C. Stover, ed. Proc. SPIE1165, 136–150 (1989).
[CrossRef]

Llebaria, A.

G. Rasigni, F. Varnier, M. Rasigni, J. Palmari, A. Llebaria, “Roughness spectrum and surface plasmons for surfaces of silver, copper, gold, and magnesium deposits,” Phys. Rev. B 27, 819–830 (1983).
[CrossRef]

Masetti, E.

D. Ristau, W. Arens, S. Bosch, A. Duparré, E. Masetti, D. Jacob, G. Kiriakidis, F. Peiro, E. Quesnel, A. V. Tikhonravov, “UV-optical and microstructural properties of MgF2 coatings deposited by IBS and PVD processes,” in Advances in Optical Interference Coatings, C. Amra, H. A. Macleod, eds., Proc. SPIE3738, 436–445 (1999).
[CrossRef]

Mattsson, L.

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

Müller, H.

A. Duparré, R. Dohle, H. Müller, “Relation between light scattering and morphology of columnar structured optical thin films,” J. Mod. Opt. 37, 1383–1390 (1990).
[CrossRef]

Notni, G.

A. Duparré, G. Notni, “Multi-type surface and thin film characterization using light scattering, scanning force microscopy and white light interferometry,” in Optical Metrology, G. A. Al-Jumailiy, ed., Vol. CR72 of SPIE Critical Review Papers (Society for Photo-Optical Instrumentation Engineers, Bellingham, Wa., 1999), pp. 213–231.

Paetzel, R.

U. Stamm, R. Paetzel, I. Bragin, J. Kleinschmidt, D. Basting, F. Voss, “Recent developments in industrial excimer laser technology,” in XI International Symposium on Gas Flow and Chemical Lasers and High-Power Laser Conference, D. R. Hall, H. J. Baker, eds., Proc. SPIE3092, 485–492 (1997).
[CrossRef]

Palmari, J.

G. Rasigni, F. Varnier, M. Rasigni, J. Palmari, A. Llebaria, “Roughness spectrum and surface plasmons for surfaces of silver, copper, gold, and magnesium deposits,” Phys. Rev. B 27, 819–830 (1983).
[CrossRef]

Peiro, F.

D. Ristau, W. Arens, S. Bosch, A. Duparré, E. Masetti, D. Jacob, G. Kiriakidis, F. Peiro, E. Quesnel, A. V. Tikhonravov, “UV-optical and microstructural properties of MgF2 coatings deposited by IBS and PVD processes,” in Advances in Optical Interference Coatings, C. Amra, H. A. Macleod, eds., Proc. SPIE3738, 436–445 (1999).
[CrossRef]

Pellé, C.

J. Dijon, E. Quesnel, B. Rolland, P. Garrec, C. Pellé, J. Hue, “High damage threshold fluoride UV mirrors made by ion beam sputtering,” in Laser-Induced Damage in Optical Materials Symposium, Boulder, 1997, G. J. Exharos, A. H. Guenther, M. R. Kozlowski, M. J. Soileau, eds., Proc. SPIE3244, 406–416 (1998).
[CrossRef]

E. Quesnel, M. Berger, J. Cigna, D. Duca, C. Pellé, F. Pierre, “Near-UV to IR optical characterization of YF3 thin films deposited by evaporation and ion beam processes,” in Developments in Optical Component Coatings, I. Reid, ed., Proc. SPIE2776, 366–372 (1996).
[CrossRef]

Pelletier, E.

Petit Dit Dariel, A.

E. Quesnel, A. Petit Dit Dariel, A. Duparré, J. Ferré-Borrull, J. Steinert, “DUV light scattering and morphology of ion beam sputtered fluoride coatings,” in Advances in Optical Interference Coatings, C. Amra, H. A. Macleod, eds., Proc. SPIE3738, 410–416 (1999).
[CrossRef]

Pierre, F.

E. Quesnel, M. Berger, J. Cigna, D. Duca, C. Pellé, F. Pierre, “Near-UV to IR optical characterization of YF3 thin films deposited by evaporation and ion beam processes,” in Developments in Optical Component Coatings, I. Reid, ed., Proc. SPIE2776, 366–372 (1996).
[CrossRef]

Press, W. H.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge U. Press, Cambridge, 1992).

Quesnel, E.

J. Ferré-Borrull, A. Duparré, E. Quesnel, “Roughness and light scattering of ion-beam-sputtered fluoride coatings for 193 nm,” Appl. Opt. 39, 5854–5864 (2000).
[CrossRef]

E. Quesnel, M. Berger, J. Cigna, D. Duca, C. Pellé, F. Pierre, “Near-UV to IR optical characterization of YF3 thin films deposited by evaporation and ion beam processes,” in Developments in Optical Component Coatings, I. Reid, ed., Proc. SPIE2776, 366–372 (1996).
[CrossRef]

E. Quesnel, A. Petit Dit Dariel, A. Duparré, J. Ferré-Borrull, J. Steinert, “DUV light scattering and morphology of ion beam sputtered fluoride coatings,” in Advances in Optical Interference Coatings, C. Amra, H. A. Macleod, eds., Proc. SPIE3738, 410–416 (1999).
[CrossRef]

J. Dijon, E. Quesnel, B. Rolland, P. Garrec, C. Pellé, J. Hue, “High damage threshold fluoride UV mirrors made by ion beam sputtering,” in Laser-Induced Damage in Optical Materials Symposium, Boulder, 1997, G. J. Exharos, A. H. Guenther, M. R. Kozlowski, M. J. Soileau, eds., Proc. SPIE3244, 406–416 (1998).
[CrossRef]

D. Ristau, W. Arens, S. Bosch, A. Duparré, E. Masetti, D. Jacob, G. Kiriakidis, F. Peiro, E. Quesnel, A. V. Tikhonravov, “UV-optical and microstructural properties of MgF2 coatings deposited by IBS and PVD processes,” in Advances in Optical Interference Coatings, C. Amra, H. A. Macleod, eds., Proc. SPIE3738, 436–445 (1999).
[CrossRef]

Rahn, J. P.

Rasigni, G.

G. Rasigni, F. Varnier, M. Rasigni, J. Palmari, A. Llebaria, “Roughness spectrum and surface plasmons for surfaces of silver, copper, gold, and magnesium deposits,” Phys. Rev. B 27, 819–830 (1983).
[CrossRef]

Rasigni, M.

G. Rasigni, F. Varnier, M. Rasigni, J. Palmari, A. Llebaria, “Roughness spectrum and surface plasmons for surfaces of silver, copper, gold, and magnesium deposits,” Phys. Rev. B 27, 819–830 (1983).
[CrossRef]

Ristau, D.

D. Ristau, W. Arens, S. Bosch, A. Duparré, E. Masetti, D. Jacob, G. Kiriakidis, F. Peiro, E. Quesnel, A. V. Tikhonravov, “UV-optical and microstructural properties of MgF2 coatings deposited by IBS and PVD processes,” in Advances in Optical Interference Coatings, C. Amra, H. A. Macleod, eds., Proc. SPIE3738, 436–445 (1999).
[CrossRef]

Robic, J. Y.

J. Y. Robic, Laboratoire d’Electronique de Technologie et d’Instrumentation, Départment Optronique, Grenoble, France (personal communication, 1997).

Rolland, B.

J. Dijon, E. Quesnel, B. Rolland, P. Garrec, C. Pellé, J. Hue, “High damage threshold fluoride UV mirrors made by ion beam sputtering,” in Laser-Induced Damage in Optical Materials Symposium, Boulder, 1997, G. J. Exharos, A. H. Guenther, M. R. Kozlowski, M. J. Soileau, eds., Proc. SPIE3244, 406–416 (1998).
[CrossRef]

Rönnow, D.

D. Rönnow, “Interface roughness statistics of thin films from angle-resolved light scattering at three wavelengths,” Opt. Eng. 37, 696–704 (1998).
[CrossRef]

D. Rönnow, “Elastic light scattering by thin films, spectroscopic measurements and analysis,” Ph.D. dissertation (Acta Universitatis Upsaliensis, Uppsala, Sweden, 1996).

Stamm, U.

U. Stamm, R. Paetzel, I. Bragin, J. Kleinschmidt, D. Basting, F. Voss, “Recent developments in industrial excimer laser technology,” in XI International Symposium on Gas Flow and Chemical Lasers and High-Power Laser Conference, D. R. Hall, H. J. Baker, eds., Proc. SPIE3092, 485–492 (1997).
[CrossRef]

Steinert, J.

E. Quesnel, A. Petit Dit Dariel, A. Duparré, J. Ferré-Borrull, J. Steinert, “DUV light scattering and morphology of ion beam sputtered fluoride coatings,” in Advances in Optical Interference Coatings, C. Amra, H. A. Macleod, eds., Proc. SPIE3738, 410–416 (1999).
[CrossRef]

Stover, J. C.

J. C. Stover, Optical Scattering: Measurement and Analysis (McGraw-Hill, New York, 1990).

Tackacs, P. Z.

E. L. Church, P. Z. Tackacs, T. A. Leonard, “The prediction of BRDFs from surface profile measurements,” in Scatter from Optical Components, J. C. Stover, ed. Proc. SPIE1165, 136–150 (1989).
[CrossRef]

Teukolsky, S. A.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge U. Press, Cambridge, 1992).

Tikhonravov, A. V.

D. Ristau, W. Arens, S. Bosch, A. Duparré, E. Masetti, D. Jacob, G. Kiriakidis, F. Peiro, E. Quesnel, A. V. Tikhonravov, “UV-optical and microstructural properties of MgF2 coatings deposited by IBS and PVD processes,” in Advances in Optical Interference Coatings, C. Amra, H. A. Macleod, eds., Proc. SPIE3738, 436–445 (1999).
[CrossRef]

Truckenbrodt, H.

Varnier, F.

G. Rasigni, F. Varnier, M. Rasigni, J. Palmari, A. Llebaria, “Roughness spectrum and surface plasmons for surfaces of silver, copper, gold, and magnesium deposits,” Phys. Rev. B 27, 819–830 (1983).
[CrossRef]

Vetterling, W. T.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge U. Press, Cambridge, 1992).

Voss, F.

U. Stamm, R. Paetzel, I. Bragin, J. Kleinschmidt, D. Basting, F. Voss, “Recent developments in industrial excimer laser technology,” in XI International Symposium on Gas Flow and Chemical Lasers and High-Power Laser Conference, D. R. Hall, H. J. Baker, eds., Proc. SPIE3092, 485–492 (1997).
[CrossRef]

Appl. Opt. (8)

J. Mod. Opt. (1)

A. Duparré, R. Dohle, H. Müller, “Relation between light scattering and morphology of columnar structured optical thin films,” J. Mod. Opt. 37, 1383–1390 (1990).
[CrossRef]

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Opt. Eng. (1)

D. Rönnow, “Interface roughness statistics of thin films from angle-resolved light scattering at three wavelengths,” Opt. Eng. 37, 696–704 (1998).
[CrossRef]

Phys. Rev. B (2)

G. Rasigni, F. Varnier, M. Rasigni, J. Palmari, A. Llebaria, “Roughness spectrum and surface plasmons for surfaces of silver, copper, gold, and magnesium deposits,” Phys. Rev. B 27, 819–830 (1983).
[CrossRef]

J. M. Elson, “Theory of light scattering from a rough surface with an inhomogeneous dielectric permitivity,” Phys. Rev. B 30, 5460–5480 (1984).
[CrossRef]

Surface Sci. (1)

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[CrossRef]

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[CrossRef]

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[CrossRef]

D. Ristau, W. Arens, S. Bosch, A. Duparré, E. Masetti, D. Jacob, G. Kiriakidis, F. Peiro, E. Quesnel, A. V. Tikhonravov, “UV-optical and microstructural properties of MgF2 coatings deposited by IBS and PVD processes,” in Advances in Optical Interference Coatings, C. Amra, H. A. Macleod, eds., Proc. SPIE3738, 436–445 (1999).
[CrossRef]

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

A. Duparré, G. Notni, “Multi-type surface and thin film characterization using light scattering, scanning force microscopy and white light interferometry,” in Optical Metrology, G. A. Al-Jumailiy, ed., Vol. CR72 of SPIE Critical Review Papers (Society for Photo-Optical Instrumentation Engineers, Bellingham, Wa., 1999), pp. 213–231.

A. Duparré, “Light scattering of thin dielectric films,” in Thin Films for Optical Coatings, R. E. Hummel, K. H. Günter, eds., Vol. 1 of Handbook of Optical Properties Series (CRC, Boca Raton, Fla., 1995), pp. 273–304.

D. Rönnow, “Elastic light scattering by thin films, spectroscopic measurements and analysis,” Ph.D. dissertation (Acta Universitatis Upsaliensis, Uppsala, Sweden, 1996).

E. L. Church, P. Z. Tackacs, T. A. Leonard, “The prediction of BRDFs from surface profile measurements,” in Scatter from Optical Components, J. C. Stover, ed. Proc. SPIE1165, 136–150 (1989).
[CrossRef]

E. Quesnel, A. Petit Dit Dariel, A. Duparré, J. Ferré-Borrull, J. Steinert, “DUV light scattering and morphology of ion beam sputtered fluoride coatings,” in Advances in Optical Interference Coatings, C. Amra, H. A. Macleod, eds., Proc. SPIE3738, 410–416 (1999).
[CrossRef]

E. Quesnel, M. Berger, J. Cigna, D. Duca, C. Pellé, F. Pierre, “Near-UV to IR optical characterization of YF3 thin films deposited by evaporation and ion beam processes,” in Developments in Optical Component Coatings, I. Reid, ed., Proc. SPIE2776, 366–372 (1996).
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Figures (9)

Fig. 1
Fig. 1

Example of the combination of PSD functions corresponding to different scan sizes.

Fig. 2
Fig. 2

Example of fitting of a measured PSD to a theoretical model. See text for the details.

Fig. 3
Fig. 3

Top view AFM image of sample S/L on CaF2.

Fig. 4
Fig. 4

Top view AFM image of sample S/L/H/L on CaF2.

Fig. 5
Fig. 5

Selected PSD functions of the samples with quarter-wave stacks. (a) FS substrate. (b) CaF2 substrate.

Fig. 6
Fig. 6

Top view AFM image measurement of sample S/(L/H)10 on CaF2.

Fig. 7
Fig. 7

Selected PSD functions of the samples with coatings consisting of half-wave layer stacks. (a) FS substrate. (b) CaF2 substrate.

Fig. 8
Fig. 8

Intrinsic rms roughness of the coatings with quarter-wave designs.

Fig. 9
Fig. 9

Intrinsic correlation length of the coatings with quarter-wave designs.

Tables (5)

Tables Icon

Table 1 Result of the Roughness Modeling of Sample S/L/H/L on CaF2

Tables Icon

Table 2 Designs of the Samples Studied in This Paper

Tables Icon

Table 3 Roughness Characterization of the Coatings Deposited on FS

Tables Icon

Table 4 Roughness Characterization of the Coatings Deposited on CaF2

Tables Icon

Table 5 Roughness Characterization of the Substrates

Equations (11)

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PSDcombinedf=i=1NPSDif1/N,
PSDgaussf; σs, τs=πσs2τs2 exp-π2τs2f2,
PSDexpf; σl, τl=2πσl2τl21+4π2τl2f23/2.
PSDfractalf; K, n=K/fn+1,
PSDABCf; A, B, C=A1+B2f2C+1/2,
σABC2=2πAB2C-1,  τABC2=C-12B22π2C.
PSDshf; σsh, τsh, fsh=πσsh2τsh2 exp-π2τsh2f-fsh2.
PSDsubstratef; K, n=PSDfractalf; K, n,
PSDcoat1f; K, n, σABC, τABC, C=PSDfractalf; K, n+PSDABCf; σABC, τABC, C.
PSDcoat2f; K, n, σABC, τABC, C, σsh, τsh, fsh=PSDfractalf; K, n+PSDABCf; σABC, τABC, C+PSDshf; σsh, τsh, fsh,
MeritP=1Ni=1Nlog PSDmeasuredfi-log PSDmodelfi; P2.

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