Abstract

Light scattered from interface imperfections carries valuable information about its origins. For single surfaces, light-scattering techniques have become a powerful tool for the characterization of surface roughness. For thin-film coatings, however, solving the inverse scattering problem seemed to be impossible because of the large number of parameters involved. A simplified model is presented that introduces two parameters: Parameter δ describes optical thickness deviations from the perfect design, and param eter β describes the roughness evolution inside the coating according to a power law. The new method is used to investigate structural and alteration effects of HR coatings for 193nm, as well as laser-induced degradation effects in Rugate filters for 355nm.

© 2011 Optical Society of America

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  1. S. Schröder and A. Duparré, “Finish assessment of complex surfaces by advanced light scattering techniques,” Proc. SPIE 7102, 71020F (2008).
  2. A. Duparré, “Scattering from surfaces and thin films,” in Encyclopedia of Modern Optics, B.D.Guenther, D.G.Steel, and L.Bayvel, eds. (Elsevier, 2004).
  3. S. Schröder, M. Kamprath, A. Duparré, A. Tünnermann, B. Kühn, and U. Klett, “Bulk scattering properties of synthetic fused silica at 193nm,” Opt. Express 14, 10537–10549 (2006).
    [CrossRef]
  4. J. Stover, Optical Scattering-Measurement and Analysis, 2nd ed. (SPIE Press, 1995).
  5. M. Trost, S. Schröder, T. Feigl, and A. Duparré, “Influence of the substrate finish and thin film roughness on the optical performance of Mo/Si multilayers,” Appl. Opt. 50, C148–C153 (2011).
  6. S. Schröder, A. Duparré, and A. Tünnermann, “Roughness evolution and scatter losses of multilayers for 193nm optics,” Appl. Opt. 47, C88–C97 (2008).
    [CrossRef]
  7. J. M. Elson, “Diffraction and diffuse scattering from dielectric multilayers,” J. Opt. Soc. Am. 69, 48–54 (1979).
    [CrossRef]
  8. P. Bousquet, F. Flory, and P. Roche, “Scattering from multilayer thin films: theory and experiment,” J. Opt. Soc. Am. 71, 1115–1123 (1981).
    [CrossRef]
  9. C. Amra, “Light scattering from multilayer optics. I. Tools of investigation,” J. Opt. Soc. Am. A 11, 197–210 (1994).
    [CrossRef]
  10. R. Messier, “Toward quantification of thin film morphology,” J. Vac. Sci. Technol. A 4, 490–495 (1986).
    [CrossRef]
  11. W. M. Tong and R. S. Williams, “Kinetics of surface growth: phenomenology, scaling, and mechanisms of smoothening and roughening,” Annu. Rev. Phys. Chem. 45, 401–438(1994).
    [CrossRef]
  12. S. Schröder, H. Uhlig, A. Duparré, and N. Kaiser, “Nanostructure and optical properties of fluoride films for high-quality DUV/VUV optical components,” Proc. SPIE 5963, 231–240(2005).
  13. D. G. Stearns, “Stochastic model for thin film growth and erosion,” Appl. Phys. Lett. 62, 1745–1747 (1993).
    [CrossRef]
  14. J. Ferré-Borrull, A. Duparre, and E. Quesnel, “Procedure to characterize microroughness of optical thin films: application to ion-beam-sputtered vacuum-ultraviolet coatings,” Appl. Opt. 40, 2190–2199 (2001).
    [CrossRef]
  15. S. Schröder, S. Gliech, and A. Duparré, “Sensitive and flexible light scatter techniques from the VUV to IR regions,” Proc. SPIE 5965, 424–432 (2005).
  16. S. Schröder, S. Gliech, and A. Duparré, “Measurement system to determine the total and angle-resolved light scattering of optical components in the deep-ultraviolet and vacuum-ultraviolet spectral regions,” Appl. Opt. 44, 6093–6107(2005).
    [CrossRef]
  17. S. Schröder, T. Herffurth, M. Trost, and A. Duparré, “Angle-resolved scattering and reflectance of extreme-ultraviolet multilayer coatings: measurement and analysis,” Appl. Opt. 49, 1503–1512 (2010).
    [CrossRef]
  18. “Optics and optical instruments-test methods for radiation scattered by optical components,” ISO 13696:2002 (International Organization for Standardization, 2002).
  19. A. Finck, M. Hauptvogel, and A. Duparré, “Instrument for close-to-process light scatter measurements of thin film coatings and substrates,” submitted to Appl. Opt.
  20. T. Herffurth, S. Schröder, M. Trost, and A. Duparré, “Roughness measurement of ultra precision surfaces using light scattering techniques and analysis,” in Optical Fabrication and Testing, OSA Technical Digest (CD) (Optical Society of America, 2010), paper OTuA5.
  21. A. Duparré, J. Ferre-Borrull, S. Gliech, G. Notni, J. Steinert, and J. M. Bennett, “Surface characterization techniques for determining the root-mean-square roughness and power spectral densities of optical components,” Appl. Opt. 41, 154–171(2002).
    [CrossRef]
  22. M. Jupé, M. Lappschies, L. Jensen, K. Starke, and D. Ristau, “Laser-induced damage in gradual index layers and Rugate filters,” Proc. SPIE 6403, 64031A (2006).
    [CrossRef]
  23. P. Bakucz, R. Krüger-Sehm, S. Schröder, A. Duparré, and A. Tünnermann, “Wavelet Filterung von fraktalen Oberflächen,” Technisches Messen 75, 339–345 (2008).
    [CrossRef]
  24. E. L. Church, “Statistical effects in the measurement and characterization of smooth scattering surfaces,” Proc. SPIE 511, 18 (1984).

2011 (1)

2010 (1)

2008 (3)

S. Schröder, A. Duparré, and A. Tünnermann, “Roughness evolution and scatter losses of multilayers for 193nm optics,” Appl. Opt. 47, C88–C97 (2008).
[CrossRef]

S. Schröder and A. Duparré, “Finish assessment of complex surfaces by advanced light scattering techniques,” Proc. SPIE 7102, 71020F (2008).

P. Bakucz, R. Krüger-Sehm, S. Schröder, A. Duparré, and A. Tünnermann, “Wavelet Filterung von fraktalen Oberflächen,” Technisches Messen 75, 339–345 (2008).
[CrossRef]

2006 (2)

M. Jupé, M. Lappschies, L. Jensen, K. Starke, and D. Ristau, “Laser-induced damage in gradual index layers and Rugate filters,” Proc. SPIE 6403, 64031A (2006).
[CrossRef]

S. Schröder, M. Kamprath, A. Duparré, A. Tünnermann, B. Kühn, and U. Klett, “Bulk scattering properties of synthetic fused silica at 193nm,” Opt. Express 14, 10537–10549 (2006).
[CrossRef]

2005 (3)

S. Schröder, S. Gliech, and A. Duparré, “Measurement system to determine the total and angle-resolved light scattering of optical components in the deep-ultraviolet and vacuum-ultraviolet spectral regions,” Appl. Opt. 44, 6093–6107(2005).
[CrossRef]

S. Schröder, S. Gliech, and A. Duparré, “Sensitive and flexible light scatter techniques from the VUV to IR regions,” Proc. SPIE 5965, 424–432 (2005).

S. Schröder, H. Uhlig, A. Duparré, and N. Kaiser, “Nanostructure and optical properties of fluoride films for high-quality DUV/VUV optical components,” Proc. SPIE 5963, 231–240(2005).

2002 (1)

2001 (1)

1994 (2)

C. Amra, “Light scattering from multilayer optics. I. Tools of investigation,” J. Opt. Soc. Am. A 11, 197–210 (1994).
[CrossRef]

W. M. Tong and R. S. Williams, “Kinetics of surface growth: phenomenology, scaling, and mechanisms of smoothening and roughening,” Annu. Rev. Phys. Chem. 45, 401–438(1994).
[CrossRef]

1993 (1)

D. G. Stearns, “Stochastic model for thin film growth and erosion,” Appl. Phys. Lett. 62, 1745–1747 (1993).
[CrossRef]

1986 (1)

R. Messier, “Toward quantification of thin film morphology,” J. Vac. Sci. Technol. A 4, 490–495 (1986).
[CrossRef]

1984 (1)

E. L. Church, “Statistical effects in the measurement and characterization of smooth scattering surfaces,” Proc. SPIE 511, 18 (1984).

1981 (1)

1979 (1)

Amra, C.

Bakucz, P.

P. Bakucz, R. Krüger-Sehm, S. Schröder, A. Duparré, and A. Tünnermann, “Wavelet Filterung von fraktalen Oberflächen,” Technisches Messen 75, 339–345 (2008).
[CrossRef]

Bennett, J. M.

Bousquet, P.

Church, E. L.

E. L. Church, “Statistical effects in the measurement and characterization of smooth scattering surfaces,” Proc. SPIE 511, 18 (1984).

Duparre, A.

Duparré, A.

M. Trost, S. Schröder, T. Feigl, and A. Duparré, “Influence of the substrate finish and thin film roughness on the optical performance of Mo/Si multilayers,” Appl. Opt. 50, C148–C153 (2011).

S. Schröder, T. Herffurth, M. Trost, and A. Duparré, “Angle-resolved scattering and reflectance of extreme-ultraviolet multilayer coatings: measurement and analysis,” Appl. Opt. 49, 1503–1512 (2010).
[CrossRef]

S. Schröder, A. Duparré, and A. Tünnermann, “Roughness evolution and scatter losses of multilayers for 193nm optics,” Appl. Opt. 47, C88–C97 (2008).
[CrossRef]

P. Bakucz, R. Krüger-Sehm, S. Schröder, A. Duparré, and A. Tünnermann, “Wavelet Filterung von fraktalen Oberflächen,” Technisches Messen 75, 339–345 (2008).
[CrossRef]

S. Schröder and A. Duparré, “Finish assessment of complex surfaces by advanced light scattering techniques,” Proc. SPIE 7102, 71020F (2008).

S. Schröder, M. Kamprath, A. Duparré, A. Tünnermann, B. Kühn, and U. Klett, “Bulk scattering properties of synthetic fused silica at 193nm,” Opt. Express 14, 10537–10549 (2006).
[CrossRef]

S. Schröder, S. Gliech, and A. Duparré, “Sensitive and flexible light scatter techniques from the VUV to IR regions,” Proc. SPIE 5965, 424–432 (2005).

S. Schröder, H. Uhlig, A. Duparré, and N. Kaiser, “Nanostructure and optical properties of fluoride films for high-quality DUV/VUV optical components,” Proc. SPIE 5963, 231–240(2005).

S. Schröder, S. Gliech, and A. Duparré, “Measurement system to determine the total and angle-resolved light scattering of optical components in the deep-ultraviolet and vacuum-ultraviolet spectral regions,” Appl. Opt. 44, 6093–6107(2005).
[CrossRef]

A. Duparré, J. Ferre-Borrull, S. Gliech, G. Notni, J. Steinert, and J. M. Bennett, “Surface characterization techniques for determining the root-mean-square roughness and power spectral densities of optical components,” Appl. Opt. 41, 154–171(2002).
[CrossRef]

A. Duparré, “Scattering from surfaces and thin films,” in Encyclopedia of Modern Optics, B.D.Guenther, D.G.Steel, and L.Bayvel, eds. (Elsevier, 2004).

T. Herffurth, S. Schröder, M. Trost, and A. Duparré, “Roughness measurement of ultra precision surfaces using light scattering techniques and analysis,” in Optical Fabrication and Testing, OSA Technical Digest (CD) (Optical Society of America, 2010), paper OTuA5.

A. Finck, M. Hauptvogel, and A. Duparré, “Instrument for close-to-process light scatter measurements of thin film coatings and substrates,” submitted to Appl. Opt.

Elson, J. M.

Feigl, T.

Ferre-Borrull, J.

Ferré-Borrull, J.

Finck, A.

A. Finck, M. Hauptvogel, and A. Duparré, “Instrument for close-to-process light scatter measurements of thin film coatings and substrates,” submitted to Appl. Opt.

Flory, F.

Gliech, S.

Hauptvogel, M.

A. Finck, M. Hauptvogel, and A. Duparré, “Instrument for close-to-process light scatter measurements of thin film coatings and substrates,” submitted to Appl. Opt.

Herffurth, T.

S. Schröder, T. Herffurth, M. Trost, and A. Duparré, “Angle-resolved scattering and reflectance of extreme-ultraviolet multilayer coatings: measurement and analysis,” Appl. Opt. 49, 1503–1512 (2010).
[CrossRef]

T. Herffurth, S. Schröder, M. Trost, and A. Duparré, “Roughness measurement of ultra precision surfaces using light scattering techniques and analysis,” in Optical Fabrication and Testing, OSA Technical Digest (CD) (Optical Society of America, 2010), paper OTuA5.

Jensen, L.

M. Jupé, M. Lappschies, L. Jensen, K. Starke, and D. Ristau, “Laser-induced damage in gradual index layers and Rugate filters,” Proc. SPIE 6403, 64031A (2006).
[CrossRef]

Jupé, M.

M. Jupé, M. Lappschies, L. Jensen, K. Starke, and D. Ristau, “Laser-induced damage in gradual index layers and Rugate filters,” Proc. SPIE 6403, 64031A (2006).
[CrossRef]

Kaiser, N.

S. Schröder, H. Uhlig, A. Duparré, and N. Kaiser, “Nanostructure and optical properties of fluoride films for high-quality DUV/VUV optical components,” Proc. SPIE 5963, 231–240(2005).

Kamprath, M.

Klett, U.

Krüger-Sehm, R.

P. Bakucz, R. Krüger-Sehm, S. Schröder, A. Duparré, and A. Tünnermann, “Wavelet Filterung von fraktalen Oberflächen,” Technisches Messen 75, 339–345 (2008).
[CrossRef]

Kühn, B.

Lappschies, M.

M. Jupé, M. Lappschies, L. Jensen, K. Starke, and D. Ristau, “Laser-induced damage in gradual index layers and Rugate filters,” Proc. SPIE 6403, 64031A (2006).
[CrossRef]

Messier, R.

R. Messier, “Toward quantification of thin film morphology,” J. Vac. Sci. Technol. A 4, 490–495 (1986).
[CrossRef]

Notni, G.

Quesnel, E.

Ristau, D.

M. Jupé, M. Lappschies, L. Jensen, K. Starke, and D. Ristau, “Laser-induced damage in gradual index layers and Rugate filters,” Proc. SPIE 6403, 64031A (2006).
[CrossRef]

Roche, P.

Schröder, S.

M. Trost, S. Schröder, T. Feigl, and A. Duparré, “Influence of the substrate finish and thin film roughness on the optical performance of Mo/Si multilayers,” Appl. Opt. 50, C148–C153 (2011).

S. Schröder, T. Herffurth, M. Trost, and A. Duparré, “Angle-resolved scattering and reflectance of extreme-ultraviolet multilayer coatings: measurement and analysis,” Appl. Opt. 49, 1503–1512 (2010).
[CrossRef]

S. Schröder, A. Duparré, and A. Tünnermann, “Roughness evolution and scatter losses of multilayers for 193nm optics,” Appl. Opt. 47, C88–C97 (2008).
[CrossRef]

P. Bakucz, R. Krüger-Sehm, S. Schröder, A. Duparré, and A. Tünnermann, “Wavelet Filterung von fraktalen Oberflächen,” Technisches Messen 75, 339–345 (2008).
[CrossRef]

S. Schröder and A. Duparré, “Finish assessment of complex surfaces by advanced light scattering techniques,” Proc. SPIE 7102, 71020F (2008).

S. Schröder, M. Kamprath, A. Duparré, A. Tünnermann, B. Kühn, and U. Klett, “Bulk scattering properties of synthetic fused silica at 193nm,” Opt. Express 14, 10537–10549 (2006).
[CrossRef]

S. Schröder, S. Gliech, and A. Duparré, “Sensitive and flexible light scatter techniques from the VUV to IR regions,” Proc. SPIE 5965, 424–432 (2005).

S. Schröder, H. Uhlig, A. Duparré, and N. Kaiser, “Nanostructure and optical properties of fluoride films for high-quality DUV/VUV optical components,” Proc. SPIE 5963, 231–240(2005).

S. Schröder, S. Gliech, and A. Duparré, “Measurement system to determine the total and angle-resolved light scattering of optical components in the deep-ultraviolet and vacuum-ultraviolet spectral regions,” Appl. Opt. 44, 6093–6107(2005).
[CrossRef]

T. Herffurth, S. Schröder, M. Trost, and A. Duparré, “Roughness measurement of ultra precision surfaces using light scattering techniques and analysis,” in Optical Fabrication and Testing, OSA Technical Digest (CD) (Optical Society of America, 2010), paper OTuA5.

Starke, K.

M. Jupé, M. Lappschies, L. Jensen, K. Starke, and D. Ristau, “Laser-induced damage in gradual index layers and Rugate filters,” Proc. SPIE 6403, 64031A (2006).
[CrossRef]

Stearns, D. G.

D. G. Stearns, “Stochastic model for thin film growth and erosion,” Appl. Phys. Lett. 62, 1745–1747 (1993).
[CrossRef]

Steinert, J.

Stover, J.

J. Stover, Optical Scattering-Measurement and Analysis, 2nd ed. (SPIE Press, 1995).

Tong, W. M.

W. M. Tong and R. S. Williams, “Kinetics of surface growth: phenomenology, scaling, and mechanisms of smoothening and roughening,” Annu. Rev. Phys. Chem. 45, 401–438(1994).
[CrossRef]

Trost, M.

Tünnermann, A.

Uhlig, H.

S. Schröder, H. Uhlig, A. Duparré, and N. Kaiser, “Nanostructure and optical properties of fluoride films for high-quality DUV/VUV optical components,” Proc. SPIE 5963, 231–240(2005).

Williams, R. S.

W. M. Tong and R. S. Williams, “Kinetics of surface growth: phenomenology, scaling, and mechanisms of smoothening and roughening,” Annu. Rev. Phys. Chem. 45, 401–438(1994).
[CrossRef]

Annu. Rev. Phys. Chem. (1)

W. M. Tong and R. S. Williams, “Kinetics of surface growth: phenomenology, scaling, and mechanisms of smoothening and roughening,” Annu. Rev. Phys. Chem. 45, 401–438(1994).
[CrossRef]

Appl. Opt. (6)

Appl. Phys. Lett. (1)

D. G. Stearns, “Stochastic model for thin film growth and erosion,” Appl. Phys. Lett. 62, 1745–1747 (1993).
[CrossRef]

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (1)

J. Vac. Sci. Technol. A (1)

R. Messier, “Toward quantification of thin film morphology,” J. Vac. Sci. Technol. A 4, 490–495 (1986).
[CrossRef]

Opt. Express (1)

Proc. SPIE (5)

E. L. Church, “Statistical effects in the measurement and characterization of smooth scattering surfaces,” Proc. SPIE 511, 18 (1984).

S. Schröder, S. Gliech, and A. Duparré, “Sensitive and flexible light scatter techniques from the VUV to IR regions,” Proc. SPIE 5965, 424–432 (2005).

M. Jupé, M. Lappschies, L. Jensen, K. Starke, and D. Ristau, “Laser-induced damage in gradual index layers and Rugate filters,” Proc. SPIE 6403, 64031A (2006).
[CrossRef]

S. Schröder, H. Uhlig, A. Duparré, and N. Kaiser, “Nanostructure and optical properties of fluoride films for high-quality DUV/VUV optical components,” Proc. SPIE 5963, 231–240(2005).

S. Schröder and A. Duparré, “Finish assessment of complex surfaces by advanced light scattering techniques,” Proc. SPIE 7102, 71020F (2008).

Technisches Messen (1)

P. Bakucz, R. Krüger-Sehm, S. Schröder, A. Duparré, and A. Tünnermann, “Wavelet Filterung von fraktalen Oberflächen,” Technisches Messen 75, 339–345 (2008).
[CrossRef]

Other (5)

A. Duparré, “Scattering from surfaces and thin films,” in Encyclopedia of Modern Optics, B.D.Guenther, D.G.Steel, and L.Bayvel, eds. (Elsevier, 2004).

J. Stover, Optical Scattering-Measurement and Analysis, 2nd ed. (SPIE Press, 1995).

“Optics and optical instruments-test methods for radiation scattered by optical components,” ISO 13696:2002 (International Organization for Standardization, 2002).

A. Finck, M. Hauptvogel, and A. Duparré, “Instrument for close-to-process light scatter measurements of thin film coatings and substrates,” submitted to Appl. Opt.

T. Herffurth, S. Schröder, M. Trost, and A. Duparré, “Roughness measurement of ultra precision surfaces using light scattering techniques and analysis,” in Optical Fabrication and Testing, OSA Technical Digest (CD) (Optical Society of America, 2010), paper OTuA5.

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Figures (6)

Fig. 1
Fig. 1

Scattering geometry and nomenclature.

Fig. 2
Fig. 2

ALBATROSS instrument for ARS measurement in UV–VIS–IR spectral range. (a) Schematic. (b) Photograph showing a sample (center) mounted onto the sample positioning system, as well as the detector and 3D goniometer.

Fig. 3
Fig. 3

Atomic force microscopy top-surface images of HR coating for 193 nm in 1 × 1 μm 2 and 10 × 10 μm 2 scan areas together with the corresponding bandwidth-limited rms roughness values.

Fig. 4
Fig. 4

Angle-resolved scattering of HR coating for 193 nm . Measurement (meas.) results obtained at 193 nm and modeling (mod.) results by varying (a) the roughness parameter and (b) the optical parameter.

Fig. 5
Fig. 5

Scatter map at 325 nm revealing different types of defects and DIC images (field of view 0.85 × 0.85 mm 2 ) of two different defects indicating surface and bulk effects.

Fig. 6
Fig. 6

Angle-resolved scattering of a Rugate film. (a) Measured at 325 nm at several positions near a defect site caused by laser-induced damage. (b) Results of ARS modeling compared to measured curve.

Tables (1)

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Table 1 Wavelengths, Associated Dynamic Ranges, and Noise-Equivalent ARS Levels of Instruments for Angle-Resolved Scattering Measurements at Fraunhofer IOF

Equations (1)

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ARS ( θ s ) = Δ P s ( θ s ) Δ Ω s P i i = 0 M j = 0 M F i F j * PSD i j ( f ) .

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