Abstract

Light-scattering measurements on rugate coatings made out of mixtures of SixTayOz and SixHfyOz were performed. Through successive optimization steps for the substrate roughness and deposition parameters, the overall scattering loss could be reduced by 96% to 3.5 ppm. In order to analyze the relevant scattering mechanisms in such coatings, different theoretical models for scattering from bulk and surface imperfections are compared to measured data. The best accordance between simulated and measured data could be achieved for the theory based on bulk imperfections, while the classical roughness based theory, which is used for conventional multilayer systems, gives reasonable good results.

© 2014 Optical Society of America

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References

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  1. 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]
  2. P. Frach, H. Bartzsch, D. Gloess, K. Taeschner, and J. Liebig, “Reactive magnetron sputter technologies for precision optical coatings,” in Optical Interference Coatings, M. Tilsch and D. Ristau, eds., OSA Technical Digest (online) (Optical Society of America, 2013), paper ThB.7.
  3. S. Schröder, T. Herffurth, H. Blaschke, and A. Duparré, “Angle-resolved scattering: an effective method for characterizing thin-film coatings,” Appl. Opt. 50, C164–C171 (2011).
    [CrossRef]
  4. S. Jakobs, A. Duparré, and H. Truckenbrodt, “Interfacial roughness and related scatter in ultraviolet optical coatings: a systematic experimental approach,” Appl. Opt. 37, 1180–1193 (1998).
    [CrossRef]
  5. 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]
  6. M. Trost, S. Schröder, T. Feigl, A. Duparré, and A. Tünnermann, “Influence of the substrate finish and thin film roughness on the optical performance of Mo/Si multilayers,” Appl. Opt. 50, C148–C153 (2011).
    [CrossRef]
  7. C. Amra, “Light scattering from multilayer optics. I. Tools of investigation,” J. Opt. Soc. Am. A 11, 197–210 (1994).
    [CrossRef]
  8. H. Bartzsch, K. Täschner, P. Frach, and E. Schultheiß, “Precision optical coatings with continuously varying refractive index deposited by reactive magnetron sputtering using nanoscale film growth control,” Nanofair, Dresden, Germany (2009).
  9. A. Duparré, J. Ferre-Borrull, S. Gliech, G. Notni, J. Steinert, and J. 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]
  10. J. C. Stover, Optical Scattering: Measurement and Analysis, 3rd ed. (SPIE, 2012).
  11. E. L. Church, H. A. Jenkinson, and J. M. Zavada, “Relationship between surface scattering and microtopographic features,” Opt. Eng. 18, 125–136 (1979).
    [CrossRef]
  12. D. G. Stearns, D. P. Gaines, D. W. Sweeney, and E. M. Gullikson, “Nonspecular x-ray scattering in a multilayer-coated imaging system,” J. Appl. Phys. 84, 1003–1028 (1998).
    [CrossRef]
  13. R. Messier, “Toward quantification of thin film morphology,” J. Vac. Sci. Technol. A 4, 490–495 (1986).
    [CrossRef]
  14. 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).
  15. “Optics and optical instruments-test methods for radiation scattered by optical components,” (International Organization for Standardization, 2002).
  16. P. Bousquet, F. Flory, and P. Roche, “Scattering from multilayer thin films: theory and experiment,” J. Opt. Soc. Am. 71, 1115–1123 (1981).
    [CrossRef]
  17. J. Elson, “Diffraction and diffuse scattering from dielectric multilayers,” J. Opt. Soc. Am. 69, 48–54 (1979).
    [CrossRef]
  18. P. Bussemer, K. Hehl, and S. Kassam, “Theory of light scattering from rough surfaces and interfaces and from volume inhomogeneities in an optical layer stack,” Waves in Random Media 1, 207–221 (1991).
    [CrossRef]
  19. J. M. Elson, “Characteristics of far-field scattering by means of surface roughness and variations in subsurface permittivity,” Waves in Random Media 7, 303–317 (1997).
    [CrossRef]
  20. C. Amra, C. Grèzes-Besset, and L. Bruel, “Comparison of surface and bulk scattering in optical multilayers,” Appl. Opt. 32, 5492–5503 (1993).
    [CrossRef]
  21. 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]
  22. A. von Finck, M. Hauptvogel, and A. Duparré, “Instrument for close-to-process light scatter measurements of thin film coatings and substrates,” Appl. Opt. 50, C321–C328 (2011).
    [CrossRef]
  23. A. von Finck, T. Herffurth, S. Schröder, S. Sinzinger, and A. Duparré, “Characterization of optical coatings using a table top scatterometer,” Appl. Opt.53, A259–A269 (2014).
  24. M. Trost, T. Herffurth, S. Schröder, A. Duparré, and A. Tünnermann, “Scattering reduction through oblique multilayer deposition,” Appl. Opt.53, A197–A204 (2014).
  25. S. Schröder, D. Unglaub, M. Trost, X. Cheng, J. Zhang, and A. Duparré, “Spectral angle resolved scattering of thin film coatings,” Appl. Opt. 53, A35–A41 (2014).
    [CrossRef]
  26. T. Herffurth, S. Schröder, M. Trost, A. Duparré, and A. Tünnermann, “Comprehensive nanostructure and defect analysis using a simple 3D light-scatter sensor,” Appl. Opt. 52, 3279–3287 (2013).
    [CrossRef]

2014 (1)

2013 (1)

2011 (3)

2010 (1)

2006 (1)

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]

2005 (1)

2002 (1)

1998 (2)

D. G. Stearns, D. P. Gaines, D. W. Sweeney, and E. M. Gullikson, “Nonspecular x-ray scattering in a multilayer-coated imaging system,” J. Appl. Phys. 84, 1003–1028 (1998).
[CrossRef]

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

1997 (1)

J. M. Elson, “Characteristics of far-field scattering by means of surface roughness and variations in subsurface permittivity,” Waves in Random Media 7, 303–317 (1997).
[CrossRef]

1994 (1)

1993 (1)

1991 (1)

P. Bussemer, K. Hehl, and S. Kassam, “Theory of light scattering from rough surfaces and interfaces and from volume inhomogeneities in an optical layer stack,” Waves in Random Media 1, 207–221 (1991).
[CrossRef]

1986 (1)

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

1981 (1)

1979 (2)

E. L. Church, H. A. Jenkinson, and J. M. Zavada, “Relationship between surface scattering and microtopographic features,” Opt. Eng. 18, 125–136 (1979).
[CrossRef]

J. Elson, “Diffraction and diffuse scattering from dielectric multilayers,” J. Opt. Soc. Am. 69, 48–54 (1979).
[CrossRef]

Amra, C.

Bartzsch, H.

P. Frach, H. Bartzsch, D. Gloess, K. Taeschner, and J. Liebig, “Reactive magnetron sputter technologies for precision optical coatings,” in Optical Interference Coatings, M. Tilsch and D. Ristau, eds., OSA Technical Digest (online) (Optical Society of America, 2013), paper ThB.7.

H. Bartzsch, K. Täschner, P. Frach, and E. Schultheiß, “Precision optical coatings with continuously varying refractive index deposited by reactive magnetron sputtering using nanoscale film growth control,” Nanofair, Dresden, Germany (2009).

Bennett, J.

Blaschke, H.

Bousquet, P.

Bruel, L.

Bussemer, P.

P. Bussemer, K. Hehl, and S. Kassam, “Theory of light scattering from rough surfaces and interfaces and from volume inhomogeneities in an optical layer stack,” Waves in Random Media 1, 207–221 (1991).
[CrossRef]

Cheng, X.

Church, E. L.

E. L. Church, H. A. Jenkinson, and J. M. Zavada, “Relationship between surface scattering and microtopographic features,” Opt. Eng. 18, 125–136 (1979).
[CrossRef]

Duparré, A.

S. Schröder, D. Unglaub, M. Trost, X. Cheng, J. Zhang, and A. Duparré, “Spectral angle resolved scattering of thin film coatings,” Appl. Opt. 53, A35–A41 (2014).
[CrossRef]

T. Herffurth, S. Schröder, M. Trost, A. Duparré, and A. Tünnermann, “Comprehensive nanostructure and defect analysis using a simple 3D light-scatter sensor,” Appl. Opt. 52, 3279–3287 (2013).
[CrossRef]

A. von Finck, M. Hauptvogel, and A. Duparré, “Instrument for close-to-process light scatter measurements of thin film coatings and substrates,” Appl. Opt. 50, C321–C328 (2011).
[CrossRef]

S. Schröder, T. Herffurth, H. Blaschke, and A. Duparré, “Angle-resolved scattering: an effective method for characterizing thin-film coatings,” Appl. Opt. 50, C164–C171 (2011).
[CrossRef]

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

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, 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. 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]

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

A. von Finck, T. Herffurth, S. Schröder, S. Sinzinger, and A. Duparré, “Characterization of optical coatings using a table top scatterometer,” Appl. Opt.53, A259–A269 (2014).

M. Trost, T. Herffurth, S. Schröder, A. Duparré, and A. Tünnermann, “Scattering reduction through oblique multilayer deposition,” Appl. Opt.53, A197–A204 (2014).

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).

Elson, J.

Elson, J. M.

J. M. Elson, “Characteristics of far-field scattering by means of surface roughness and variations in subsurface permittivity,” Waves in Random Media 7, 303–317 (1997).
[CrossRef]

Feigl, T.

Ferre-Borrull, J.

Flory, F.

Frach, P.

P. Frach, H. Bartzsch, D. Gloess, K. Taeschner, and J. Liebig, “Reactive magnetron sputter technologies for precision optical coatings,” in Optical Interference Coatings, M. Tilsch and D. Ristau, eds., OSA Technical Digest (online) (Optical Society of America, 2013), paper ThB.7.

H. Bartzsch, K. Täschner, P. Frach, and E. Schultheiß, “Precision optical coatings with continuously varying refractive index deposited by reactive magnetron sputtering using nanoscale film growth control,” Nanofair, Dresden, Germany (2009).

Gaines, D. P.

D. G. Stearns, D. P. Gaines, D. W. Sweeney, and E. M. Gullikson, “Nonspecular x-ray scattering in a multilayer-coated imaging system,” J. Appl. Phys. 84, 1003–1028 (1998).
[CrossRef]

Gliech, S.

Gloess, D.

P. Frach, H. Bartzsch, D. Gloess, K. Taeschner, and J. Liebig, “Reactive magnetron sputter technologies for precision optical coatings,” in Optical Interference Coatings, M. Tilsch and D. Ristau, eds., OSA Technical Digest (online) (Optical Society of America, 2013), paper ThB.7.

Grèzes-Besset, C.

Gullikson, E. M.

D. G. Stearns, D. P. Gaines, D. W. Sweeney, and E. M. Gullikson, “Nonspecular x-ray scattering in a multilayer-coated imaging system,” J. Appl. Phys. 84, 1003–1028 (1998).
[CrossRef]

Hauptvogel, M.

Hehl, K.

P. Bussemer, K. Hehl, and S. Kassam, “Theory of light scattering from rough surfaces and interfaces and from volume inhomogeneities in an optical layer stack,” Waves in Random Media 1, 207–221 (1991).
[CrossRef]

Herffurth, T.

Jakobs, S.

Jenkinson, H. A.

E. L. Church, H. A. Jenkinson, and J. M. Zavada, “Relationship between surface scattering and microtopographic features,” Opt. Eng. 18, 125–136 (1979).
[CrossRef]

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]

Kassam, S.

P. Bussemer, K. Hehl, and S. Kassam, “Theory of light scattering from rough surfaces and interfaces and from volume inhomogeneities in an optical layer stack,” Waves in Random Media 1, 207–221 (1991).
[CrossRef]

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]

Liebig, J.

P. Frach, H. Bartzsch, D. Gloess, K. Taeschner, and J. Liebig, “Reactive magnetron sputter technologies for precision optical coatings,” in Optical Interference Coatings, M. Tilsch and D. Ristau, eds., OSA Technical Digest (online) (Optical Society of America, 2013), paper ThB.7.

Messier, R.

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

Notni, G.

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.

S. Schröder, D. Unglaub, M. Trost, X. Cheng, J. Zhang, and A. Duparré, “Spectral angle resolved scattering of thin film coatings,” Appl. Opt. 53, A35–A41 (2014).
[CrossRef]

T. Herffurth, S. Schröder, M. Trost, A. Duparré, and A. Tünnermann, “Comprehensive nanostructure and defect analysis using a simple 3D light-scatter sensor,” Appl. Opt. 52, 3279–3287 (2013).
[CrossRef]

S. Schröder, T. Herffurth, H. Blaschke, and A. Duparré, “Angle-resolved scattering: an effective method for characterizing thin-film coatings,” Appl. Opt. 50, C164–C171 (2011).
[CrossRef]

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

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, 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. von Finck, T. Herffurth, S. Schröder, S. Sinzinger, and A. Duparré, “Characterization of optical coatings using a table top scatterometer,” Appl. Opt.53, A259–A269 (2014).

M. Trost, T. Herffurth, S. Schröder, A. Duparré, and A. Tünnermann, “Scattering reduction through oblique multilayer deposition,” Appl. Opt.53, A197–A204 (2014).

Schultheiß, E.

H. Bartzsch, K. Täschner, P. Frach, and E. Schultheiß, “Precision optical coatings with continuously varying refractive index deposited by reactive magnetron sputtering using nanoscale film growth control,” Nanofair, Dresden, Germany (2009).

Sinzinger, S.

A. von Finck, T. Herffurth, S. Schröder, S. Sinzinger, and A. Duparré, “Characterization of optical coatings using a table top scatterometer,” Appl. Opt.53, A259–A269 (2014).

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, D. P. Gaines, D. W. Sweeney, and E. M. Gullikson, “Nonspecular x-ray scattering in a multilayer-coated imaging system,” J. Appl. Phys. 84, 1003–1028 (1998).
[CrossRef]

Steinert, J.

Stover, J. C.

J. C. Stover, Optical Scattering: Measurement and Analysis, 3rd ed. (SPIE, 2012).

Sweeney, D. W.

D. G. Stearns, D. P. Gaines, D. W. Sweeney, and E. M. Gullikson, “Nonspecular x-ray scattering in a multilayer-coated imaging system,” J. Appl. Phys. 84, 1003–1028 (1998).
[CrossRef]

Taeschner, K.

P. Frach, H. Bartzsch, D. Gloess, K. Taeschner, and J. Liebig, “Reactive magnetron sputter technologies for precision optical coatings,” in Optical Interference Coatings, M. Tilsch and D. Ristau, eds., OSA Technical Digest (online) (Optical Society of America, 2013), paper ThB.7.

Täschner, K.

H. Bartzsch, K. Täschner, P. Frach, and E. Schultheiß, “Precision optical coatings with continuously varying refractive index deposited by reactive magnetron sputtering using nanoscale film growth control,” Nanofair, Dresden, Germany (2009).

Trost, M.

Truckenbrodt, H.

Tünnermann, A.

Unglaub, D.

von Finck, A.

A. von Finck, M. Hauptvogel, and A. Duparré, “Instrument for close-to-process light scatter measurements of thin film coatings and substrates,” Appl. Opt. 50, C321–C328 (2011).
[CrossRef]

A. von Finck, T. Herffurth, S. Schröder, S. Sinzinger, and A. Duparré, “Characterization of optical coatings using a table top scatterometer,” Appl. Opt.53, A259–A269 (2014).

Zavada, J. M.

E. L. Church, H. A. Jenkinson, and J. M. Zavada, “Relationship between surface scattering and microtopographic features,” Opt. Eng. 18, 125–136 (1979).
[CrossRef]

Zhang, J.

Appl. Opt. (10)

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

C. Amra, C. Grèzes-Besset, and L. Bruel, “Comparison of surface and bulk scattering in optical multilayers,” Appl. Opt. 32, 5492–5503 (1993).
[CrossRef]

A. Duparré, J. Ferre-Borrull, S. Gliech, G. Notni, J. Steinert, and J. 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]

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, 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]

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

S. Schröder, T. Herffurth, H. Blaschke, and A. Duparré, “Angle-resolved scattering: an effective method for characterizing thin-film coatings,” Appl. Opt. 50, C164–C171 (2011).
[CrossRef]

A. von Finck, M. Hauptvogel, and A. Duparré, “Instrument for close-to-process light scatter measurements of thin film coatings and substrates,” Appl. Opt. 50, C321–C328 (2011).
[CrossRef]

T. Herffurth, S. Schröder, M. Trost, A. Duparré, and A. Tünnermann, “Comprehensive nanostructure and defect analysis using a simple 3D light-scatter sensor,” Appl. Opt. 52, 3279–3287 (2013).
[CrossRef]

S. Schröder, D. Unglaub, M. Trost, X. Cheng, J. Zhang, and A. Duparré, “Spectral angle resolved scattering of thin film coatings,” Appl. Opt. 53, A35–A41 (2014).
[CrossRef]

J. Appl. Phys. (1)

D. G. Stearns, D. P. Gaines, D. W. Sweeney, and E. M. Gullikson, “Nonspecular x-ray scattering in a multilayer-coated imaging system,” J. Appl. Phys. 84, 1003–1028 (1998).
[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. Eng. (1)

E. L. Church, H. A. Jenkinson, and J. M. Zavada, “Relationship between surface scattering and microtopographic features,” Opt. Eng. 18, 125–136 (1979).
[CrossRef]

Proc. SPIE (1)

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]

Waves in Random Media (2)

P. Bussemer, K. Hehl, and S. Kassam, “Theory of light scattering from rough surfaces and interfaces and from volume inhomogeneities in an optical layer stack,” Waves in Random Media 1, 207–221 (1991).
[CrossRef]

J. M. Elson, “Characteristics of far-field scattering by means of surface roughness and variations in subsurface permittivity,” Waves in Random Media 7, 303–317 (1997).
[CrossRef]

Other (7)

H. Bartzsch, K. Täschner, P. Frach, and E. Schultheiß, “Precision optical coatings with continuously varying refractive index deposited by reactive magnetron sputtering using nanoscale film growth control,” Nanofair, Dresden, Germany (2009).

A. von Finck, T. Herffurth, S. Schröder, S. Sinzinger, and A. Duparré, “Characterization of optical coatings using a table top scatterometer,” Appl. Opt.53, A259–A269 (2014).

M. Trost, T. Herffurth, S. Schröder, A. Duparré, and A. Tünnermann, “Scattering reduction through oblique multilayer deposition,” Appl. Opt.53, A197–A204 (2014).

P. Frach, H. Bartzsch, D. Gloess, K. Taeschner, and J. Liebig, “Reactive magnetron sputter technologies for precision optical coatings,” in Optical Interference Coatings, M. Tilsch and D. Ristau, eds., OSA Technical Digest (online) (Optical Society of America, 2013), paper ThB.7.

J. C. Stover, Optical Scattering: Measurement and Analysis, 3rd ed. (SPIE, 2012).

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).

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

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Figures (11)

Fig. 1.
Fig. 1.

Light-scattering geometry and definitions of the scattering angles (φs, θs), the angle of incidence θi, and the solid angle ΔΩs.

Fig. 2.
Fig. 2.

Refractive index profiles of the SixTayOz and the SixHfyOz rugate coatings. The vertical lines indicate the interruption of the coating process.

Fig. 3.
Fig. 3.

Spectral properties of the SixTayOz and the SixHfyOz rugate coatings determined at θi=6°.

Fig. 4.
Fig. 4.

3D-ARS distributions of the rugate coatings demonstrate the reduction of the scattering losses and provide information on the origins of the scatter losses. (The artifacts at the perimeter in the upper ARS distribution are caused by the sample mount).

Fig. 5.
Fig. 5.

Dark field images of rugate coatings on fused-silica substrate; SixTayOz (left) exhibits significantly more defects than SixHfyOz (right).

Fig. 6.
Fig. 6.

10μm×10μm AFM surface profiles and rms roughness values, as well as measured and modeled PSD functions of the 1/3, 2/3, and complete SixHfyOz rugate coatings and the silicon substrate.

Fig. 7.
Fig. 7.

10μm×10μm AFM surface profiles and rms roughness values as well as measured and modeled PSD functions of the SixHfyOz and SixTayOz rugate coatings on superpolished fused-silica substrates.

Fig. 8.
Fig. 8.

In-plane ARS for SixHfyOz rugate series on the silicon substrate.

Fig. 9.
Fig. 9.

ARS measurement and modeling of the SixHfyOz rugate coating on silicon substrate. Scattering models are based on interface roughness and bulk imperfections.

Fig. 10.
Fig. 10.

ARS measurement and modeling of the SixHfyOz rugate coating on fused-silica substrate. Scattering models are based on interface roughness and bulk imperfections.

Fig. 11.
Fig. 11.

ARS measurement and modeling for a conventional quarter-wave stack HfO2/(SiO2/HfO2)10 on superpolished fused silica.

Tables (2)

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Table 1. Contributions to the RMS Roughness from Substrate and Intrinsic Thin Film Roughness in Nanometer

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Table 2. Correlation of Scattering Losses, Substrate, and Thin Film Roughness, as well as Reflectance, R, for the SixHfyOz Rugate Series on Silicon Substrate

Equations (10)

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PSD(fx,fy)=limA1A|FT[z(x,y)]|2.
σ2=2πfminfmaxPSD(f)fdf.
PSDsub(f)=K1fm1+1+K2fm2+1.
PSDint(f)=Ω1exp(2ν|2πf|ηt)2ν|2πf|η.
PSD(f)=a2PSDsub(f)+PSDint(f,t,β)PSD(f)=a2PSDsub(f)+Ω1exp(2ν|2πf|ηt2β)2ν|2πf|ηa=exp(ν|2πf|ηt2β).
ARS(θs,φs)=ΔPs(θs,φs)PiΔΩs.
TS=π|θs|<2°|θs|>85°ARS(θs)sinθsdθs.
ARS(θs)=1λ4i=0Nj=0NFi(δ)Fj(δ)PSDij(f).
λf=sinθssinθi.
Δni=π2|εi|PSDbulk,ifdf,

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