Abstract

Light scattering measurement and analysis is a powerful tool for the characterization of optical and nonoptical surfaces. A new 3D scatter measurement system based on a detector matrix is presented. A compact light-scatter sensor is used to characterize the scattering and nanostructures of surfaces and to identify the origins of anisotropic scattering features. The results from the scatter sensor are directly compared with white light interferometry to analyze surface defects as well as surface roughness and the corresponding scattering distributions. The scattering of surface defects is modeled based on the Kirchhoff integral equation and the approach of Beckmann for rough surfaces.

© 2013 Optical Society of America

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  1. 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]
  2. 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]
  3. 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]
  4. T. A. Germer and C. C. Asmail, “Goniometric optical scatter instrument for out-of-plane ellipsometry measurements,” Rev. Sci. Instrum. 70, 3688–3695 (1999).
    [CrossRef]
  5. D. R. Cheever, F. M. Cady, K. A. Klicker, and J. C. Stover, “Design review of a unique complete angle-scatter instrument (CASI),” Proc. SPIE 818, 13–20 (1987).
    [CrossRef]
  6. F. D. Orazio, W. K. Stockwell, and R. M. Silva, “Instrumentation for a variable angle scatterometer (VAS),” Proc. SPIE 362, 165–171 (1983).
    [CrossRef]
  7. T. A. Germer, “Multidetector hemispherical polarized optical scattering instrument,” Proc. SPIE 3784, 304–313 (1999).
    [CrossRef]
  8. L. Cao, T. Vorburger, A. G. Lieberman, and T. Lettieri, “Light-scattering measurement of the rms slopes of rough surfaces,” Appl. Opt. 30, 3221–3227 (1991).
    [CrossRef]
  9. M. Gebhardt and H. Truckenbrodt, “Surface defect detection and classification with light scattering,” Proc. SPIE 1500, 135–143 (1991).
    [CrossRef]
  10. J. C. Stover, Optical Scattering: Measurement and Analysis, 3rd ed. (SPIE, 2012).
  11. G. J. Ward, “Measuring and modeling of anisotropic reflection,” SIGGRAPH Comput. Graph. 26, 265–272 (1992).
    [CrossRef]
  12. V. A. Sterligov, E. V. Shunko, I. O. Grytsaienko, and L. V. Poperenko, “Fabrication and properties of ITO films treated by excited atomic oxygen,” Appl. Opt. 51, 1997–2003 (2012).
    [CrossRef]
  13. O. G. Rodriguez-Herrera, M. Rosete-Aguilar, and N. C. Bruce, “Scatterometer of visible light for 2D rough surfaces,” Rev. Sci. Instrum. 75, 4820–4823 (2004).
    [CrossRef]
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    [CrossRef]
  16. C. Hahlweg and H. Rothe, “Theoretical and experimental investigations of non-goniometric scatterometry,” Proc. SPIE 6672, 66720K (2007).
    [CrossRef]
  17. R. Brodmann, O. Gerstorfer, and G. Thurn, “Optical roughness measuring instrument for fine-machined surfaces.” Opt. Eng. 24, 243408 (1985).
    [CrossRef]
  18. J. C. Stover and E. L. Hegstrom, “Scatter metrology of photovoltaic textured surfaces.” Proc. SPIE 7771, 777109 (2010).
    [CrossRef]
  19. Cz. Lukianowicz and T. Karpinski, “Optical system for measurement of surface form and roughness,” Meas. Sci. Rev. 1, 151–154 (2001).
  20. S. Holler, J.-C. Auger, B. Stout, Y. Pan, J. R. Bottiger, R. K. Chang, and G. Videen, “Observations and calculations of light scattering from clusters of spheres,” Appl. Opt. 39, 6873–6887 (2000).
    [CrossRef]
  21. R. Lu and G. Y. Tian, “On-line measurement of surface roughness by laser light scattering,” Meas. Sci. Technol. 17, 1496–1502 (2006).
    [CrossRef]
  22. 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).
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  26. S. Schröder, A. Duparré, L. Coriand, A. Tünnermann, D. Penalver, and J. Harvey, “Modeling of light scattering in different regimes of surface roughness,” Opt. Express 19, 9820–9835 (2011).
    [CrossRef]
  27. 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]
  28. E. L. Church, H. A. Jenkinson, and J. M. Zavada, “Relationship between surface scattering and microtopographic features,” Opt. Eng. 18, 182125 (1979).
    [CrossRef]
  29. J. Elson and J. Bennett, “Calculation of the power spectral density from surface profile data,” Appl. Opt. 34, 201–208 (1995).
    [CrossRef]
  30. S. Maure, G. Albrand, and C. Amra, “Low-level scattering and localized defects,” Appl. Opt. 35, 5573–5582 (1996).
    [CrossRef]
  31. S. K. Nayar, K. Ikeuchi, and T. Kanade, “Surface reflection: physical and geometrical perspectives,” IEEE Trans. Pattern Anal. Mach. Intell. 13, 611–634 (1991).
    [CrossRef]
  32. S. Schröder, T. Herffurth, A. Duparré, and G. Notni, “Device and method for angularly resolved scattered light measurement,” Patent WO 002,010,127,872 (11November2010).
  33. 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]
  34. T. A. Germer, “Light scattering by slightly nonspherical particles on surfaces,” Opt. Lett. 27, 1159–1161 (2002).
    [CrossRef]
  35. P. A. Bobbert and J. Vlieger, “Light scattering by a sphere on a substrate,” Physica A 137, 209–242 (1986).
    [CrossRef]
  36. R. P. Young, “Low-scatter mirror degradation by particle contamination,” Opt. Eng. 15, 516–520 (1976).
  37. K. B. Nahm and W. L. Wolfe, “Light-scattering models for spheres on a conducting plane: comparison with experiment,” Appl. Opt. 26, 2995–2999 (1987).
    [CrossRef]
  38. P. W. Barber and S. C. Hill, Light Scattering by Particles: Computational Methods (World Scientific, 1990).
  39. H. C. van de Hulst, Light Scattering by Small Particles (Dover, 1981).
  40. V. I. Ivakhnenko, C. A. Scheer, and J. C. Stover, “Modeling of scatter from small pits of arbitrary shape.” Proc. SPIE 3275, 112–120 (1998).
    [CrossRef]

2012 (1)

2011 (5)

2010 (2)

2007 (1)

C. Hahlweg and H. Rothe, “Theoretical and experimental investigations of non-goniometric scatterometry,” Proc. SPIE 6672, 66720K (2007).
[CrossRef]

2006 (1)

R. Lu and G. Y. Tian, “On-line measurement of surface roughness by laser light scattering,” Meas. Sci. Technol. 17, 1496–1502 (2006).
[CrossRef]

2004 (1)

O. G. Rodriguez-Herrera, M. Rosete-Aguilar, and N. C. Bruce, “Scatterometer of visible light for 2D rough surfaces,” Rev. Sci. Instrum. 75, 4820–4823 (2004).
[CrossRef]

2002 (2)

2001 (1)

Cz. Lukianowicz and T. Karpinski, “Optical system for measurement of surface form and roughness,” Meas. Sci. Rev. 1, 151–154 (2001).

2000 (1)

1999 (2)

T. A. Germer, “Multidetector hemispherical polarized optical scattering instrument,” Proc. SPIE 3784, 304–313 (1999).
[CrossRef]

T. A. Germer and C. C. Asmail, “Goniometric optical scatter instrument for out-of-plane ellipsometry measurements,” Rev. Sci. Instrum. 70, 3688–3695 (1999).
[CrossRef]

1998 (3)

A. Kasper and H. Rothe, “Evaluation of in-situ ARS sensors for characterizing smooth and rough surfaces,” Proc. SPIE 3426, 252–261 (1998).
[CrossRef]

V. I. Ivakhnenko, C. A. Scheer, and J. C. Stover, “Modeling of scatter from small pits of arbitrary shape.” Proc. SPIE 3275, 112–120 (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]

1996 (1)

1995 (1)

1992 (1)

G. J. Ward, “Measuring and modeling of anisotropic reflection,” SIGGRAPH Comput. Graph. 26, 265–272 (1992).
[CrossRef]

1991 (3)

L. Cao, T. Vorburger, A. G. Lieberman, and T. Lettieri, “Light-scattering measurement of the rms slopes of rough surfaces,” Appl. Opt. 30, 3221–3227 (1991).
[CrossRef]

M. Gebhardt and H. Truckenbrodt, “Surface defect detection and classification with light scattering,” Proc. SPIE 1500, 135–143 (1991).
[CrossRef]

S. K. Nayar, K. Ikeuchi, and T. Kanade, “Surface reflection: physical and geometrical perspectives,” IEEE Trans. Pattern Anal. Mach. Intell. 13, 611–634 (1991).
[CrossRef]

1987 (2)

K. B. Nahm and W. L. Wolfe, “Light-scattering models for spheres on a conducting plane: comparison with experiment,” Appl. Opt. 26, 2995–2999 (1987).
[CrossRef]

D. R. Cheever, F. M. Cady, K. A. Klicker, and J. C. Stover, “Design review of a unique complete angle-scatter instrument (CASI),” Proc. SPIE 818, 13–20 (1987).
[CrossRef]

1986 (1)

P. A. Bobbert and J. Vlieger, “Light scattering by a sphere on a substrate,” Physica A 137, 209–242 (1986).
[CrossRef]

1985 (1)

R. Brodmann, O. Gerstorfer, and G. Thurn, “Optical roughness measuring instrument for fine-machined surfaces.” Opt. Eng. 24, 243408 (1985).
[CrossRef]

1983 (1)

F. D. Orazio, W. K. Stockwell, and R. M. Silva, “Instrumentation for a variable angle scatterometer (VAS),” Proc. SPIE 362, 165–171 (1983).
[CrossRef]

1979 (1)

E. L. Church, H. A. Jenkinson, and J. M. Zavada, “Relationship between surface scattering and microtopographic features,” Opt. Eng. 18, 182125 (1979).
[CrossRef]

1976 (1)

R. P. Young, “Low-scatter mirror degradation by particle contamination,” Opt. Eng. 15, 516–520 (1976).

Albrand, G.

Amra, C.

Asmail, C. C.

T. A. Germer and C. C. Asmail, “Goniometric optical scatter instrument for out-of-plane ellipsometry measurements,” Rev. Sci. Instrum. 70, 3688–3695 (1999).
[CrossRef]

Auger, J.-C.

Barber, P. W.

P. W. Barber and S. C. Hill, Light Scattering by Particles: Computational Methods (World Scientific, 1990).

Beckmann, P.

P. Beckmann and A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Artech House, 1987).

Bennett, J.

Blaschke, H.

Bobbert, P. A.

P. A. Bobbert and J. Vlieger, “Light scattering by a sphere on a substrate,” Physica A 137, 209–242 (1986).
[CrossRef]

Bottiger, J. R.

Brodmann, R.

R. Brodmann, O. Gerstorfer, and G. Thurn, “Optical roughness measuring instrument for fine-machined surfaces.” Opt. Eng. 24, 243408 (1985).
[CrossRef]

Bruce, N. C.

O. G. Rodriguez-Herrera, M. Rosete-Aguilar, and N. C. Bruce, “Scatterometer of visible light for 2D rough surfaces,” Rev. Sci. Instrum. 75, 4820–4823 (2004).
[CrossRef]

Cady, F. M.

D. R. Cheever, F. M. Cady, K. A. Klicker, and J. C. Stover, “Design review of a unique complete angle-scatter instrument (CASI),” Proc. SPIE 818, 13–20 (1987).
[CrossRef]

Cao, L.

Chang, R. K.

Cheever, D. R.

D. R. Cheever, F. M. Cady, K. A. Klicker, and J. C. Stover, “Design review of a unique complete angle-scatter instrument (CASI),” Proc. SPIE 818, 13–20 (1987).
[CrossRef]

Choi, N.

Church, E. L.

E. L. Church, H. A. Jenkinson, and J. M. Zavada, “Relationship between surface scattering and microtopographic features,” Opt. Eng. 18, 182125 (1979).
[CrossRef]

Coriand, L.

Duparré, A.

S. Schröder, A. Duparré, L. Coriand, A. Tünnermann, D. Penalver, and J. Harvey, “Modeling of light scattering in different regimes of surface roughness,” Opt. Express 19, 9820–9835 (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]

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]

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]

S. Schröder, T. Herffurth, A. Duparré, and G. Notni, “Device and method for angularly resolved scattered light measurement,” Patent WO 002,010,127,872 (11November2010).

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.

Feigl, T.

Ferre-Borrull, J.

Gebhardt, M.

M. Gebhardt and H. Truckenbrodt, “Surface defect detection and classification with light scattering,” Proc. SPIE 1500, 135–143 (1991).
[CrossRef]

Germer, T. A.

T. A. Germer, “Light scattering by slightly nonspherical particles on surfaces,” Opt. Lett. 27, 1159–1161 (2002).
[CrossRef]

T. A. Germer, “Multidetector hemispherical polarized optical scattering instrument,” Proc. SPIE 3784, 304–313 (1999).
[CrossRef]

T. A. Germer and C. C. Asmail, “Goniometric optical scatter instrument for out-of-plane ellipsometry measurements,” Rev. Sci. Instrum. 70, 3688–3695 (1999).
[CrossRef]

Gerstorfer, O.

R. Brodmann, O. Gerstorfer, and G. Thurn, “Optical roughness measuring instrument for fine-machined surfaces.” Opt. Eng. 24, 243408 (1985).
[CrossRef]

Gliech, S.

Grytsaienko, I. O.

Hahlweg, C.

C. Hahlweg and H. Rothe, “Theoretical and experimental investigations of non-goniometric scatterometry,” Proc. SPIE 6672, 66720K (2007).
[CrossRef]

Harvey, J.

Harvey, J. E.

Hauptvogel, M.

Hegstrom, E. L.

J. C. Stover and E. L. Hegstrom, “Scatter metrology of photovoltaic textured surfaces.” Proc. SPIE 7771, 777109 (2010).
[CrossRef]

Herffurth, T.

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]

S. Schröder, T. Herffurth, A. Duparré, and G. Notni, “Device and method for angularly resolved scattered light measurement,” Patent WO 002,010,127,872 (11November2010).

Hill, S. C.

P. W. Barber and S. C. Hill, Light Scattering by Particles: Computational Methods (World Scientific, 1990).

Holler, S.

Ikeuchi, K.

S. K. Nayar, K. Ikeuchi, and T. Kanade, “Surface reflection: physical and geometrical perspectives,” IEEE Trans. Pattern Anal. Mach. Intell. 13, 611–634 (1991).
[CrossRef]

Ivakhnenko, V. I.

V. I. Ivakhnenko, C. A. Scheer, and J. C. Stover, “Modeling of scatter from small pits of arbitrary shape.” Proc. SPIE 3275, 112–120 (1998).
[CrossRef]

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, 182125 (1979).
[CrossRef]

Kanade, T.

S. K. Nayar, K. Ikeuchi, and T. Kanade, “Surface reflection: physical and geometrical perspectives,” IEEE Trans. Pattern Anal. Mach. Intell. 13, 611–634 (1991).
[CrossRef]

Karpinski, T.

Cz. Lukianowicz and T. Karpinski, “Optical system for measurement of surface form and roughness,” Meas. Sci. Rev. 1, 151–154 (2001).

Kasper, A.

A. Kasper and H. Rothe, “Evaluation of in-situ ARS sensors for characterizing smooth and rough surfaces,” Proc. SPIE 3426, 252–261 (1998).
[CrossRef]

Klicker, K. A.

D. R. Cheever, F. M. Cady, K. A. Klicker, and J. C. Stover, “Design review of a unique complete angle-scatter instrument (CASI),” Proc. SPIE 818, 13–20 (1987).
[CrossRef]

Krywonos, A.

Lettieri, T.

Lieberman, A. G.

Lu, R.

R. Lu and G. Y. Tian, “On-line measurement of surface roughness by laser light scattering,” Meas. Sci. Technol. 17, 1496–1502 (2006).
[CrossRef]

Lukianowicz, Cz.

Cz. Lukianowicz and T. Karpinski, “Optical system for measurement of surface form and roughness,” Meas. Sci. Rev. 1, 151–154 (2001).

Maure, S.

Nahm, K. B.

Nayar, S. K.

S. K. Nayar, K. Ikeuchi, and T. Kanade, “Surface reflection: physical and geometrical perspectives,” IEEE Trans. Pattern Anal. Mach. Intell. 13, 611–634 (1991).
[CrossRef]

Notni, G.

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, T. Herffurth, A. Duparré, and G. Notni, “Device and method for angularly resolved scattered light measurement,” Patent WO 002,010,127,872 (11November2010).

Orazio, F. D.

F. D. Orazio, W. K. Stockwell, and R. M. Silva, “Instrumentation for a variable angle scatterometer (VAS),” Proc. SPIE 362, 165–171 (1983).
[CrossRef]

Pan, Y.

Penalver, D.

Poperenko, L. V.

Ren, J.

Rodriguez-Herrera, O. G.

O. G. Rodriguez-Herrera, M. Rosete-Aguilar, and N. C. Bruce, “Scatterometer of visible light for 2D rough surfaces,” Rev. Sci. Instrum. 75, 4820–4823 (2004).
[CrossRef]

Rosete-Aguilar, M.

O. G. Rodriguez-Herrera, M. Rosete-Aguilar, and N. C. Bruce, “Scatterometer of visible light for 2D rough surfaces,” Rev. Sci. Instrum. 75, 4820–4823 (2004).
[CrossRef]

Rothe, H.

C. Hahlweg and H. Rothe, “Theoretical and experimental investigations of non-goniometric scatterometry,” Proc. SPIE 6672, 66720K (2007).
[CrossRef]

A. Kasper and H. Rothe, “Evaluation of in-situ ARS sensors for characterizing smooth and rough surfaces,” Proc. SPIE 3426, 252–261 (1998).
[CrossRef]

Scheer, C. A.

V. I. Ivakhnenko, C. A. Scheer, and J. C. Stover, “Modeling of scatter from small pits of arbitrary shape.” Proc. SPIE 3275, 112–120 (1998).
[CrossRef]

Schröder, S.

Shunko, E. V.

Silva, R. M.

F. D. Orazio, W. K. Stockwell, and R. M. Silva, “Instrumentation for a variable angle scatterometer (VAS),” Proc. SPIE 362, 165–171 (1983).
[CrossRef]

Spizzichino, A.

P. Beckmann and A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Artech House, 1987).

Steinert, J.

Sterligov, V. A.

Stockwell, W. K.

F. D. Orazio, W. K. Stockwell, and R. M. Silva, “Instrumentation for a variable angle scatterometer (VAS),” Proc. SPIE 362, 165–171 (1983).
[CrossRef]

Stout, B.

Stover, J. C.

J. C. Stover and E. L. Hegstrom, “Scatter metrology of photovoltaic textured surfaces.” Proc. SPIE 7771, 777109 (2010).
[CrossRef]

V. I. Ivakhnenko, C. A. Scheer, and J. C. Stover, “Modeling of scatter from small pits of arbitrary shape.” Proc. SPIE 3275, 112–120 (1998).
[CrossRef]

D. R. Cheever, F. M. Cady, K. A. Klicker, and J. C. Stover, “Design review of a unique complete angle-scatter instrument (CASI),” Proc. SPIE 818, 13–20 (1987).
[CrossRef]

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

Thurn, G.

R. Brodmann, O. Gerstorfer, and G. Thurn, “Optical roughness measuring instrument for fine-machined surfaces.” Opt. Eng. 24, 243408 (1985).
[CrossRef]

Tian, G. Y.

R. Lu and G. Y. Tian, “On-line measurement of surface roughness by laser light scattering,” Meas. Sci. Technol. 17, 1496–1502 (2006).
[CrossRef]

Trost, M.

Truckenbrodt, H.

Tünnermann, A.

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Dover, 1981).

Videen, G.

Vlieger, J.

P. A. Bobbert and J. Vlieger, “Light scattering by a sphere on a substrate,” Physica A 137, 209–242 (1986).
[CrossRef]

von Finck, A.

Vorburger, T.

Ward, G. J.

G. J. Ward, “Measuring and modeling of anisotropic reflection,” SIGGRAPH Comput. Graph. 26, 265–272 (1992).
[CrossRef]

Wolfe, W. L.

Young, R. P.

R. P. Young, “Low-scatter mirror degradation by particle contamination,” Opt. Eng. 15, 516–520 (1976).

Zavada, J. M.

E. L. Church, H. A. Jenkinson, and J. M. Zavada, “Relationship between surface scattering and microtopographic features,” Opt. Eng. 18, 182125 (1979).
[CrossRef]

Zhao, J.

Appl. Opt. (11)

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]

L. Cao, T. Vorburger, A. G. Lieberman, and T. Lettieri, “Light-scattering measurement of the rms slopes of rough surfaces,” Appl. Opt. 30, 3221–3227 (1991).
[CrossRef]

V. A. Sterligov, E. V. Shunko, I. O. Grytsaienko, and L. V. Poperenko, “Fabrication and properties of ITO films treated by excited atomic oxygen,” Appl. Opt. 51, 1997–2003 (2012).
[CrossRef]

S. Holler, J.-C. Auger, B. Stout, Y. Pan, J. R. Bottiger, R. K. Chang, and G. Videen, “Observations and calculations of light scattering from clusters of spheres,” Appl. Opt. 39, 6873–6887 (2000).
[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]

J. Elson and J. Bennett, “Calculation of the power spectral density from surface profile data,” Appl. Opt. 34, 201–208 (1995).
[CrossRef]

S. Maure, G. Albrand, and C. Amra, “Low-level scattering and localized defects,” Appl. Opt. 35, 5573–5582 (1996).
[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]

K. B. Nahm and W. L. Wolfe, “Light-scattering models for spheres on a conducting plane: comparison with experiment,” Appl. Opt. 26, 2995–2999 (1987).
[CrossRef]

IEEE Trans. Pattern Anal. Mach. Intell. (1)

S. K. Nayar, K. Ikeuchi, and T. Kanade, “Surface reflection: physical and geometrical perspectives,” IEEE Trans. Pattern Anal. Mach. Intell. 13, 611–634 (1991).
[CrossRef]

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

Meas. Sci. Rev. (1)

Cz. Lukianowicz and T. Karpinski, “Optical system for measurement of surface form and roughness,” Meas. Sci. Rev. 1, 151–154 (2001).

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Figures (12)

Fig. 1.
Fig. 1.

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

Fig. 2.
Fig. 2.

Left: possible implementation of the light-scatter sensor. Right: scheme of the sensor setup [32].

Fig. 3.
Fig. 3.

Left: typical result of an ARS measurement with the sensor on a super-polished silicon wafer. Right: scheme of the section of the scattering sphere covered by the sensor.

Fig. 4.
Fig. 4.

ARS (λ=650nm, θi=20°, Δθ0.01°) and corresponding surface profiles (WLI, 10× Objective, 523μm×523μm measurement area) for float-glass substrates with 200 nm (No. 1), 1000 nm (No. 2) Ti thin films and a diamond-turned Al surface (No. 3, different ARS scale). The rms roughness values are the standard deviation of the topography data.

Fig. 5.
Fig. 5.

PSDs and rms roughness σ determined from ARS and combined PSDs from WLI and AFM data [no. 1 (blue) are lowest 2 curves, no. 2 (green) are in the middle, and no. 3 (red) are the upper curves].

Fig. 6.
Fig. 6.

Roughness determined from ARS measurements as a function of the direction on the surface. No. 3 is the red square-shaped graph, no. 2 is the green circular shape, and the other more irregular shape is no. 1 (blue).

Fig. 7.
Fig. 7.

Scheme of the combined setup of scatter sensor and white light interferometer.

Fig. 8.
Fig. 8.

Selected defects. Left: ARS. Right: corresponding WLI topography data (scan area: 370μm×370μm). I and II label the axes and the corresponding scatter features of pit “c.”

Fig. 9.
Fig. 9.

Modeled 3D ARS of the digs in Figs. 8(c) and 8(d) using the WLI topography data as input (gray frames represent scatter angles recorded in a light-scatter sensor measurement, inset: 3D PSD of the dig).

Fig. 10.
Fig. 10.

Modeled ARS (φs=0°) of digs with diameters of 20 μm as a function of the defect edge (slope, inset), according to z(r)=z0(1(2r/D)2)1/n.

Fig. 11.
Fig. 11.

Modeled ARS (φs=0°) of digs with ellipsoidal edge profile (inset) and a diameter of 20 μm as function of depth.

Fig. 12.
Fig. 12.

Correlation of pit diameters, D, determined from ARS and WLI data.

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

ARS(θs,φs)=ΔPs(θs,φs)PiΔΩs,
PSD(fx,fy)=λ416π2cosθicos2θsQARS(θs,φs),
PSD(fx,fy)=limA1A|FT[z(x,y)]|2.
sinθmin1=1.22λD.
U=14πSEψnEnψdSEei(kr1ωt),(En)S=(1F)E,ψ=eikr2r2,

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