Abstract

Light scattering measurement and analysis is a powerful tool for the characterization of optical and nonoptical surfaces. To enable a more comprehensive postmeasurement characterization, three visible laser sources were recently implemented in a highly sensitive table-top scatterometer with 3D spherical detection capability. Based on wavelength scaling, the instrument is utilized to characterize thin-film coatings and their substrates with respect to surface roughness, roughness growth, and contamination. Topographic measurement techniques are used to verify the results. The spectral sensitivity to contamination (scatter loss) is demonstrated to be significantly different for single surfaces and interference coatings. In addition, power losses of a highly reflective coating are analyzed.

© 2014 Optical Society of America

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  3. D. Cheever, F. Cady, K. A. Klicker, and J. C. Stover, “Design review of a unique complete angle-scatter instrument (CASI),” Proc. SPIE 818, 13–20 (1987).
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    [CrossRef]
  5. 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]
  6. 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]
  7. 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).
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  10. 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).
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  32. C. Amra, J. H. Apfel, and E. Pelletier, “Role of interface correlation in light scattering by a multilayer,” Appl. Opt. 31, 3134–3151 (1992).
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  33. J. M. Elson, J. P. Rahn, and 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]
  34. C. Asmail, J. Hsia, A. Parr, and J. Hoeft, “Rayleigh scattering limits for low-level bidirectional reflectance distribution function measurements,” Appl. Opt. 33, 6084–6091 (1994).
    [CrossRef]
  35. C. Asmail, A. Parr, and J. Hsia, “Rayleigh scattering limits for low-level bidirectional reflectance distribution function measurements: corrigendum,” Appl. Opt. 38, 6027–6028 (1999).
    [CrossRef]
  36. A. von Finck, “Table top system for angle resolved light scattering measurement,” Ph.D. thesis (Technische Universität Ilmenau, 2013).
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  38. J. C. Stover, M. Bernt, E. L. Church, and P. Takacs, “Measurement and analysis of scatter from silicon wafers,” Proc. SPIE 2260, 182–191 (1994).
    [CrossRef]
  39. J. Elson, “Theory of light scattering from a rough surface with an inhomogeneous dielectric permittivity,” Phys. Rev. B 30, 5460–5480 (1984).
    [CrossRef]
  40. C. Amra, “Light scattering from multilayer optics. II. Application to experiment,” J. Opt. Soc. Am. A 11, 211–226 (1994).
    [CrossRef]
  41. S. Kassam, A. Duparré, K. Hehl, P. Bussemer, and J. Neubert, “Light scattering from the volume of optical thin films: theory and experiment,” Appl. Opt. 31, 1304–1313 (1992).
    [CrossRef]
  42. Spectroscopic layer thickness analysis performed by Olaf Stenzel, Fraunhofer IOF, Jena.
  43. O. Stenzel, S. Wilbrandt, K. Friedrich, and N. Kaiser, “Realistische Modellierung der NIR/VIS/UV-optischen Konstanten dünner optischer Schichten im Rahmen des Oszillatormodells,” Vak. Forsch. Prax. 21, 15–23 (2009).
    [CrossRef]
  44. D. Rönnow, “Interface roughness statistics of thin films from angle-resolved light scattering at three wavelengths,” Opt. Eng. 37, 696–704 (1998).
    [CrossRef]
  45. 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).

2014 (1)

2013 (1)

2011 (3)

2010 (1)

2009 (1)

O. Stenzel, S. Wilbrandt, K. Friedrich, and N. Kaiser, “Realistische Modellierung der NIR/VIS/UV-optischen Konstanten dünner optischer Schichten im Rahmen des Oszillatormodells,” Vak. Forsch. Prax. 21, 15–23 (2009).
[CrossRef]

2005 (1)

2002 (1)

1999 (2)

C. Asmail, A. Parr, and J. Hsia, “Rayleigh scattering limits for low-level bidirectional reflectance distribution function measurements: corrigendum,” Appl. Opt. 38, 6027–6028 (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 (1)

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

1996 (2)

C. Ruppe and A. Duparré, “Roughness analysis of optical films and substrates by atomic force microscopy,” Thin Solid Films 288, 8–13 (1996).
[CrossRef]

C. Deumie, R. Richier, P. Dumas, and C. Amra, “Multiscale roughness in optical multilayers: atomic force microscopy and light scattering,” Appl. Opt. 35, 5583–5594 (1996).
[CrossRef]

1995 (1)

1994 (4)

1993 (4)

1992 (3)

1989 (2)

J. Stover, M. Bernt, D. E. McGary, and J. Rifkin, “An investigation of anomalous scatter from beryllium mirrors,” Proc. SPIE 1165, 100 (1989).
[CrossRef]

E. L. Church and P. Takacs, “Prediction of mirror performance from laboratory measurements,” Proc. SPIE 1160, 323–3361989).
[CrossRef]

1988 (2)

J. C. Stover, J. Rifkin, D. R. Cheever, K. H. Kirchner, and T. F. Schiff, “Comparison of wavelength scaling data to experiment,” Proc. SPIE 967, 44–49 (1988).
[CrossRef]

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

1987 (1)

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

1984 (1)

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

1983 (3)

1981 (1)

1980 (1)

1977 (1)

E. L. Church, H. A. Jenkinson, and J. M. Zavada, “Measurement of the finish of diamond-turned metal surfaces by differential light scattering,” Opt. Eng. 16, 360–374 (1977).
[CrossRef]

Al-Jumaily, G. A.

Amra, C.

Andre, E.

P. Dumas, B. Bouffakhreddine, C. Amra, O. Vatel, E. Andre, R. Galindo, and F. Salvan, “Quantitative micro-roughness analysis down to the nanometer scale,” Europhys. Lett. 22, 717–722 (1993).
[CrossRef]

Apfel, J. H.

Asmail, 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]

Bennett, J.

Bennett, J. M.

Bernt, M.

J. C. Stover, M. Bernt, E. L. Church, and P. Takacs, “Measurement and analysis of scatter from silicon wafers,” Proc. SPIE 2260, 182–191 (1994).
[CrossRef]

J. Stover, M. Bernt, D. E. McGary, and J. Rifkin, “An investigation of anomalous scatter from beryllium mirrors,” Proc. SPIE 1165, 100 (1989).
[CrossRef]

Blaschke, H.

Bouffakhreddine, B.

P. Dumas, B. Bouffakhreddine, C. Amra, O. Vatel, E. Andre, R. Galindo, and F. Salvan, “Quantitative micro-roughness analysis down to the nanometer scale,” Europhys. Lett. 22, 717–722 (1993).
[CrossRef]

Bousquet, P.

Bussemer, P.

Cady, F.

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

Cheever, D.

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

Cheever, D. R.

J. C. Stover, J. Rifkin, D. R. Cheever, K. H. Kirchner, and T. F. Schiff, “Comparison of wavelength scaling data to experiment,” Proc. SPIE 967, 44–49 (1988).
[CrossRef]

Cheng, X.

Church, E. L.

J. C. Stover, M. Bernt, E. L. Church, and P. Takacs, “Measurement and analysis of scatter from silicon wafers,” Proc. SPIE 2260, 182–191 (1994).
[CrossRef]

E. L. Church and P. Takacs, “Prediction of mirror performance from laboratory measurements,” Proc. SPIE 1160, 323–3361989).
[CrossRef]

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

E. L. Church, H. A. Jenkinson, and J. M. Zavada, “Measurement of the finish of diamond-turned metal surfaces by differential light scattering,” Opt. Eng. 16, 360–374 (1977).
[CrossRef]

E. L. Church and P. Takacs, “Surface scattering,” in Handbook of Optics, M. Bass, ed. (McGraw-Hill, 1995), Vol. 1, pp. 7.1–7.16.

Deumie, C.

Dumas, P.

C. Deumie, R. Richier, P. Dumas, and C. Amra, “Multiscale roughness in optical multilayers: atomic force microscopy and light scattering,” Appl. Opt. 35, 5583–5594 (1996).
[CrossRef]

P. Dumas, B. Bouffakhreddine, C. Amra, O. Vatel, E. Andre, R. Galindo, and F. Salvan, “Quantitative micro-roughness analysis down to the nanometer scale,” Europhys. Lett. 22, 717–722 (1993).
[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).

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]

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]

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. 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]

C. Ruppe and A. Duparré, “Roughness analysis of optical films and substrates by atomic force microscopy,” Thin Solid Films 288, 8–13 (1996).
[CrossRef]

A. Duparré and S. Kassam, “Relation between light scattering and the microstructure of optical thin films,” Appl. Opt. 32, 5475–5480 (1993).
[CrossRef]

S. Kassam, A. Duparré, K. Hehl, P. Bussemer, and J. Neubert, “Light scattering from the volume of optical thin films: theory and experiment,” Appl. Opt. 31, 1304–1313 (1992).
[CrossRef]

A. Duparré, “Scattering from surfaces and thin films,” in Encyclopedia of Modern Optics, R. D. Guenther, D. G. Steel, and L. Bayvel, eds. (Elsevier, 2004), pp. 314–321.

Elson, J.

Elson, J. M.

Feigl, T.

Ferre-Borrull, J.

Flory, F.

Friedrich, K.

O. Stenzel, S. Wilbrandt, K. Friedrich, and N. Kaiser, “Realistische Modellierung der NIR/VIS/UV-optischen Konstanten dünner optischer Schichten im Rahmen des Oszillatormodells,” Vak. Forsch. Prax. 21, 15–23 (2009).
[CrossRef]

Galindo, R.

P. Dumas, B. Bouffakhreddine, C. Amra, O. Vatel, E. Andre, R. Galindo, and F. Salvan, “Quantitative micro-roughness analysis down to the nanometer scale,” Europhys. Lett. 22, 717–722 (1993).
[CrossRef]

Germer, T. A.

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]

Gliech, S.

Hauptvogel, M.

Hehl, K.

Herffurth, T.

Hoeft, J.

Hsia, J.

Jacobson, R. D.

Jenkinson, H. A.

E. L. Church, H. A. Jenkinson, and J. M. Zavada, “Measurement of the finish of diamond-turned metal surfaces by differential light scattering,” Opt. Eng. 16, 360–374 (1977).
[CrossRef]

Kaiser, N.

O. Stenzel, S. Wilbrandt, K. Friedrich, and N. Kaiser, “Realistische Modellierung der NIR/VIS/UV-optischen Konstanten dünner optischer Schichten im Rahmen des Oszillatormodells,” Vak. Forsch. Prax. 21, 15–23 (2009).
[CrossRef]

Kassam, S.

Kirchner, K. H.

J. C. Stover, J. Rifkin, D. R. Cheever, K. H. Kirchner, and T. F. Schiff, “Comparison of wavelength scaling data to experiment,” Proc. SPIE 967, 44–49 (1988).
[CrossRef]

Klicker, K. A.

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

Mattsson, L.

McGary, D. E.

J. Stover, M. Bernt, D. E. McGary, and J. Rifkin, “An investigation of anomalous scatter from beryllium mirrors,” Proc. SPIE 1165, 100 (1989).
[CrossRef]

McNeil, J. R.

Neubert, J.

Notni, G.

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]

Parr, A.

Pelletier, E.

Rahn, J. P.

Richier, R.

Rifkin, J.

J. Stover, M. Bernt, D. E. McGary, and J. Rifkin, “An investigation of anomalous scatter from beryllium mirrors,” Proc. SPIE 1165, 100 (1989).
[CrossRef]

J. C. Stover, J. Rifkin, D. R. Cheever, K. H. Kirchner, and T. F. Schiff, “Comparison of wavelength scaling data to experiment,” Proc. SPIE 967, 44–49 (1988).
[CrossRef]

Roche, P.

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]

Ruppe, C.

C. Ruppe and A. Duparré, “Roughness analysis of optical films and substrates by atomic force microscopy,” Thin Solid Films 288, 8–13 (1996).
[CrossRef]

Salvan, F.

P. Dumas, B. Bouffakhreddine, C. Amra, O. Vatel, E. Andre, R. Galindo, and F. Salvan, “Quantitative micro-roughness analysis down to the nanometer scale,” Europhys. Lett. 22, 717–722 (1993).
[CrossRef]

Schiff, T. F.

J. C. Stover, J. Rifkin, D. R. Cheever, K. H. Kirchner, and T. F. Schiff, “Comparison of wavelength scaling data to experiment,” Proc. SPIE 967, 44–49 (1988).
[CrossRef]

Schröder, S.

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]

Steinert, J.

Stenzel, O.

O. Stenzel, S. Wilbrandt, K. Friedrich, and N. Kaiser, “Realistische Modellierung der NIR/VIS/UV-optischen Konstanten dünner optischer Schichten im Rahmen des Oszillatormodells,” Vak. Forsch. Prax. 21, 15–23 (2009).
[CrossRef]

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]

Stover, J.

J. Stover, M. Bernt, D. E. McGary, and J. Rifkin, “An investigation of anomalous scatter from beryllium mirrors,” Proc. SPIE 1165, 100 (1989).
[CrossRef]

Stover, J. C.

J. C. Stover, M. Bernt, E. L. Church, and P. Takacs, “Measurement and analysis of scatter from silicon wafers,” Proc. SPIE 2260, 182–191 (1994).
[CrossRef]

J. Elson, J. M. Bennett, and J. C. Stover, “Wavelength and angular dependence of light scattering from beryllium: comparison of theory and experiment,” Appl. Opt. 32, 3362–3376 (1993).
[CrossRef]

J. C. Stover, J. Rifkin, D. R. Cheever, K. H. Kirchner, and T. F. Schiff, “Comparison of wavelength scaling data to experiment,” Proc. SPIE 967, 44–49 (1988).
[CrossRef]

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

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

Takacs, P.

J. C. Stover, M. Bernt, E. L. Church, and P. Takacs, “Measurement and analysis of scatter from silicon wafers,” Proc. SPIE 2260, 182–191 (1994).
[CrossRef]

E. L. Church and P. Takacs, “Prediction of mirror performance from laboratory measurements,” Proc. SPIE 1160, 323–3361989).
[CrossRef]

E. L. Church and P. Takacs, “Surface scattering,” in Handbook of Optics, M. Bass, ed. (McGraw-Hill, 1995), Vol. 1, pp. 7.1–7.16.

Torricini, D.

Trost, M.

Tünnermann, A.

Unglaub, D.

Vatel, O.

P. Dumas, B. Bouffakhreddine, C. Amra, O. Vatel, E. Andre, R. Galindo, and F. Salvan, “Quantitative micro-roughness analysis down to the nanometer scale,” Europhys. Lett. 22, 717–722 (1993).
[CrossRef]

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, “Table top system for angle resolved light scattering measurement,” Ph.D. thesis (Technische Universität Ilmenau, 2013).

Wang, Y.

Wilbrandt, S.

O. Stenzel, S. Wilbrandt, K. Friedrich, and N. Kaiser, “Realistische Modellierung der NIR/VIS/UV-optischen Konstanten dünner optischer Schichten im Rahmen des Oszillatormodells,” Vak. Forsch. Prax. 21, 15–23 (2009).
[CrossRef]

Wilson, S. R.

Wolfe, W.

Zavada, J. M.

E. L. Church, H. A. Jenkinson, and J. M. Zavada, “Measurement of the finish of diamond-turned metal surfaces by differential light scattering,” Opt. Eng. 16, 360–374 (1977).
[CrossRef]

Zhang, J.

Appl. Opt. (21)

J. M. Elson, J. P. Rahn, and J. M. Bennett, “Light scattering from multilayer optics: comparison of theory and experiment,” Appl. Opt. 19, 669–679 (1980).
[CrossRef]

J. M. Elson, J. P. Rahn, and 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]

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

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Figures (12)

Fig. 1.
Fig. 1.

Light scattering geometry and definitions: 1, sample; 2, incident beam; 3, reflected beam; 4, transmitted beam; θi, angle of incidence; θs, polar scattering angle; ϕs, azimuth scattering angle.

Fig. 2.
Fig. 2.

Schematic of the optical layout of the TTS with integrated sources of λ=405, 532, and 640 nm. The background shows a picture of the instrument [9].

Fig. 3.
Fig. 3.

Instrument signature scans performed at 405, 532, and 640 nm demonstrate the Rayleigh-limited performance. The noise-equivalent ARS level (NEARS) was measured with the detector closed. Inset: near angle scan performed at λ=532nm.

Fig. 4.
Fig. 4.

Power losses at λ=640nm determined for a highly reflective coating designed for 640–680 nm. The total scatter losses are determined by integration, and the residual transmittance is measured by scanning the specular transmitted beam.

Fig. 5.
Fig. 5.

ARS and PSD analysis of a titanium-coated fused silica substrate.

Fig. 6.
Fig. 6.

ARS and PSD analysis of an aluminum-coated B270 glass substrate with a 40 nm SiO2 top coat.

Fig. 7.
Fig. 7.

ARS and PSD analysis of an aluminum-coated fused silica substrate with a 250 nm SiO2 top coat.

Fig. 8.
Fig. 8.

Value of the merit function MF (a.u.) of the SiO2 coating displayed in Fig. 7 is plotted over the free parameters AAl, ASiO2, and H. The parameter that is not shown in each diagram was adapted to yield a minimum MF value.

Fig. 9.
Fig. 9.

Total scattering (TS) calculated for an Al/SiO2 coating with different layer thicknesses of the SiO2 protection layer. It is compared to the performance of the unprotected Al coating. The vertical solid lines correspond to the discrete wavelengths used for the characterization.

Fig. 10.
Fig. 10.

ARS and PSD analysis of an uncoated polished RG1000 substrate.

Fig. 11.
Fig. 11.

ARS and PSD analysis of an aluminum-coated BK7 substrate with a 180 nm SiO2 top coat.

Fig. 12.
Fig. 12.

Standing field distribution of the Al/SiO2 coating displayed in Fig. 11. The dashed horizontal lines mark the illumination wavelengths used; the solid vertical lines show the layer interfaces.

Tables (2)

Tables Icon

Table 1. Spatial Frequency Ranges in the VIS Spectrum for Scatter Angles of 2° and 85° and Normal Incidence

Tables Icon

Table 2. Effect of Contamination on the Total Scatter Loss for the RG1000 Substrate and the Al/SiO2 Coating

Equations (6)

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

ARS(θs,φs)=ΔPs(θs,φs)PiΔΩs,
PSD(fx,fy)=λ416π2cosθicos2θsQARS(ϕs,θs).
PSDfractal(f)=Kfη+1,PSDABC(f)=A(1+B2f2)C+12,
ARS(ϕs,θs)=i=0Mj=0MFiFj*PSDij(fx,fy),
R+A=1TTSbTSf.
MF=θs,λw·|logARSexplogARSmod(PSDAl,PSDSiO2,H)|,

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