Abstract

A total integrated scattering (TIS) measurement was performed to investigate the surface and volume scattering of K9 glass substrates with low reflectance. Ag layers with thicknesses of 60 nm were deposited on the front and back surfaces of the K9 glass substrates by the magnetron sputtering technique. Surface scattering of the K9 glass substrate was obtained by the TIS measurement of the Ag layers on the assumption that the Ag layers and the K9 substrate had the same surface profile. Volume scattering of the substrates was deduced by subtracting the front and back surface scattering from the total scattering of the substrates.

© 2005 Optical Society of America

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  1. K. H. Guenther, H. L. Gruber, H. K. Pulker, “Morphology and light scattering of dielectric multilayer systems,” Thin Solid Films 34, 363–367 (1976).
    [CrossRef]
  2. C. K. Carniglia, “Scalar scattering theory for multilayer optical coatings,” Opt. Eng. 18, 104–114 (1979).
    [CrossRef]
  3. S. Kassam, A. Duparré, K. Hehl, P. Bussemer, J. Neuber, “Light scattering from the volume of optical thin films: theory and experiment,” Appl. Opt. 31, 1304–1313 (1992).
    [CrossRef] [PubMed]
  4. P. Bussemer, K. Hehl, S. Kassam, “Theory of light scattering from rough surfaces and interfaces and from volume inhomogeneities in an optical layer stack,” Wave Random Media 1, 207–221 (1991).
    [CrossRef]
  5. C. Kylner, L. Mattsson, “Enhanced optical performance of aluminum films by copper inclusion,” Thin Solid Films 348, 222–226 (1999).
    [CrossRef]
  6. A. Duparré, S. Kassam, “Relation between light scattering and the microstructure of optical thin films,” Appl. Opt. 32, 5475–5480 (1993).
    [CrossRef] [PubMed]
  7. J. M. Bennett, “Comparison of techniques for measuring the roughness of optical surfaces,” Opt. Eng. 24, 380–387 (1985).
    [CrossRef]
  8. 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]
  9. C. Amra, P. Bousquet, “Scattering from surfaces and multilayer coatings: recent advances for a better investigation of experiment,” Proc. Soc. Photo-Opt. Instrum. Eng. 1009, 82–97 (1998).
  10. K. H. Guenther, P. G. Wierer, J. M. Bennett, “Surface roughness measurement of low-scatter mirrors and roughness standards,” Appl. Opt. 23, 3820–3836 (1984).
    [CrossRef]
  11. C. F. Hickey, C. Amra, E. Pelletier, “Scattering study of single layer titania films,” Appl. Opt. 28, 2754–2761 (1989).
    [CrossRef] [PubMed]
  12. P. Beckmann, A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, 1963).
  13. A. V. Tikhonravov, M. K. Trubetskov, A. A. Tikhonravov, A. Duparré, “Impact of surface roughness on spectral properties of thin films and multilayers,” in Optical Interference Coatings, Vol. 63 of OSA Trends in Optics and Photonics Series (Optical Society of America, 2001), pp. THB5-1–THB5-3.
  14. Ph. Dumas, B. Bouffakhreddine, C. Amra, O. Vatel, E. Andre, R. Galindo, F. Salvan, “Quantitative microroughness analysis down to the nanometer scale,” Europhys. Lett. 22, 717–722 (1993).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  17. C. Amra, C. Denmie, D. Torricini, P. Roche, R. Galindo, P. Dumas, F. Salvan, “Overlapping of roughness spectra measured in macroscopic (optical) and mocroscopic (AFM) bandwidths,” Proc. SPIE 2253, 614–630 (1994).
    [CrossRef]

1999 (1)

C. Kylner, L. Mattsson, “Enhanced optical performance of aluminum films by copper inclusion,” Thin Solid Films 348, 222–226 (1999).
[CrossRef]

1998 (1)

C. Amra, P. Bousquet, “Scattering from surfaces and multilayer coatings: recent advances for a better investigation of experiment,” Proc. Soc. Photo-Opt. Instrum. Eng. 1009, 82–97 (1998).

1995 (1)

1994 (1)

C. Amra, C. Denmie, D. Torricini, P. Roche, R. Galindo, P. Dumas, F. Salvan, “Overlapping of roughness spectra measured in macroscopic (optical) and mocroscopic (AFM) bandwidths,” Proc. SPIE 2253, 614–630 (1994).
[CrossRef]

1993 (3)

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

A. Duparré, N. Kaiser, H. Truckenbrodt, M. Berger, A. Köhler, “Microtopography investigations of optical surfaces and thin films by light scattering, optical profilometry, and atomic force microscopy,” Proc. SPIE 1995, 181–192 (1993).
[CrossRef]

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

1992 (1)

1991 (1)

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

1989 (1)

1985 (1)

J. M. Bennett, “Comparison of techniques for measuring the roughness of optical surfaces,” Opt. Eng. 24, 380–387 (1985).
[CrossRef]

1984 (1)

1983 (1)

1979 (1)

C. K. Carniglia, “Scalar scattering theory for multilayer optical coatings,” Opt. Eng. 18, 104–114 (1979).
[CrossRef]

1976 (1)

K. H. Guenther, H. L. Gruber, H. K. Pulker, “Morphology and light scattering of dielectric multilayer systems,” Thin Solid Films 34, 363–367 (1976).
[CrossRef]

Amra, C.

C. Amra, P. Bousquet, “Scattering from surfaces and multilayer coatings: recent advances for a better investigation of experiment,” Proc. Soc. Photo-Opt. Instrum. Eng. 1009, 82–97 (1998).

C. Amra, C. Denmie, D. Torricini, P. Roche, R. Galindo, P. Dumas, F. Salvan, “Overlapping of roughness spectra measured in macroscopic (optical) and mocroscopic (AFM) bandwidths,” Proc. SPIE 2253, 614–630 (1994).
[CrossRef]

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

C. F. Hickey, C. Amra, E. Pelletier, “Scattering study of single layer titania films,” Appl. Opt. 28, 2754–2761 (1989).
[CrossRef] [PubMed]

Andre, E.

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

Balter, T. L.

Beckmann, P.

P. Beckmann, A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, 1963).

Bennett, J. M.

Berger, M.

A. Duparré, N. Kaiser, H. Truckenbrodt, M. Berger, A. Köhler, “Microtopography investigations of optical surfaces and thin films by light scattering, optical profilometry, and atomic force microscopy,” Proc. SPIE 1995, 181–192 (1993).
[CrossRef]

Bouffakhreddine, B.

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

Bousquet, P.

C. Amra, P. Bousquet, “Scattering from surfaces and multilayer coatings: recent advances for a better investigation of experiment,” Proc. Soc. Photo-Opt. Instrum. Eng. 1009, 82–97 (1998).

Bussemer, P.

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

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

Carniglia, C. K.

C. K. Carniglia, “Scalar scattering theory for multilayer optical coatings,” Opt. Eng. 18, 104–114 (1979).
[CrossRef]

Denmie, C.

C. Amra, C. Denmie, D. Torricini, P. Roche, R. Galindo, P. Dumas, F. Salvan, “Overlapping of roughness spectra measured in macroscopic (optical) and mocroscopic (AFM) bandwidths,” Proc. SPIE 2253, 614–630 (1994).
[CrossRef]

Dumas, P.

C. Amra, C. Denmie, D. Torricini, P. Roche, R. Galindo, P. Dumas, F. Salvan, “Overlapping of roughness spectra measured in macroscopic (optical) and mocroscopic (AFM) bandwidths,” Proc. SPIE 2253, 614–630 (1994).
[CrossRef]

Dumas, Ph.

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

Duparré, A.

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

A. Duparré, N. Kaiser, H. Truckenbrodt, M. Berger, A. Köhler, “Microtopography investigations of optical surfaces and thin films by light scattering, optical profilometry, and atomic force microscopy,” Proc. SPIE 1995, 181–192 (1993).
[CrossRef]

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

A. V. Tikhonravov, M. K. Trubetskov, A. A. Tikhonravov, A. Duparré, “Impact of surface roughness on spectral properties of thin films and multilayers,” in Optical Interference Coatings, Vol. 63 of OSA Trends in Optics and Photonics Series (Optical Society of America, 2001), pp. THB5-1–THB5-3.

Elson, J. M.

Galindo, R.

C. Amra, C. Denmie, D. Torricini, P. Roche, R. Galindo, P. Dumas, F. Salvan, “Overlapping of roughness spectra measured in macroscopic (optical) and mocroscopic (AFM) bandwidths,” Proc. SPIE 2253, 614–630 (1994).
[CrossRef]

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

Gruber, H. L.

K. H. Guenther, H. L. Gruber, H. K. Pulker, “Morphology and light scattering of dielectric multilayer systems,” Thin Solid Films 34, 363–367 (1976).
[CrossRef]

Guenther, K. H.

K. H. Guenther, P. G. Wierer, J. M. Bennett, “Surface roughness measurement of low-scatter mirrors and roughness standards,” Appl. Opt. 23, 3820–3836 (1984).
[CrossRef]

K. H. Guenther, H. L. Gruber, H. K. Pulker, “Morphology and light scattering of dielectric multilayer systems,” Thin Solid Films 34, 363–367 (1976).
[CrossRef]

Hehl, K.

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

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

Hickey, C. F.

Hobbs, D. T.

Jahannir, J.

Kaiser, N.

A. Duparré, N. Kaiser, H. Truckenbrodt, M. Berger, A. Köhler, “Microtopography investigations of optical surfaces and thin films by light scattering, optical profilometry, and atomic force microscopy,” Proc. SPIE 1995, 181–192 (1993).
[CrossRef]

Kassam, S.

Köhler, A.

A. Duparré, N. Kaiser, H. Truckenbrodt, M. Berger, A. Köhler, “Microtopography investigations of optical surfaces and thin films by light scattering, optical profilometry, and atomic force microscopy,” Proc. SPIE 1995, 181–192 (1993).
[CrossRef]

Kylner, C.

C. Kylner, L. Mattsson, “Enhanced optical performance of aluminum films by copper inclusion,” Thin Solid Films 348, 222–226 (1999).
[CrossRef]

Mattsson, L.

C. Kylner, L. Mattsson, “Enhanced optical performance of aluminum films by copper inclusion,” Thin Solid Films 348, 222–226 (1999).
[CrossRef]

Neuber, J.

Pelletier, E.

Podlesny, J. C.

Pulker, H. K.

K. H. Guenther, H. L. Gruber, H. K. Pulker, “Morphology and light scattering of dielectric multilayer systems,” Thin Solid Films 34, 363–367 (1976).
[CrossRef]

Rahn, J. P.

Roche, P.

C. Amra, C. Denmie, D. Torricini, P. Roche, R. Galindo, P. Dumas, F. Salvan, “Overlapping of roughness spectra measured in macroscopic (optical) and mocroscopic (AFM) bandwidths,” Proc. SPIE 2253, 614–630 (1994).
[CrossRef]

Salvan, F.

C. Amra, C. Denmie, D. Torricini, P. Roche, R. Galindo, P. Dumas, F. Salvan, “Overlapping of roughness spectra measured in macroscopic (optical) and mocroscopic (AFM) bandwidths,” Proc. SPIE 2253, 614–630 (1994).
[CrossRef]

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

Spizzichino, A.

P. Beckmann, A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, 1963).

Tikhonravov, A. A.

A. V. Tikhonravov, M. K. Trubetskov, A. A. Tikhonravov, A. Duparré, “Impact of surface roughness on spectral properties of thin films and multilayers,” in Optical Interference Coatings, Vol. 63 of OSA Trends in Optics and Photonics Series (Optical Society of America, 2001), pp. THB5-1–THB5-3.

Tikhonravov, A. V.

A. V. Tikhonravov, M. K. Trubetskov, A. A. Tikhonravov, A. Duparré, “Impact of surface roughness on spectral properties of thin films and multilayers,” in Optical Interference Coatings, Vol. 63 of OSA Trends in Optics and Photonics Series (Optical Society of America, 2001), pp. THB5-1–THB5-3.

Torricini, D.

C. Amra, C. Denmie, D. Torricini, P. Roche, R. Galindo, P. Dumas, F. Salvan, “Overlapping of roughness spectra measured in macroscopic (optical) and mocroscopic (AFM) bandwidths,” Proc. SPIE 2253, 614–630 (1994).
[CrossRef]

Trubetskov, M. K.

A. V. Tikhonravov, M. K. Trubetskov, A. A. Tikhonravov, A. Duparré, “Impact of surface roughness on spectral properties of thin films and multilayers,” in Optical Interference Coatings, Vol. 63 of OSA Trends in Optics and Photonics Series (Optical Society of America, 2001), pp. THB5-1–THB5-3.

Truckenbrodt, H.

A. Duparré, N. Kaiser, H. Truckenbrodt, M. Berger, A. Köhler, “Microtopography investigations of optical surfaces and thin films by light scattering, optical profilometry, and atomic force microscopy,” Proc. SPIE 1995, 181–192 (1993).
[CrossRef]

Vatel, O.

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

Wierer, P. G.

Appl. Opt. (6)

Europhys. Lett. (1)

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

Opt. Eng. (2)

C. K. Carniglia, “Scalar scattering theory for multilayer optical coatings,” Opt. Eng. 18, 104–114 (1979).
[CrossRef]

J. M. Bennett, “Comparison of techniques for measuring the roughness of optical surfaces,” Opt. Eng. 24, 380–387 (1985).
[CrossRef]

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

C. Amra, P. Bousquet, “Scattering from surfaces and multilayer coatings: recent advances for a better investigation of experiment,” Proc. Soc. Photo-Opt. Instrum. Eng. 1009, 82–97 (1998).

Proc. SPIE (2)

A. Duparré, N. Kaiser, H. Truckenbrodt, M. Berger, A. Köhler, “Microtopography investigations of optical surfaces and thin films by light scattering, optical profilometry, and atomic force microscopy,” Proc. SPIE 1995, 181–192 (1993).
[CrossRef]

C. Amra, C. Denmie, D. Torricini, P. Roche, R. Galindo, P. Dumas, F. Salvan, “Overlapping of roughness spectra measured in macroscopic (optical) and mocroscopic (AFM) bandwidths,” Proc. SPIE 2253, 614–630 (1994).
[CrossRef]

Thin Solid Films (2)

K. H. Guenther, H. L. Gruber, H. K. Pulker, “Morphology and light scattering of dielectric multilayer systems,” Thin Solid Films 34, 363–367 (1976).
[CrossRef]

C. Kylner, L. Mattsson, “Enhanced optical performance of aluminum films by copper inclusion,” Thin Solid Films 348, 222–226 (1999).
[CrossRef]

Wave Random Media (1)

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

Other (2)

P. Beckmann, A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, 1963).

A. V. Tikhonravov, M. K. Trubetskov, A. A. Tikhonravov, A. Duparré, “Impact of surface roughness on spectral properties of thin films and multilayers,” in Optical Interference Coatings, Vol. 63 of OSA Trends in Optics and Photonics Series (Optical Society of America, 2001), pp. THB5-1–THB5-3.

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Figures (2)

Fig. 1
Fig. 1

Schematic diagram of the TIS instrument.

Fig. 2
Fig. 2

Transmission spectra of the K9 glass with and without a Ag layer. The solid curve is with a Ag layer and the dashed curve is without a Ag layer.

Tables (2)

Tables Icon

Table 1 Comparison of rms Roughness of Ag Layers Measured by the TIS and AFM Methods

Tables Icon

Table 2 Surface Scattering and Volume Scattering of the K9 Glass Substrates Measured by the TIS Method

Equations (7)

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

S t = S s 1 + S s 2 = S v ,
S v = S t - S s 1 - S s 2 .
S = R 0 ( 4 π σ λ ) 2 ,
S s 1 = R g ( 4 π σ 1 λ ) 2 ,
S Ag = R Ag ( 4 π σ Ag λ ) 2 ,
S s 1 = S Ag R g R Ag .
σ 1 σ Ag = λ 4 π ( S Ag R Ag ) 1 / 2 .

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