Abstract

An alternative scattering method is developed to characterize surface roughness from the two faces of transparent substrates. Specific weights are attributed to each surface in the scattering process, due to the large substrate thickness. The resulting roughness spectra are shown to quasi-overlap those of near field microscopy.

© 2007 Optical Society of America

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References

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  1. J. M. Elson and J. M. Bennett, "Relation between the angular dependence of scattering and the statistical properties of optical surfaces," J. Opt. Soc. Am. 69, 31-47 (1979).
    [CrossRef]
  2. J. M. Bennett, "Comparison of techniques for measuring the roughness of optical surfaces," Opt. Eng. 24, 380-387 1(985).
  3. C. Amra, "From light scattering to the microstructure of thin-film multilayers," Appl. Opt. 32,5481-5491 (1993).
    [CrossRef] [PubMed]
  4. C. Amra, C. Grezes-Besset, P. Roche, and E. Pelletier, "Description of a scattering apparatus: application to the problems of characterization of opaque surfaces," Appl. Opt. 28, 2723-2730 (1989).
    [CrossRef] [PubMed]
  5. O. Kienzle, J. Staub, and T. Tschudi, "Light scattering from transparent substrates: theory and experiment," Phys. Rev. B 50, 1848-1860 (1994).
    [CrossRef]
  6. M. Zerrad, C. Deumié, M. Lequime, C. Amra, and M. Ewart, "Light-scattering characterization of transparent substrates," Appl. Opt. 45, 1402-1409 (2006).
    [CrossRef] [PubMed]
  7. P. Kadkhoda, A. Muller, D. Ristau, A. Duparre, S. Gliech, H. Lauth, U. Schuhmann, N. Reng, M. Tilsch, R. Schuhmann, C. Amra, C. Deumie, C. Jolie, H. Kessler, T. Lindstrom, C. G. Ribbing, and J. M. Bennett, "International round-robin experiment to test the International Organization for Standardization total-scattering draft standard," Appl. Opt. 39, 3321-3332 (2000).
    [CrossRef]
  8. J. M. Elson, "Theory of light scattering from a rough surface with an inhomogeneous dielectric permittivity," Phys. Rev. B 30, 5460-5480 (1984).
    [CrossRef]
  9. C. Amra, G. Albrand, and P. Roche, "Theory and application of antiscattering single layers: antiscattering antireflection coatings," Appl. Opt. 25,2695-2702 (1986).
    [CrossRef] [PubMed]
  10. C. Amra, "Light scattering from multilayer optics. Part A: Investigation tools," J. Opt. Soc. Am. A 11, 197-210 (1994).
    [CrossRef]
  11. C. Amra, "Light scattering from multilayer optics. Part B: Application to experiment," J. Opt. Soc. Am. A 11, 211-226 (1994).
    [CrossRef]
  12. 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] [PubMed]
  13. C. Amra, C. Grezes-Besset, and L. Bruel, "Comparison of surface and bulk scattering in optical multilayers," Appl. Opt. 32, 5492-5503 (1993).
    [CrossRef] [PubMed]
  14. A. Duparre and S. Kassam, "Relation between light scattering and the microstructure of optical thin films," Appl. Opt. 32, 5475-5480 (1993).
    [CrossRef] [PubMed]
  15. C. Amra, D. Torricini, and P. Roche, "Multiwavelength (0.45-10.6 mu m) angle-resolved scatterometer or how to extend the optical window," Appl. Opt. 32, 5462-5474 (1993).
    [CrossRef]
  16. O. Gilbert, C. Deumie, and C. Amra, "Angle-resolved ellipsometry of scattering patterns from arbitrary surfaces and bulks," Opt. Express 13, 2403-2418 (2005).
    [CrossRef] [PubMed]
  17. 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] [PubMed]
  18. P. Dumas, B. Bouffakhreddine, C. Amra, O. Vatel, E. Andre, R. Galindo, and F. Salvan, "Quantitative microroughness analysis down to the nanometer scale," Europhys. Lett. 22, 717-722 (1993).
    [CrossRef]
  19. S. Maure, G. Albrand, and C. Amra, "Low-level scattering and localized defects," Appl. Opt. 35, 5573-5582 (1996).
    [CrossRef] [PubMed]

2006 (1)

2005 (1)

O. Gilbert, C. Deumie, and C. Amra, "Angle-resolved ellipsometry of scattering patterns from arbitrary surfaces and bulks," Opt. Express 13, 2403-2418 (2005).
[CrossRef] [PubMed]

2000 (1)

1996 (2)

1994 (3)

1993 (5)

1989 (1)

1986 (1)

1984 (1)

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

1983 (1)

1979 (1)

Albrand, G.

Amra, C.

M. Zerrad, C. Deumié, M. Lequime, C. Amra, and M. Ewart, "Light-scattering characterization of transparent substrates," Appl. Opt. 45, 1402-1409 (2006).
[CrossRef] [PubMed]

O. Gilbert, C. Deumie, and C. Amra, "Angle-resolved ellipsometry of scattering patterns from arbitrary surfaces and bulks," Opt. Express 13, 2403-2418 (2005).
[CrossRef] [PubMed]

P. Kadkhoda, A. Muller, D. Ristau, A. Duparre, S. Gliech, H. Lauth, U. Schuhmann, N. Reng, M. Tilsch, R. Schuhmann, C. Amra, C. Deumie, C. Jolie, H. Kessler, T. Lindstrom, C. G. Ribbing, and J. M. Bennett, "International round-robin experiment to test the International Organization for Standardization total-scattering draft standard," Appl. Opt. 39, 3321-3332 (2000).
[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] [PubMed]

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

C. Amra, "Light scattering from multilayer optics. Part A: Investigation tools," J. Opt. Soc. Am. A 11, 197-210 (1994).
[CrossRef]

C. Amra, "Light scattering from multilayer optics. Part B: Application to experiment," J. Opt. Soc. Am. A 11, 211-226 (1994).
[CrossRef]

C. Amra, "From light scattering to the microstructure of thin-film multilayers," Appl. Opt. 32,5481-5491 (1993).
[CrossRef] [PubMed]

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

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

C. Amra, D. Torricini, and P. Roche, "Multiwavelength (0.45-10.6 mu m) angle-resolved scatterometer or how to extend the optical window," Appl. Opt. 32, 5462-5474 (1993).
[CrossRef]

C. Amra, C. Grezes-Besset, P. Roche, and E. Pelletier, "Description of a scattering apparatus: application to the problems of characterization of opaque surfaces," Appl. Opt. 28, 2723-2730 (1989).
[CrossRef] [PubMed]

C. Amra, G. Albrand, and P. Roche, "Theory and application of antiscattering single layers: antiscattering antireflection coatings," Appl. Opt. 25,2695-2702 (1986).
[CrossRef] [PubMed]

Andre, E.

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

Bennett, J. M.

Bouffakhreddine, B.

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

Bruel, L.

Deumie, C.

Deumié, 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] [PubMed]

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

Duparre, A.

Elson, J. M.

Ewart, M.

Galindo, R.

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

Gilbert, O.

O. Gilbert, C. Deumie, and C. Amra, "Angle-resolved ellipsometry of scattering patterns from arbitrary surfaces and bulks," Opt. Express 13, 2403-2418 (2005).
[CrossRef] [PubMed]

Gliech, S.

Grezes-Besset, C.

Jolie, C.

Kadkhoda, P.

Kassam, S.

Kessler, H.

Kienzle, O.

O. Kienzle, J. Staub, and T. Tschudi, "Light scattering from transparent substrates: theory and experiment," Phys. Rev. B 50, 1848-1860 (1994).
[CrossRef]

Lauth, H.

Lequime, M.

Lindstrom, T.

Maure, S.

Muller, A.

Pelletier, E.

Rahn, J. P.

Reng, N.

Ribbing, C. G.

Richier, R.

Ristau, D.

Roche, P.

Salvan, F.

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

Schuhmann, R.

Schuhmann, U.

Staub, J.

O. Kienzle, J. Staub, and T. Tschudi, "Light scattering from transparent substrates: theory and experiment," Phys. Rev. B 50, 1848-1860 (1994).
[CrossRef]

Tilsch, M.

Torricini, D.

Tschudi, T.

O. Kienzle, J. Staub, and T. Tschudi, "Light scattering from transparent substrates: theory and experiment," Phys. Rev. B 50, 1848-1860 (1994).
[CrossRef]

Vatel, O.

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

Zerrad, M.

Appl. Opt. (11)

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] [PubMed]

C. Amra, G. Albrand, and P. Roche, "Theory and application of antiscattering single layers: antiscattering antireflection coatings," Appl. Opt. 25,2695-2702 (1986).
[CrossRef] [PubMed]

C. Amra, C. Grezes-Besset, P. Roche, and E. Pelletier, "Description of a scattering apparatus: application to the problems of characterization of opaque surfaces," Appl. Opt. 28, 2723-2730 (1989).
[CrossRef] [PubMed]

C. Amra, D. Torricini, and P. Roche, "Multiwavelength (0.45-10.6 mu m) angle-resolved scatterometer or how to extend the optical window," Appl. Opt. 32, 5462-5474 (1993).
[CrossRef]

C. Amra, "From light scattering to the microstructure of thin-film multilayers," Appl. Opt. 32,5481-5491 (1993).
[CrossRef] [PubMed]

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

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

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

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] [PubMed]

P. Kadkhoda, A. Muller, D. Ristau, A. Duparre, S. Gliech, H. Lauth, U. Schuhmann, N. Reng, M. Tilsch, R. Schuhmann, C. Amra, C. Deumie, C. Jolie, H. Kessler, T. Lindstrom, C. G. Ribbing, and J. M. Bennett, "International round-robin experiment to test the International Organization for Standardization total-scattering draft standard," Appl. Opt. 39, 3321-3332 (2000).
[CrossRef]

M. Zerrad, C. Deumié, M. Lequime, C. Amra, and M. Ewart, "Light-scattering characterization of transparent substrates," Appl. Opt. 45, 1402-1409 (2006).
[CrossRef] [PubMed]

Europhys. Lett. (1)

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

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (2)

Opt. Express (1)

O. Gilbert, C. Deumie, and C. Amra, "Angle-resolved ellipsometry of scattering patterns from arbitrary surfaces and bulks," Opt. Express 13, 2403-2418 (2005).
[CrossRef] [PubMed]

Phys. Rev. B (2)

O. Kienzle, J. Staub, and T. Tschudi, "Light scattering from transparent substrates: theory and experiment," Phys. Rev. B 50, 1848-1860 (1994).
[CrossRef]

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

Other (1)

J. M. Bennett, "Comparison of techniques for measuring the roughness of optical surfaces," Opt. Eng. 24, 380-387 1(985).

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Figures (7)

Fig. 1.
Fig. 1.

Light scattering from a single interface

Fig. 2.
Fig. 2.

Scattering from the two surfaces of a transparent substrate

Fig. 3.
Fig. 3.

Scattering measurements by reflection for two specific configurations

Fig. 4.
Fig. 4.

Roughness spectra determined with and without the separation method

Fig. 5.
Fig. 5.

Roughness spectra of interface 0 measured with AFM microscopy and light scattering, with and without the separation method.

Fig. 6.
Fig. 6.

Roughness spectra of interface 1 measured with AFM microscopy and light scattering, with and without the separation method.

Fig. 7.
Fig. 7.

Roughness spectra deduced from simulated surfaces with and without any localized defects. The units of σ and γ are respectively nm-1 and nm4.

Equations (22)

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

I ± ( θ , ϕ ) = C ± ( θ , ϕ ) . γ ( θ , ϕ )
γ ( σ ) = 4 π 2 S h ̂ ( σ ) 2
γ ¯ ( θ ) = γ ¯ ( σ ) = 1 2 π ϕ = 0 2 π γ ( θ , ϕ ) d ϕ
σ = σ = 2 π λ sin θ = 2 π ν
δ 2 = σ γ ( σ ) d σ
= 2 π σ min σ max σ γ ¯ ( σ ) d σ
= 2 π n 0 λ Φ = 0 2 π θ min θ max γ ( θ , Φ ) sin θ cos θ d θ d Φ
I r ( θ 0 , ϕ ) = { C 0 ( θ 0 ) + C 0 + ( θ S ) R ( θ S ) 1 R 2 ( θ S ) β ( θ S ) } γ 0 ( θ , ϕ ) + C 1 ( θ S ) 1 1 R 2 ( θ S ) β ( θ S ) γ 1 ( θ , ϕ )
β ( θ s ) = T ( θ s ) ( n 0 n s ) 2 cos θ 0 cos θ s
α i = E i 2 Φ 0 +
α 0 = 1 + 2 ( r S + R S 1 + R S ) with r S = R S
α 1 = 1 R S 1 + R S = T S 1 + R S
I - = D 0 γ 0 + D 1 γ 1
D 0 = ( C 0 ( θ 0 ) + C 0 + ( θ S ) R ( θ S ) 1 R 2 ( θ S ) β ( θ S ) ) α 0
D 1 = ( C 1 ( θ S ) 1 1 R 2 ( θ S ) β ( θ S ) ) α 1
I - = D 0 γ 1 + D 1 γ 0
γ 0 = D 0 I - D 1 I - ( D 0 ) 2 ( D 1 ) 2
γ 1 = D 0 I - D 1 I - ( D 0 ) 2 ( D 1 ) 2
ν min = 1 L
ν max = 1 2 Δ x
B ARS = ( 2 π sin θ min λ , 2 π λ )
B M ( Δ x ) = ( 2 π L , π N L )

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