Abstract

We present a white light scatterometer operating at a unique scattering direction. Mechanical motions and wavelength scans are removed. The technique provides an immediate flexible characterization of roughness with no loss of resolution.

© 2018 Optical Society of America

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References

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  1. S. O. Rice, “Reflection of electromagnetic waves from slightly rough surfaces,” Commun. Pure Appl. Math. 4(2-3), 351–378 (1951).
    [Crossref]
  2. J. M. Eastman, “Surface scattering in optical interference coatings,” J. Opt. Soc. Am. 66, 164 (1976).
  3. J. W. Goodman, Laser Speckle and Related Phenomena (Springer-Verlag, 1984).
  4. J. M. Bennett, H. H. Hurt, J. P. Rahn, J. M. Elson, K. H. Guenther, M. Rasigni, and F. Varnier, “Relation between optical scattering, microstructure and topography of thin silver films. 1: Optical scattering and topography,” Appl. Opt. 24(16), 2701–2711 (1985).
    [Crossref] [PubMed]
  5. 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(20), 3207–3219 (1983).
    [Crossref] [PubMed]
  6. P. Roche and E. Pelletier, “Characterizations of optical surfaces by measurement of scattering distribution,” Appl. Opt. 23(20), 3561–3566 (1984).
    [Crossref] [PubMed]
  7. C. Amra, “From light scattering to the microstructure of thin-film multilayers,” Appl. Opt. 32(28), 5481–5491 (1993).
    [Crossref] [PubMed]
  8. C. Amra, “Light scattering from multilayer optics. II. Application to experiment,” J. Opt. Soc. Am. A 11(1), 211–226 (1994).
    [Crossref]
  9. A. Duparré and S. Kassam, “Relation between light scattering and the microstructure of optical thin films,” Appl. Opt. 32(28), 5475–5480 (1993).
    [Crossref] [PubMed]
  10. S. Schröder, D. Unglaub, M. Trost, X. Cheng, J. Zhang, and A. Duparré, “Spectral angle resolved scattering of thin film coatings,” Appl. Opt. 53(4), A35–A41 (2014).
    [Crossref] [PubMed]
  11. T. A. Germer, C. Wolters, and D. Brayton, “Calibration of wafer surface inspection systems using spherical silica nanoparticles,” Opt. Express 16(7), 4698–4705 (2008).
    [Crossref] [PubMed]
  12. J. E. Harvey, S. Schroder, N. Choi, and A. Duparre, “Total integrated scatter from surfaces with arbitrary roughness, correlation widths, and incident angles,” Opt. Eng. 51(1), 013402 (2012).
    [Crossref]
  13. S. Schroder, T. Herffurth, A. Duparre, and J. E. Harvey, “Impact of surface roughness on scatter losses and the scattering distribution of surfaces and thin film coatings,” in Optical Fabrication, Testing, and Metrology IV, A. Duparre and R. Geyl, eds. (2011), Vol. 8169.
  14. C. John, Stover, Optical Scattering: Measurement and Analysis, Third Edition, (SPIE Press, 2012).
  15. J. M. 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(19), 3362–3376 (1993).
    [Crossref] [PubMed]
  16. P. Kadkhoda, A. Müller, D. Ristau, A. Duparré, S. Gliech, H. Lauth, U. Schuhmann, N. Reng, M. Tilsch, R. Schuhmann, C. Amra, C. Deumie, C. Jolie, H. Kessler, T. Lindström, 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(19), 3321–3332 (2000).
    [Crossref] [PubMed]
  17. M. Lequime, M. Zerrad, C. Deumie, and C. Amra, “A goniometric light scattering instrument with high-resolution imaging,” Opt. Commun. 282(7), 1265–1273 (2009).
    [Crossref]
  18. S. Liukaityte, M. Lequime, M. Zerrad, T. Begou, and C. Amra, “Broadband spectral transmittance measurements of complex thin-film filters with optical densities of up to 12,” Opt. Lett. 40(14), 3225–3228 (2015).
    [Crossref] [PubMed]
  19. A. von Finck, M. Trost, S. Schröder, and A. Duparré, “Parallelized multichannel BSDF measurements,” Opt. Express 23(26), 33493–33505 (2015).
    [Crossref] [PubMed]
  20. M. Zerrad, M. Lequime, and C. Amra, “Far-field spatially angle-resolved scattering measurements: practical way to recover surface topography,” Opt. Eng. 53(9), 092012 (2014).
    [Crossref]
  21. M. Lequime, S. Liukaityte, M. Zerrad, and C. Amra, “Ultra-wide-range measurements of thin-film filter optical density over the visible and near-infrared spectrum,” Opt. Express 23(20), 26863–26878 (2015).
    [Crossref] [PubMed]
  22. M. Zerrad, S. Liukaityte, M. Lequime, and C. Amra, “Light scattered by optical coatings: numerical predictions and comparison to experiment for a global analysis,” Appl. Opt. 55(34), 9680–9687 (2016).
    [Crossref] [PubMed]
  23. S. Schroder, M. Trost, T. Herffurth, A. von Finck, and A. Duparre, “Sophisticated light scattering techniques from the VUV to the IR regions,” in Reflection, Scattering, and Diffraction from Surfaces Iii, L. M. Hanssen, ed. (2012), Vol. 8495.
  24. 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. EPL 22(9), 717–722 (1993).
    [Crossref]
  25. C. Amra, D. Torricini, and P. Roche, “Multiwavelength (0.45 µm -10.6 µm) angle-resolved scatterometer or how to extend the optical window,” Appl. Opt. 32(28), 5462–5474 (1993).
    [Crossref] [PubMed]
  26. C. Deumié, R. Richier, P. Dumas, and C. Amra, “Multiscale roughness in optical multilayers: atomic force microscopy and light scattering,” Appl. Opt. 35(28), 5583–5594 (1996).
    [Crossref] [PubMed]
  27. M. Zerrad, C. Deumié, M. Lequime, and C. Amra, “An alternative scattering method to characterize surface roughness from transparent substrates,” Opt. Express 15(15), 9222–9231 (2007).
    [Crossref] [PubMed]
  28. 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(1), 154–171 (2002).
    [Crossref] [PubMed]
  29. C. Amra, C. Deumie, D. Torricini, P. J. Roche, R. Galindo, P. Dumas, and F. Salvan, “Overlapping of roughness spectra measured in macroscopic (optical) and microscopic (AFM) bandwIDths,” in F. Abeles, ed. (1994), p. 614.
  30. B. G. Hoover and P. A. Reyes, “Extended-range AFM imaging for applications to reflectance modeling,” Proc. SPIE 9961, 99610R (2016).
    [Crossref]
  31. C. Amra, C. Grèzes-Besset, and L. Bruel, “Comparison of surface and bulk scattering in optical multilayers,” Appl. Opt. 32(28), 5492–5503 (1993).
    [Crossref] [PubMed]
  32. C. Amra, J. H. Apfel, and E. Pelletier, “Role of interface correlation in light scattering by a multilayer,” Appl. Opt. 31(16), 3134–3151 (1992).
    [Crossref] [PubMed]
  33. H. A. Macleod, Thin-Film Optical Filters, 4th ed, Series in Optics and Optoelectronics (CRC Press/Taylor & Francis, 2010).
  34. R. A. Probst, T. Steinmetz, T. Wilken, G. K. L. Wong, H. Hundertmark, S. P. Stark, P. S. J. Russell, T. W. Hänsch, R. Holzwarth, and T. Udem, “Spectral flattening of supercontinua with a spatial light modulator,” Proc. SPIE 8864, 88641Z (2013).
    [Crossref]

2016 (2)

2015 (3)

2014 (2)

M. Zerrad, M. Lequime, and C. Amra, “Far-field spatially angle-resolved scattering measurements: practical way to recover surface topography,” Opt. Eng. 53(9), 092012 (2014).
[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(4), A35–A41 (2014).
[Crossref] [PubMed]

2013 (1)

R. A. Probst, T. Steinmetz, T. Wilken, G. K. L. Wong, H. Hundertmark, S. P. Stark, P. S. J. Russell, T. W. Hänsch, R. Holzwarth, and T. Udem, “Spectral flattening of supercontinua with a spatial light modulator,” Proc. SPIE 8864, 88641Z (2013).
[Crossref]

2012 (1)

J. E. Harvey, S. Schroder, N. Choi, and A. Duparre, “Total integrated scatter from surfaces with arbitrary roughness, correlation widths, and incident angles,” Opt. Eng. 51(1), 013402 (2012).
[Crossref]

2009 (1)

M. Lequime, M. Zerrad, C. Deumie, and C. Amra, “A goniometric light scattering instrument with high-resolution imaging,” Opt. Commun. 282(7), 1265–1273 (2009).
[Crossref]

2008 (1)

2007 (1)

2002 (1)

2000 (1)

1996 (1)

1994 (1)

1993 (6)

1992 (1)

1985 (1)

1984 (1)

1983 (1)

1976 (1)

J. M. Eastman, “Surface scattering in optical interference coatings,” J. Opt. Soc. Am. 66, 164 (1976).

1951 (1)

S. O. Rice, “Reflection of electromagnetic waves from slightly rough surfaces,” Commun. Pure Appl. Math. 4(2-3), 351–378 (1951).
[Crossref]

Amra, C.

M. Zerrad, S. Liukaityte, M. Lequime, and C. Amra, “Light scattered by optical coatings: numerical predictions and comparison to experiment for a global analysis,” Appl. Opt. 55(34), 9680–9687 (2016).
[Crossref] [PubMed]

S. Liukaityte, M. Lequime, M. Zerrad, T. Begou, and C. Amra, “Broadband spectral transmittance measurements of complex thin-film filters with optical densities of up to 12,” Opt. Lett. 40(14), 3225–3228 (2015).
[Crossref] [PubMed]

M. Lequime, S. Liukaityte, M. Zerrad, and C. Amra, “Ultra-wide-range measurements of thin-film filter optical density over the visible and near-infrared spectrum,” Opt. Express 23(20), 26863–26878 (2015).
[Crossref] [PubMed]

M. Zerrad, M. Lequime, and C. Amra, “Far-field spatially angle-resolved scattering measurements: practical way to recover surface topography,” Opt. Eng. 53(9), 092012 (2014).
[Crossref]

M. Lequime, M. Zerrad, C. Deumie, and C. Amra, “A goniometric light scattering instrument with high-resolution imaging,” Opt. Commun. 282(7), 1265–1273 (2009).
[Crossref]

M. Zerrad, C. Deumié, M. Lequime, and C. Amra, “An alternative scattering method to characterize surface roughness from transparent substrates,” Opt. Express 15(15), 9222–9231 (2007).
[Crossref] [PubMed]

P. Kadkhoda, A. Müller, D. Ristau, A. Duparré, S. Gliech, H. Lauth, U. Schuhmann, N. Reng, M. Tilsch, R. Schuhmann, C. Amra, C. Deumie, C. Jolie, H. Kessler, T. Lindström, 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(19), 3321–3332 (2000).
[Crossref] [PubMed]

C. Deumié, R. Richier, P. Dumas, and C. Amra, “Multiscale roughness in optical multilayers: atomic force microscopy and light scattering,” Appl. Opt. 35(28), 5583–5594 (1996).
[Crossref] [PubMed]

C. Amra, “Light scattering from multilayer optics. II. Application to experiment,” J. Opt. Soc. Am. A 11(1), 211–226 (1994).
[Crossref]

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. EPL 22(9), 717–722 (1993).
[Crossref]

C. Amra, D. Torricini, and P. Roche, “Multiwavelength (0.45 µm -10.6 µm) angle-resolved scatterometer or how to extend the optical window,” Appl. Opt. 32(28), 5462–5474 (1993).
[Crossref] [PubMed]

C. Amra, “From light scattering to the microstructure of thin-film multilayers,” Appl. Opt. 32(28), 5481–5491 (1993).
[Crossref] [PubMed]

C. Amra, C. Grèzes-Besset, and L. Bruel, “Comparison of surface and bulk scattering in optical multilayers,” Appl. Opt. 32(28), 5492–5503 (1993).
[Crossref] [PubMed]

C. Amra, J. H. Apfel, and E. Pelletier, “Role of interface correlation in light scattering by a multilayer,” Appl. Opt. 31(16), 3134–3151 (1992).
[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. EPL 22(9), 717–722 (1993).
[Crossref]

Apfel, J. H.

Begou, T.

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. EPL 22(9), 717–722 (1993).
[Crossref]

Brayton, D.

Bruel, L.

Cheng, X.

Choi, N.

J. E. Harvey, S. Schroder, N. Choi, and A. Duparre, “Total integrated scatter from surfaces with arbitrary roughness, correlation widths, and incident angles,” Opt. Eng. 51(1), 013402 (2012).
[Crossref]

Deumie, C.

Deumié, C.

Dumas, P.

C. Deumié, R. Richier, P. Dumas, and C. Amra, “Multiscale roughness in optical multilayers: atomic force microscopy and light scattering,” Appl. Opt. 35(28), 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. EPL 22(9), 717–722 (1993).
[Crossref]

Duparre, A.

J. E. Harvey, S. Schroder, N. Choi, and A. Duparre, “Total integrated scatter from surfaces with arbitrary roughness, correlation widths, and incident angles,” Opt. Eng. 51(1), 013402 (2012).
[Crossref]

Duparré, A.

Eastman, J. M.

J. M. Eastman, “Surface scattering in optical interference coatings,” J. Opt. Soc. Am. 66, 164 (1976).

Elson, J. M.

Ferre-Borrull, J.

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. EPL 22(9), 717–722 (1993).
[Crossref]

Germer, T. A.

Gliech, S.

Grèzes-Besset, C.

Guenther, K. H.

Hänsch, T. W.

R. A. Probst, T. Steinmetz, T. Wilken, G. K. L. Wong, H. Hundertmark, S. P. Stark, P. S. J. Russell, T. W. Hänsch, R. Holzwarth, and T. Udem, “Spectral flattening of supercontinua with a spatial light modulator,” Proc. SPIE 8864, 88641Z (2013).
[Crossref]

Harvey, J. E.

J. E. Harvey, S. Schroder, N. Choi, and A. Duparre, “Total integrated scatter from surfaces with arbitrary roughness, correlation widths, and incident angles,” Opt. Eng. 51(1), 013402 (2012).
[Crossref]

Holzwarth, R.

R. A. Probst, T. Steinmetz, T. Wilken, G. K. L. Wong, H. Hundertmark, S. P. Stark, P. S. J. Russell, T. W. Hänsch, R. Holzwarth, and T. Udem, “Spectral flattening of supercontinua with a spatial light modulator,” Proc. SPIE 8864, 88641Z (2013).
[Crossref]

Hoover, B. G.

B. G. Hoover and P. A. Reyes, “Extended-range AFM imaging for applications to reflectance modeling,” Proc. SPIE 9961, 99610R (2016).
[Crossref]

Hundertmark, H.

R. A. Probst, T. Steinmetz, T. Wilken, G. K. L. Wong, H. Hundertmark, S. P. Stark, P. S. J. Russell, T. W. Hänsch, R. Holzwarth, and T. Udem, “Spectral flattening of supercontinua with a spatial light modulator,” Proc. SPIE 8864, 88641Z (2013).
[Crossref]

Hurt, H. H.

Jolie, C.

Kadkhoda, P.

Kassam, S.

Kessler, H.

Lauth, H.

Lequime, M.

Lindström, T.

Liukaityte, S.

Müller, A.

Notni, G.

Pelletier, E.

Probst, R. A.

R. A. Probst, T. Steinmetz, T. Wilken, G. K. L. Wong, H. Hundertmark, S. P. Stark, P. S. J. Russell, T. W. Hänsch, R. Holzwarth, and T. Udem, “Spectral flattening of supercontinua with a spatial light modulator,” Proc. SPIE 8864, 88641Z (2013).
[Crossref]

Rahn, J. P.

Rasigni, M.

Reng, N.

Reyes, P. A.

B. G. Hoover and P. A. Reyes, “Extended-range AFM imaging for applications to reflectance modeling,” Proc. SPIE 9961, 99610R (2016).
[Crossref]

Ribbing, C. G.

Rice, S. O.

S. O. Rice, “Reflection of electromagnetic waves from slightly rough surfaces,” Commun. Pure Appl. Math. 4(2-3), 351–378 (1951).
[Crossref]

Richier, R.

Ristau, D.

Roche, P.

Russell, P. S. J.

R. A. Probst, T. Steinmetz, T. Wilken, G. K. L. Wong, H. Hundertmark, S. P. Stark, P. S. J. Russell, T. W. Hänsch, R. Holzwarth, and T. Udem, “Spectral flattening of supercontinua with a spatial light modulator,” Proc. SPIE 8864, 88641Z (2013).
[Crossref]

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. EPL 22(9), 717–722 (1993).
[Crossref]

Schroder, S.

J. E. Harvey, S. Schroder, N. Choi, and A. Duparre, “Total integrated scatter from surfaces with arbitrary roughness, correlation widths, and incident angles,” Opt. Eng. 51(1), 013402 (2012).
[Crossref]

Schröder, S.

Schuhmann, R.

Schuhmann, U.

Stark, S. P.

R. A. Probst, T. Steinmetz, T. Wilken, G. K. L. Wong, H. Hundertmark, S. P. Stark, P. S. J. Russell, T. W. Hänsch, R. Holzwarth, and T. Udem, “Spectral flattening of supercontinua with a spatial light modulator,” Proc. SPIE 8864, 88641Z (2013).
[Crossref]

Steinert, J.

Steinmetz, T.

R. A. Probst, T. Steinmetz, T. Wilken, G. K. L. Wong, H. Hundertmark, S. P. Stark, P. S. J. Russell, T. W. Hänsch, R. Holzwarth, and T. Udem, “Spectral flattening of supercontinua with a spatial light modulator,” Proc. SPIE 8864, 88641Z (2013).
[Crossref]

Stover, J. C.

Tilsch, M.

Torricini, D.

Trost, M.

Udem, T.

R. A. Probst, T. Steinmetz, T. Wilken, G. K. L. Wong, H. Hundertmark, S. P. Stark, P. S. J. Russell, T. W. Hänsch, R. Holzwarth, and T. Udem, “Spectral flattening of supercontinua with a spatial light modulator,” Proc. SPIE 8864, 88641Z (2013).
[Crossref]

Unglaub, D.

Varnier, F.

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. EPL 22(9), 717–722 (1993).
[Crossref]

von Finck, A.

Wilken, T.

R. A. Probst, T. Steinmetz, T. Wilken, G. K. L. Wong, H. Hundertmark, S. P. Stark, P. S. J. Russell, T. W. Hänsch, R. Holzwarth, and T. Udem, “Spectral flattening of supercontinua with a spatial light modulator,” Proc. SPIE 8864, 88641Z (2013).
[Crossref]

Wolters, C.

Wong, G. K. L.

R. A. Probst, T. Steinmetz, T. Wilken, G. K. L. Wong, H. Hundertmark, S. P. Stark, P. S. J. Russell, T. W. Hänsch, R. Holzwarth, and T. Udem, “Spectral flattening of supercontinua with a spatial light modulator,” Proc. SPIE 8864, 88641Z (2013).
[Crossref]

Zerrad, M.

Zhang, J.

Appl. Opt. (14)

J. M. Bennett, H. H. Hurt, J. P. Rahn, J. M. Elson, K. H. Guenther, M. Rasigni, and F. Varnier, “Relation between optical scattering, microstructure and topography of thin silver films. 1: Optical scattering and topography,” Appl. Opt. 24(16), 2701–2711 (1985).
[Crossref] [PubMed]

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(20), 3207–3219 (1983).
[Crossref] [PubMed]

P. Roche and E. Pelletier, “Characterizations of optical surfaces by measurement of scattering distribution,” Appl. Opt. 23(20), 3561–3566 (1984).
[Crossref] [PubMed]

C. Amra, “From light scattering to the microstructure of thin-film multilayers,” Appl. Opt. 32(28), 5481–5491 (1993).
[Crossref] [PubMed]

A. Duparré and S. Kassam, “Relation between light scattering and the microstructure of optical thin films,” Appl. Opt. 32(28), 5475–5480 (1993).
[Crossref] [PubMed]

S. Schröder, D. Unglaub, M. Trost, X. Cheng, J. Zhang, and A. Duparré, “Spectral angle resolved scattering of thin film coatings,” Appl. Opt. 53(4), A35–A41 (2014).
[Crossref] [PubMed]

J. M. 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(19), 3362–3376 (1993).
[Crossref] [PubMed]

P. Kadkhoda, A. Müller, D. Ristau, A. Duparré, S. Gliech, H. Lauth, U. Schuhmann, N. Reng, M. Tilsch, R. Schuhmann, C. Amra, C. Deumie, C. Jolie, H. Kessler, T. Lindström, 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(19), 3321–3332 (2000).
[Crossref] [PubMed]

M. Zerrad, S. Liukaityte, M. Lequime, and C. Amra, “Light scattered by optical coatings: numerical predictions and comparison to experiment for a global analysis,” Appl. Opt. 55(34), 9680–9687 (2016).
[Crossref] [PubMed]

C. Amra, D. Torricini, and P. Roche, “Multiwavelength (0.45 µm -10.6 µm) angle-resolved scatterometer or how to extend the optical window,” Appl. Opt. 32(28), 5462–5474 (1993).
[Crossref] [PubMed]

C. Deumié, R. Richier, P. Dumas, and C. Amra, “Multiscale roughness in optical multilayers: atomic force microscopy and light scattering,” Appl. Opt. 35(28), 5583–5594 (1996).
[Crossref] [PubMed]

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(1), 154–171 (2002).
[Crossref] [PubMed]

C. Amra, C. Grèzes-Besset, and L. Bruel, “Comparison of surface and bulk scattering in optical multilayers,” Appl. Opt. 32(28), 5492–5503 (1993).
[Crossref] [PubMed]

C. Amra, J. H. Apfel, and E. Pelletier, “Role of interface correlation in light scattering by a multilayer,” Appl. Opt. 31(16), 3134–3151 (1992).
[Crossref] [PubMed]

Commun. Pure Appl. Math. (1)

S. O. Rice, “Reflection of electromagnetic waves from slightly rough surfaces,” Commun. Pure Appl. Math. 4(2-3), 351–378 (1951).
[Crossref]

Europhys. Lett. EPL (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. EPL 22(9), 717–722 (1993).
[Crossref]

J. Opt. Soc. Am. (1)

J. M. Eastman, “Surface scattering in optical interference coatings,” J. Opt. Soc. Am. 66, 164 (1976).

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

Opt. Commun. (1)

M. Lequime, M. Zerrad, C. Deumie, and C. Amra, “A goniometric light scattering instrument with high-resolution imaging,” Opt. Commun. 282(7), 1265–1273 (2009).
[Crossref]

Opt. Eng. (2)

J. E. Harvey, S. Schroder, N. Choi, and A. Duparre, “Total integrated scatter from surfaces with arbitrary roughness, correlation widths, and incident angles,” Opt. Eng. 51(1), 013402 (2012).
[Crossref]

M. Zerrad, M. Lequime, and C. Amra, “Far-field spatially angle-resolved scattering measurements: practical way to recover surface topography,” Opt. Eng. 53(9), 092012 (2014).
[Crossref]

Opt. Express (4)

Opt. Lett. (1)

Proc. SPIE (2)

B. G. Hoover and P. A. Reyes, “Extended-range AFM imaging for applications to reflectance modeling,” Proc. SPIE 9961, 99610R (2016).
[Crossref]

R. A. Probst, T. Steinmetz, T. Wilken, G. K. L. Wong, H. Hundertmark, S. P. Stark, P. S. J. Russell, T. W. Hänsch, R. Holzwarth, and T. Udem, “Spectral flattening of supercontinua with a spatial light modulator,” Proc. SPIE 8864, 88641Z (2013).
[Crossref]

Other (6)

H. A. Macleod, Thin-Film Optical Filters, 4th ed, Series in Optics and Optoelectronics (CRC Press/Taylor & Francis, 2010).

C. Amra, C. Deumie, D. Torricini, P. J. Roche, R. Galindo, P. Dumas, and F. Salvan, “Overlapping of roughness spectra measured in macroscopic (optical) and microscopic (AFM) bandwIDths,” in F. Abeles, ed. (1994), p. 614.

S. Schroder, M. Trost, T. Herffurth, A. von Finck, and A. Duparre, “Sophisticated light scattering techniques from the VUV to the IR regions,” in Reflection, Scattering, and Diffraction from Surfaces Iii, L. M. Hanssen, ed. (2012), Vol. 8495.

S. Schroder, T. Herffurth, A. Duparre, and J. E. Harvey, “Impact of surface roughness on scatter losses and the scattering distribution of surfaces and thin film coatings,” in Optical Fabrication, Testing, and Metrology IV, A. Duparre and R. Geyl, eds. (2011), Vol. 8169.

C. John, Stover, Optical Scattering: Measurement and Analysis, Third Edition, (SPIE Press, 2012).

J. W. Goodman, Laser Speckle and Related Phenomena (Springer-Verlag, 1984).

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Figures (9)

Fig. 1
Fig. 1 Draft of an integrated sphere.
Fig. 2
Fig. 2 (a): Sampling a surface profile h with a step Δx. The resulting roughness δ(Δx) is step-dependent. (b): Sampling one sample at different scales (two decades in the bandpass). From the top left figure to the bottom left figure, the resolution is increased. Measurements were performed with white light interfometry using 5 different scan lengths (from 5mm to 50μm).
Fig. 3
Fig. 3 Roughness spectrum plotted versus spatial frequency, in a band-pass limited by the inverse scan length (1/L) and the inverse sampling step (1/Δx) classically involved in a profilometry or near-field technique.
Fig. 4
Fig. 4 Spectral dispersion of roughness from the infrared to the UV. The quadratic value δ2 is given by the spectrum integral over the dashed region at each wavelength λi. The horizontal axis is for the spatial frequency.
Fig. 5
Fig. 5 (a)-5(c): Comparison of absolute bandwidths (see text). Figure 5 (a) on the top left is relative to the wavelength range [400nm, 800nm]. Figure 5 (b) on the top right concerns the range [350nm, 1μm]. Figure 5 (c) is bottom centered and given for the range [300nm, 2μm]. In all figures the bandpass of the motionless scatterometer is plotted versus the working scattering angle θ0. This bandpass has to be compared to that (red arrow on the left vertical scale) of a classical 1WS scatterometer operating at 633nm.
Fig. 6
Fig. 6 Comparison of the spatial frequency ν for different wavelengths covering the range [λmin = 350 nm – λmax = 2µm] vs the angle (left), and for different angles in the range [θmin = 5°– θmax = 85°] vs the illumination wavelength (right). The color corresponds to the wavelength. Non visible wavelengths are plotted in dark colors.
Fig. 7
Fig. 7 Roughness spectrum measured with the techniques of the one-angle scatterometer (1AS) and the one-wavelength scatterometer (1WS). We notice the superimposition of all data issued from the two techniques. Colors are given to identify the measurement wavelengths. Both horizontal and vertical scales are log scales.
Fig. 8
Fig. 8 Shematic view of the motionless one-angle white light scatterometer.
Fig. 9
Fig. 9 Approximation of the λ/[F(λ)K(λ)] curve with an optical coating (see text).

Equations (49)

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TI S R = S R R = ( 4π n 0 δ λ cos i 0 ) 2
δ 2 = 1 Σ r h 2 ( r )dr
TI S T = S T T = [(2π δ λ )( n 0 cos i 0 n S cos i S )] 2
δ 2 = 1 N 2 n,m h 2 ( nΔx,mΔx )= δ 2 ( Δx )
δ 2 ( L,Δx )= ν γ( ν ) dν=2π ν ν γ * ( ν ) dν
γ( ν )= 1 Σ | h ^ ( ν ) | 2
γ * ( ν )= 1 2π φ γ( ν,φ ) dφ
BP( λ 0 )=[ n 0 λ 0 sin θ min , n 0 λ 0 ]
γ( ν )= I ± ( ν ) C ± ( ν )
C ( ν )= 1 4 π 2 k 0 2 2 [ cos 2 θ 0 | q S | 2 + | q p | 2 ]
C + ( ν )= 1 4 π 2 k S 3 2 k 0 [ cos 2 θ S | q S | 2 + | q p | 2 ]
q S =j 2π λ 2 n 0 ( n 0 n S ) n 0 cos θ 0 + n S cos θ S
q p =j 2π λ 2 n 0 ( n 0 n S ) n 0 / cos θ 0 + n S / cos θ S
n 0 sin θ 0 = n S sin θ S k i = 2π n i λ ν= nsinθ λ
δ 2 ( λ, θ min )=2π ν ν γ * ( ν ) dν=2π ( n 0 λ ) 2 θ γ * ( θ )cosθsinθ dθ
I ( θ 0 )= 1 4 π 2 4R ( 2π n 0 λ ) 4 γ( ν )
I + ( θ S )= 1 4 π 2 4R n S 3 n 0 ( 2π λ ) 4 γ( ν )
BP( θ 0 )=[ sin θ 0 λ 2 , sin θ 0 λ 1 ]
λ 2 λ 1 = 1 sin θ min
1 λ 0 = sin θ 0 λ 1
I( θ,λ )=C( θ,λ )γ( θ,λ )
V( θ 0 )=ΔΩ λ C( θ 0 ,λ )γ( θ 0 ,λ )F( λ )K( λ )dλ
δ 2 = ν γ( ν )dν = ν,φ γ( ν,φ )νdνdφ =2π ν γ( ν )νdν
ν= n 0 sin θ 0 λ δ 2 =2π ( n 0 sin θ 0 ) 2 λ γ( θ,λ ) dλ λ 3
C( θ 0 ,λ )F( λ )K( λ )= η λ 3
η( θ 0 )= η 0 ( θ 0 )2π ( n 0 sin θ 0 ) 2 /ΔΩ
T η ( λ )= η( θ 0 ) λ 3 1 C( θ 0 ,λ )F( λ )K( λ )
V η ( θ 0 )= η 0 ( θ 0 ) δ 2 ( θ 0 )
C( θ 0 ,λ ) 1 4 π 2 4R( λ ) ( 2π n 0 λ ) 4
T β ( λ )=β( θ 0 ) λ F( λ )K( λ )
β( θ 0 )=(η/R)(1/16 π 2 n 0 4 )= η 0 (1/8π)(1/RΔΩ) (sin θ 0 / n 0 ) 2
T( λ )<1β< min λ [ F( λ )K( λ ) λ ]
δ 2 ( θ 0 )= δ E 2 ( θ 0 )V( θ 0 )/ V E ( θ 0 )
V L ( θ 0 )=ΔΩ λ ρ( λ )cos θ 0 F( λ )K( λ )T( λ )dλ =βcos θ 0 ΔΩ λ ρ( λ )λdλ
V L ( θ 0 )=(1/2π)β( θ 0 )cos θ 0 ΔΩ( λ max 2 λ min 2 )
V L ( θ 0 )= (1/4π n 0 ) 2 [ η 0 ( θ 0 )/R] (sin θ 0 ) 2 cos θ 0 ( λ max 2 λ min 2 )
δ k 2 =2π ν ν k+1 γ( ν )dν
δ k 2 =2π ( n 0 sin θ 0 ) k+2 λ γ( λ ) λ k+3 dλ
T k ( λ )= η k λ k+3 1 C( λ )F( λ )K( λ )
η k = η 0k 2π ( n 0 sin θ 0 ) k+2 /ΔΩ
V ηk ( θ 0 )= η 0k ( θ 0 ) δ k 2 ( θ 0 )
T k ( λ )= β k λ 1k F( λ )K( λ )
β k = η 0k (1/8π)(1/RΔΩ) (nsinθ) k+2 (1/ n 0 4 )
V Lk ( θ 0 )=( η 0k /R)(1/8 π 2 n 0 4 )cosθ (nsinθ) k+2 [1/(2k)]( λ max 2k λ min 2k )
Γ( τ )=2π ν νγ( ν ) J 0 ( 2πτν )dν
J 0 ( 2πτν )= 1 2π ψ exp( 2jπντcosψ )dψ
exp( 2jπντcosψ )= k ( 2jπντcosψ ) k k!
Γ( τ )= 1 2π k δ 2k 2 ( 2πτ ) 2k 2 k ( k! ) 2
T k ( λ )<1 β k < min λ [ F( λ )K( λ ) λ 1k ]

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