Abstract

We develop a rigorous methodology named TRACK based on the collection of multi-angle spectrophotometric transmission and reflection data in order to assess the extinction coefficient of quasi-transparent optical films. The accuracy of extinction coefficient values obtained by this method is not affected by sample non-idealities (thickness non-uniformity, refractive index inhomogeneities, anisotropy, interfaces, etc.) and therefore a simple two-layer (substrate/film) optical model can be used. The method requires the acquisition of transmission and reflection data at two angles of incidence: 10° and 65° in p polarization. Data acquired at 10° provide information about the film thickness and the refractive index, while data collected at 65° are used for absorption evaluation and extinction coefficient computation. We test this method on three types of samples: (i) a CR-39 plastic substrate coated with a thick protective coating; (ii) the same substrate coated with a thin TiO2 film; (iii) and a thick Si3N4 film deposited on Gorilla glass that presents thickness non-uniformity and refractive index gradient non-idealities. We also compare absorption and extinction coefficient values obtained at 410 and 550 nm by both TRACK and Laser Induced Deflection techniques in the case of a 1 micron thick TiO2 coating. Both methods display consistent extinction coefficient values in the 10−4 and 10−5 ranges at 410 and 550 nm, respectively, which proves the validity of the methodology and provides an estimate of its accuracy limit.

© 2015 Optical Society of America

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References

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  11. L. Miao, P. Jin, K. Kaneko, A. Terai, N. Nabatova-Gabain, and S. Tanemura, “Preparation and characterization of polycrystalline anatase and rutile TiO2 thin films by rf magnetron sputtering,” Thin Solid Films 212–213, 255–263 (2003).
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    [Crossref]
  13. G. E. Jellison and F. A. Modine, “Parameterization of the optical functions of amorphous materials in the interband region,” Appl. Phys. Lett. 69, 371–373 (1996).
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  15. D. E. Aspnes, “Optical properties of thin films,” Thin Solid Films 89, 249–262 (1982).
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  16. H. A. Macleod, “Turning value monitoring of narrow-band all-dielectric thin-film optical filters,” Opt. Acta 19, 1–28 (1972).
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2011 (1)

C. Mühlig, S. Kufert, S. Bublitz, and U. Speck, “Laser induced deflection technique for absolute thin film absorption measurement: optimized concepts and experimental results,” Appl. Optics 50, C449–C456 (2011).
[Crossref]

2008 (2)

C. Mühlig, W. Triebel, S. Kufert, and S. Bublitz, “Characterization of low losses in optical thin films and materials,” Appl. Optics 47, C135–C142 (2008).
[Crossref]

A. Duparré and D. Ristau, “Optical interference coatings 2007 measurement problem,” Appl. Optics 47, C179–C184 (2008).
[Crossref]

2006 (1)

D. De Souza Meneses, M. Malki, and P. Echegut, “Structure and lattice dynamics of binary lead silicate glasses investigated by infrared spectroscopy,” J. Non-Cryst. Solids 351, 769–776 (2006).
[Crossref]

2003 (1)

L. Miao, P. Jin, K. Kaneko, A. Terai, N. Nabatova-Gabain, and S. Tanemura, “Preparation and characterization of polycrystalline anatase and rutile TiO2 thin films by rf magnetron sputtering,” Thin Solid Films 212–213, 255–263 (2003).

2000 (1)

L. Martinu and D. Poitras, “Plasma deposition of optical films and coatings: A review”, J. Vac. Sci. Technol. A 18, 2619–2645 (2000).
[Crossref]

1996 (2)

G. E. Jellison and F. A. Modine, “Parameterization of the optical functions of amorphous materials in the interband region,” Appl. Phys. Lett. 69, 371–373 (1996).
[Crossref]

G. E. Jellison and F. A. Modine, “Erratum: Parameterization of the optical functions of amorphous materials in the interband region,” Appl. Phys. Lett. 69, 2137 (1996).
[Crossref]

1991 (1)

K.-E. Peiponen and E. M. Vartiainen, “Kramers-Kronig relations in optical data inversion,” Phys. Rev. B 44, 8301–8303 (1991).
[Crossref]

1984 (1)

D. P. Arndt, R. M. A. Azzam, J. M. Bennett, J. P. Borgogno, C. K. Carniglia, W. E. Case, J. A. Dobrowolski, U. J. Gibson, T. Tuttle Hart, F. C. Ho, V. A. Hodgkin, W. P. Klapp, H. A. Macleod, E. Pelletier, M. K. Purvis, D. M. Quinn, D. H. Strome, R. Swenson, P. A. Temple, and T. F. Thonn, “Multiple determination of the optical constants of thin-film coating materials,” Appl. Optics 23, 3571–3596 (1984).
[Crossref]

1983 (1)

J. A. Dobrowolski, F. C. Ho, and A. Waldorf, “Determination of optical constants of thin film coating materials based on inverse synthesis,” Appl. Optics 22, 3191–3200 (1983).
[Crossref]

1982 (1)

D. E. Aspnes, “Optical properties of thin films,” Thin Solid Films 89, 249–262 (1982).
[Crossref]

1980 (1)

A. Rosencwaig and J. B. Willis, “Photoacoustic absorption measurements of optical materials and thin films,” J. Appl. Phys. 51, 4361–4364 (1980).
[Crossref]

1972 (1)

H. A. Macleod, “Turning value monitoring of narrow-band all-dielectric thin-film optical filters,” Opt. Acta 19, 1–28 (1972).
[Crossref]

Arndt, D. P.

D. P. Arndt, R. M. A. Azzam, J. M. Bennett, J. P. Borgogno, C. K. Carniglia, W. E. Case, J. A. Dobrowolski, U. J. Gibson, T. Tuttle Hart, F. C. Ho, V. A. Hodgkin, W. P. Klapp, H. A. Macleod, E. Pelletier, M. K. Purvis, D. M. Quinn, D. H. Strome, R. Swenson, P. A. Temple, and T. F. Thonn, “Multiple determination of the optical constants of thin-film coating materials,” Appl. Optics 23, 3571–3596 (1984).
[Crossref]

Aspnes, D. E.

D. E. Aspnes, “Optical properties of thin films,” Thin Solid Films 89, 249–262 (1982).
[Crossref]

Azzam, R. M. A.

D. P. Arndt, R. M. A. Azzam, J. M. Bennett, J. P. Borgogno, C. K. Carniglia, W. E. Case, J. A. Dobrowolski, U. J. Gibson, T. Tuttle Hart, F. C. Ho, V. A. Hodgkin, W. P. Klapp, H. A. Macleod, E. Pelletier, M. K. Purvis, D. M. Quinn, D. H. Strome, R. Swenson, P. A. Temple, and T. F. Thonn, “Multiple determination of the optical constants of thin-film coating materials,” Appl. Optics 23, 3571–3596 (1984).
[Crossref]

Bennett, J. M.

D. P. Arndt, R. M. A. Azzam, J. M. Bennett, J. P. Borgogno, C. K. Carniglia, W. E. Case, J. A. Dobrowolski, U. J. Gibson, T. Tuttle Hart, F. C. Ho, V. A. Hodgkin, W. P. Klapp, H. A. Macleod, E. Pelletier, M. K. Purvis, D. M. Quinn, D. H. Strome, R. Swenson, P. A. Temple, and T. F. Thonn, “Multiple determination of the optical constants of thin-film coating materials,” Appl. Optics 23, 3571–3596 (1984).
[Crossref]

Borgogno, J. P.

D. P. Arndt, R. M. A. Azzam, J. M. Bennett, J. P. Borgogno, C. K. Carniglia, W. E. Case, J. A. Dobrowolski, U. J. Gibson, T. Tuttle Hart, F. C. Ho, V. A. Hodgkin, W. P. Klapp, H. A. Macleod, E. Pelletier, M. K. Purvis, D. M. Quinn, D. H. Strome, R. Swenson, P. A. Temple, and T. F. Thonn, “Multiple determination of the optical constants of thin-film coating materials,” Appl. Optics 23, 3571–3596 (1984).
[Crossref]

Bublitz, S.

C. Mühlig, S. Kufert, S. Bublitz, and U. Speck, “Laser induced deflection technique for absolute thin film absorption measurement: optimized concepts and experimental results,” Appl. Optics 50, C449–C456 (2011).
[Crossref]

C. Mühlig, W. Triebel, S. Kufert, and S. Bublitz, “Characterization of low losses in optical thin films and materials,” Appl. Optics 47, C135–C142 (2008).
[Crossref]

Carniglia, C. K.

D. P. Arndt, R. M. A. Azzam, J. M. Bennett, J. P. Borgogno, C. K. Carniglia, W. E. Case, J. A. Dobrowolski, U. J. Gibson, T. Tuttle Hart, F. C. Ho, V. A. Hodgkin, W. P. Klapp, H. A. Macleod, E. Pelletier, M. K. Purvis, D. M. Quinn, D. H. Strome, R. Swenson, P. A. Temple, and T. F. Thonn, “Multiple determination of the optical constants of thin-film coating materials,” Appl. Optics 23, 3571–3596 (1984).
[Crossref]

Case, W. E.

D. P. Arndt, R. M. A. Azzam, J. M. Bennett, J. P. Borgogno, C. K. Carniglia, W. E. Case, J. A. Dobrowolski, U. J. Gibson, T. Tuttle Hart, F. C. Ho, V. A. Hodgkin, W. P. Klapp, H. A. Macleod, E. Pelletier, M. K. Purvis, D. M. Quinn, D. H. Strome, R. Swenson, P. A. Temple, and T. F. Thonn, “Multiple determination of the optical constants of thin-film coating materials,” Appl. Optics 23, 3571–3596 (1984).
[Crossref]

De Souza Meneses, D.

D. De Souza Meneses, M. Malki, and P. Echegut, “Structure and lattice dynamics of binary lead silicate glasses investigated by infrared spectroscopy,” J. Non-Cryst. Solids 351, 769–776 (2006).
[Crossref]

Dobrowolski, J. A.

D. P. Arndt, R. M. A. Azzam, J. M. Bennett, J. P. Borgogno, C. K. Carniglia, W. E. Case, J. A. Dobrowolski, U. J. Gibson, T. Tuttle Hart, F. C. Ho, V. A. Hodgkin, W. P. Klapp, H. A. Macleod, E. Pelletier, M. K. Purvis, D. M. Quinn, D. H. Strome, R. Swenson, P. A. Temple, and T. F. Thonn, “Multiple determination of the optical constants of thin-film coating materials,” Appl. Optics 23, 3571–3596 (1984).
[Crossref]

J. A. Dobrowolski, F. C. Ho, and A. Waldorf, “Determination of optical constants of thin film coating materials based on inverse synthesis,” Appl. Optics 22, 3191–3200 (1983).
[Crossref]

Duparré, A.

A. Duparré and D. Ristau, “Optical interference coatings 2007 measurement problem,” Appl. Optics 47, C179–C184 (2008).
[Crossref]

Echegut, P.

D. De Souza Meneses, M. Malki, and P. Echegut, “Structure and lattice dynamics of binary lead silicate glasses investigated by infrared spectroscopy,” J. Non-Cryst. Solids 351, 769–776 (2006).
[Crossref]

Gibson, U. J.

D. P. Arndt, R. M. A. Azzam, J. M. Bennett, J. P. Borgogno, C. K. Carniglia, W. E. Case, J. A. Dobrowolski, U. J. Gibson, T. Tuttle Hart, F. C. Ho, V. A. Hodgkin, W. P. Klapp, H. A. Macleod, E. Pelletier, M. K. Purvis, D. M. Quinn, D. H. Strome, R. Swenson, P. A. Temple, and T. F. Thonn, “Multiple determination of the optical constants of thin-film coating materials,” Appl. Optics 23, 3571–3596 (1984).
[Crossref]

Ho, F. C.

D. P. Arndt, R. M. A. Azzam, J. M. Bennett, J. P. Borgogno, C. K. Carniglia, W. E. Case, J. A. Dobrowolski, U. J. Gibson, T. Tuttle Hart, F. C. Ho, V. A. Hodgkin, W. P. Klapp, H. A. Macleod, E. Pelletier, M. K. Purvis, D. M. Quinn, D. H. Strome, R. Swenson, P. A. Temple, and T. F. Thonn, “Multiple determination of the optical constants of thin-film coating materials,” Appl. Optics 23, 3571–3596 (1984).
[Crossref]

J. A. Dobrowolski, F. C. Ho, and A. Waldorf, “Determination of optical constants of thin film coating materials based on inverse synthesis,” Appl. Optics 22, 3191–3200 (1983).
[Crossref]

Hodgkin, V. A.

D. P. Arndt, R. M. A. Azzam, J. M. Bennett, J. P. Borgogno, C. K. Carniglia, W. E. Case, J. A. Dobrowolski, U. J. Gibson, T. Tuttle Hart, F. C. Ho, V. A. Hodgkin, W. P. Klapp, H. A. Macleod, E. Pelletier, M. K. Purvis, D. M. Quinn, D. H. Strome, R. Swenson, P. A. Temple, and T. F. Thonn, “Multiple determination of the optical constants of thin-film coating materials,” Appl. Optics 23, 3571–3596 (1984).
[Crossref]

Jellison, G. E.

G. E. Jellison and F. A. Modine, “Erratum: Parameterization of the optical functions of amorphous materials in the interband region,” Appl. Phys. Lett. 69, 2137 (1996).
[Crossref]

G. E. Jellison and F. A. Modine, “Parameterization of the optical functions of amorphous materials in the interband region,” Appl. Phys. Lett. 69, 371–373 (1996).
[Crossref]

Jin, P.

L. Miao, P. Jin, K. Kaneko, A. Terai, N. Nabatova-Gabain, and S. Tanemura, “Preparation and characterization of polycrystalline anatase and rutile TiO2 thin films by rf magnetron sputtering,” Thin Solid Films 212–213, 255–263 (2003).

Kaneko, K.

L. Miao, P. Jin, K. Kaneko, A. Terai, N. Nabatova-Gabain, and S. Tanemura, “Preparation and characterization of polycrystalline anatase and rutile TiO2 thin films by rf magnetron sputtering,” Thin Solid Films 212–213, 255–263 (2003).

Klapp, W. P.

D. P. Arndt, R. M. A. Azzam, J. M. Bennett, J. P. Borgogno, C. K. Carniglia, W. E. Case, J. A. Dobrowolski, U. J. Gibson, T. Tuttle Hart, F. C. Ho, V. A. Hodgkin, W. P. Klapp, H. A. Macleod, E. Pelletier, M. K. Purvis, D. M. Quinn, D. H. Strome, R. Swenson, P. A. Temple, and T. F. Thonn, “Multiple determination of the optical constants of thin-film coating materials,” Appl. Optics 23, 3571–3596 (1984).
[Crossref]

Kufert, S.

C. Mühlig, S. Kufert, S. Bublitz, and U. Speck, “Laser induced deflection technique for absolute thin film absorption measurement: optimized concepts and experimental results,” Appl. Optics 50, C449–C456 (2011).
[Crossref]

C. Mühlig, W. Triebel, S. Kufert, and S. Bublitz, “Characterization of low losses in optical thin films and materials,” Appl. Optics 47, C135–C142 (2008).
[Crossref]

Macleod, H. A.

D. P. Arndt, R. M. A. Azzam, J. M. Bennett, J. P. Borgogno, C. K. Carniglia, W. E. Case, J. A. Dobrowolski, U. J. Gibson, T. Tuttle Hart, F. C. Ho, V. A. Hodgkin, W. P. Klapp, H. A. Macleod, E. Pelletier, M. K. Purvis, D. M. Quinn, D. H. Strome, R. Swenson, P. A. Temple, and T. F. Thonn, “Multiple determination of the optical constants of thin-film coating materials,” Appl. Optics 23, 3571–3596 (1984).
[Crossref]

H. A. Macleod, “Turning value monitoring of narrow-band all-dielectric thin-film optical filters,” Opt. Acta 19, 1–28 (1972).
[Crossref]

Malki, M.

D. De Souza Meneses, M. Malki, and P. Echegut, “Structure and lattice dynamics of binary lead silicate glasses investigated by infrared spectroscopy,” J. Non-Cryst. Solids 351, 769–776 (2006).
[Crossref]

Martinu, L.

L. Martinu and D. Poitras, “Plasma deposition of optical films and coatings: A review”, J. Vac. Sci. Technol. A 18, 2619–2645 (2000).
[Crossref]

Miao, L.

L. Miao, P. Jin, K. Kaneko, A. Terai, N. Nabatova-Gabain, and S. Tanemura, “Preparation and characterization of polycrystalline anatase and rutile TiO2 thin films by rf magnetron sputtering,” Thin Solid Films 212–213, 255–263 (2003).

Modine, F. A.

G. E. Jellison and F. A. Modine, “Parameterization of the optical functions of amorphous materials in the interband region,” Appl. Phys. Lett. 69, 371–373 (1996).
[Crossref]

G. E. Jellison and F. A. Modine, “Erratum: Parameterization of the optical functions of amorphous materials in the interband region,” Appl. Phys. Lett. 69, 2137 (1996).
[Crossref]

Mühlig, C.

C. Mühlig, S. Kufert, S. Bublitz, and U. Speck, “Laser induced deflection technique for absolute thin film absorption measurement: optimized concepts and experimental results,” Appl. Optics 50, C449–C456 (2011).
[Crossref]

C. Mühlig, W. Triebel, S. Kufert, and S. Bublitz, “Characterization of low losses in optical thin films and materials,” Appl. Optics 47, C135–C142 (2008).
[Crossref]

Nabatova-Gabain, N.

L. Miao, P. Jin, K. Kaneko, A. Terai, N. Nabatova-Gabain, and S. Tanemura, “Preparation and characterization of polycrystalline anatase and rutile TiO2 thin films by rf magnetron sputtering,” Thin Solid Films 212–213, 255–263 (2003).

Palmer, J. M.

J. M. Palmer, “Measurement of transmission, absorption, emission, and reflection,” in Handbook of optics, M. Bass, C. DeCusatis, and J. M. Enoch, eds. (McGraw-Hill Professional Publishing, New York, 2009), 2, Chap. 35, pp. 8–10.

Peiponen, K.-E.

K.-E. Peiponen and E. M. Vartiainen, “Kramers-Kronig relations in optical data inversion,” Phys. Rev. B 44, 8301–8303 (1991).
[Crossref]

Pelletier, E.

D. P. Arndt, R. M. A. Azzam, J. M. Bennett, J. P. Borgogno, C. K. Carniglia, W. E. Case, J. A. Dobrowolski, U. J. Gibson, T. Tuttle Hart, F. C. Ho, V. A. Hodgkin, W. P. Klapp, H. A. Macleod, E. Pelletier, M. K. Purvis, D. M. Quinn, D. H. Strome, R. Swenson, P. A. Temple, and T. F. Thonn, “Multiple determination of the optical constants of thin-film coating materials,” Appl. Optics 23, 3571–3596 (1984).
[Crossref]

Poitras, D.

L. Martinu and D. Poitras, “Plasma deposition of optical films and coatings: A review”, J. Vac. Sci. Technol. A 18, 2619–2645 (2000).
[Crossref]

Purvis, M. K.

D. P. Arndt, R. M. A. Azzam, J. M. Bennett, J. P. Borgogno, C. K. Carniglia, W. E. Case, J. A. Dobrowolski, U. J. Gibson, T. Tuttle Hart, F. C. Ho, V. A. Hodgkin, W. P. Klapp, H. A. Macleod, E. Pelletier, M. K. Purvis, D. M. Quinn, D. H. Strome, R. Swenson, P. A. Temple, and T. F. Thonn, “Multiple determination of the optical constants of thin-film coating materials,” Appl. Optics 23, 3571–3596 (1984).
[Crossref]

Quinn, D. M.

D. P. Arndt, R. M. A. Azzam, J. M. Bennett, J. P. Borgogno, C. K. Carniglia, W. E. Case, J. A. Dobrowolski, U. J. Gibson, T. Tuttle Hart, F. C. Ho, V. A. Hodgkin, W. P. Klapp, H. A. Macleod, E. Pelletier, M. K. Purvis, D. M. Quinn, D. H. Strome, R. Swenson, P. A. Temple, and T. F. Thonn, “Multiple determination of the optical constants of thin-film coating materials,” Appl. Optics 23, 3571–3596 (1984).
[Crossref]

Ristau, D.

A. Duparré and D. Ristau, “Optical interference coatings 2007 measurement problem,” Appl. Optics 47, C179–C184 (2008).
[Crossref]

Rosencwaig, A.

A. Rosencwaig and J. B. Willis, “Photoacoustic absorption measurements of optical materials and thin films,” J. Appl. Phys. 51, 4361–4364 (1980).
[Crossref]

Speck, U.

C. Mühlig, S. Kufert, S. Bublitz, and U. Speck, “Laser induced deflection technique for absolute thin film absorption measurement: optimized concepts and experimental results,” Appl. Optics 50, C449–C456 (2011).
[Crossref]

Strome, D. H.

D. P. Arndt, R. M. A. Azzam, J. M. Bennett, J. P. Borgogno, C. K. Carniglia, W. E. Case, J. A. Dobrowolski, U. J. Gibson, T. Tuttle Hart, F. C. Ho, V. A. Hodgkin, W. P. Klapp, H. A. Macleod, E. Pelletier, M. K. Purvis, D. M. Quinn, D. H. Strome, R. Swenson, P. A. Temple, and T. F. Thonn, “Multiple determination of the optical constants of thin-film coating materials,” Appl. Optics 23, 3571–3596 (1984).
[Crossref]

Swenson, R.

D. P. Arndt, R. M. A. Azzam, J. M. Bennett, J. P. Borgogno, C. K. Carniglia, W. E. Case, J. A. Dobrowolski, U. J. Gibson, T. Tuttle Hart, F. C. Ho, V. A. Hodgkin, W. P. Klapp, H. A. Macleod, E. Pelletier, M. K. Purvis, D. M. Quinn, D. H. Strome, R. Swenson, P. A. Temple, and T. F. Thonn, “Multiple determination of the optical constants of thin-film coating materials,” Appl. Optics 23, 3571–3596 (1984).
[Crossref]

Tanemura, S.

L. Miao, P. Jin, K. Kaneko, A. Terai, N. Nabatova-Gabain, and S. Tanemura, “Preparation and characterization of polycrystalline anatase and rutile TiO2 thin films by rf magnetron sputtering,” Thin Solid Films 212–213, 255–263 (2003).

Temple, P. A.

D. P. Arndt, R. M. A. Azzam, J. M. Bennett, J. P. Borgogno, C. K. Carniglia, W. E. Case, J. A. Dobrowolski, U. J. Gibson, T. Tuttle Hart, F. C. Ho, V. A. Hodgkin, W. P. Klapp, H. A. Macleod, E. Pelletier, M. K. Purvis, D. M. Quinn, D. H. Strome, R. Swenson, P. A. Temple, and T. F. Thonn, “Multiple determination of the optical constants of thin-film coating materials,” Appl. Optics 23, 3571–3596 (1984).
[Crossref]

Terai, A.

L. Miao, P. Jin, K. Kaneko, A. Terai, N. Nabatova-Gabain, and S. Tanemura, “Preparation and characterization of polycrystalline anatase and rutile TiO2 thin films by rf magnetron sputtering,” Thin Solid Films 212–213, 255–263 (2003).

Thonn, T. F.

D. P. Arndt, R. M. A. Azzam, J. M. Bennett, J. P. Borgogno, C. K. Carniglia, W. E. Case, J. A. Dobrowolski, U. J. Gibson, T. Tuttle Hart, F. C. Ho, V. A. Hodgkin, W. P. Klapp, H. A. Macleod, E. Pelletier, M. K. Purvis, D. M. Quinn, D. H. Strome, R. Swenson, P. A. Temple, and T. F. Thonn, “Multiple determination of the optical constants of thin-film coating materials,” Appl. Optics 23, 3571–3596 (1984).
[Crossref]

Triebel, W.

C. Mühlig, W. Triebel, S. Kufert, and S. Bublitz, “Characterization of low losses in optical thin films and materials,” Appl. Optics 47, C135–C142 (2008).
[Crossref]

Tuttle Hart, T.

D. P. Arndt, R. M. A. Azzam, J. M. Bennett, J. P. Borgogno, C. K. Carniglia, W. E. Case, J. A. Dobrowolski, U. J. Gibson, T. Tuttle Hart, F. C. Ho, V. A. Hodgkin, W. P. Klapp, H. A. Macleod, E. Pelletier, M. K. Purvis, D. M. Quinn, D. H. Strome, R. Swenson, P. A. Temple, and T. F. Thonn, “Multiple determination of the optical constants of thin-film coating materials,” Appl. Optics 23, 3571–3596 (1984).
[Crossref]

Vartiainen, E. M.

K.-E. Peiponen and E. M. Vartiainen, “Kramers-Kronig relations in optical data inversion,” Phys. Rev. B 44, 8301–8303 (1991).
[Crossref]

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J. A. Dobrowolski, F. C. Ho, and A. Waldorf, “Determination of optical constants of thin film coating materials based on inverse synthesis,” Appl. Optics 22, 3191–3200 (1983).
[Crossref]

Welsch, E.

E. Welsch, “Absorption Measurements,” in Handbook of optical properties, R. E. Hummel and K. H. Guenther, eds. (CRC Press Inc., Boca Raton, Florida, 1995), 1, pp. 243–272.

Willis, J. B.

A. Rosencwaig and J. B. Willis, “Photoacoustic absorption measurements of optical materials and thin films,” J. Appl. Phys. 51, 4361–4364 (1980).
[Crossref]

Appl. Optics (5)

D. P. Arndt, R. M. A. Azzam, J. M. Bennett, J. P. Borgogno, C. K. Carniglia, W. E. Case, J. A. Dobrowolski, U. J. Gibson, T. Tuttle Hart, F. C. Ho, V. A. Hodgkin, W. P. Klapp, H. A. Macleod, E. Pelletier, M. K. Purvis, D. M. Quinn, D. H. Strome, R. Swenson, P. A. Temple, and T. F. Thonn, “Multiple determination of the optical constants of thin-film coating materials,” Appl. Optics 23, 3571–3596 (1984).
[Crossref]

A. Duparré and D. Ristau, “Optical interference coatings 2007 measurement problem,” Appl. Optics 47, C179–C184 (2008).
[Crossref]

J. A. Dobrowolski, F. C. Ho, and A. Waldorf, “Determination of optical constants of thin film coating materials based on inverse synthesis,” Appl. Optics 22, 3191–3200 (1983).
[Crossref]

C. Mühlig, W. Triebel, S. Kufert, and S. Bublitz, “Characterization of low losses in optical thin films and materials,” Appl. Optics 47, C135–C142 (2008).
[Crossref]

C. Mühlig, S. Kufert, S. Bublitz, and U. Speck, “Laser induced deflection technique for absolute thin film absorption measurement: optimized concepts and experimental results,” Appl. Optics 50, C449–C456 (2011).
[Crossref]

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[Crossref]

G. E. Jellison and F. A. Modine, “Erratum: Parameterization of the optical functions of amorphous materials in the interband region,” Appl. Phys. Lett. 69, 2137 (1996).
[Crossref]

J. Appl. Phys. (1)

A. Rosencwaig and J. B. Willis, “Photoacoustic absorption measurements of optical materials and thin films,” J. Appl. Phys. 51, 4361–4364 (1980).
[Crossref]

J. Non-Cryst. Solids (1)

D. De Souza Meneses, M. Malki, and P. Echegut, “Structure and lattice dynamics of binary lead silicate glasses investigated by infrared spectroscopy,” J. Non-Cryst. Solids 351, 769–776 (2006).
[Crossref]

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[Crossref]

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Phys. Rev. B (1)

K.-E. Peiponen and E. M. Vartiainen, “Kramers-Kronig relations in optical data inversion,” Phys. Rev. B 44, 8301–8303 (1991).
[Crossref]

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[Crossref]

L. Miao, P. Jin, K. Kaneko, A. Terai, N. Nabatova-Gabain, and S. Tanemura, “Preparation and characterization of polycrystalline anatase and rutile TiO2 thin films by rf magnetron sputtering,” Thin Solid Films 212–213, 255–263 (2003).

Other (5)

E. Welsch, “Absorption Measurements,” in Handbook of optical properties, R. E. Hummel and K. H. Guenther, eds. (CRC Press Inc., Boca Raton, Florida, 1995), 1, pp. 243–272.

J. M. Palmer, “Measurement of transmission, absorption, emission, and reflection,” in Handbook of optics, M. Bass, C. DeCusatis, and J. M. Enoch, eds. (McGraw-Hill Professional Publishing, New York, 2009), 2, Chap. 35, pp. 8–10.

https://pypi.python.org/pypi/tmm

https://pypi.python.org/pypi/lmfit

ISO 13696:2002 , “Optics and optical instruments – Test methods for radiation scattered by optical components,” Geneva, Switzerland, (2002).

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Figures (6)

Fig. 1
Fig. 1 Diagram of the methodology used for the evaluation of the film thickness and the optical constants of coatings. The same methodology can be applied for the determination of the optical constants of substrates.
Fig. 2
Fig. 2 Transmission, reflection and absorption spectra simulated for different film materials in p polarized light at two angles of incidence. Spectra calculated at near-normal incidence (10°) and near-Brewster incidence (65°) are shown in (a–b) and (c–d), respectively. Film materials with low (SiO2: 1.46), medium (Al2O3: 1.77) and high (TiO2: 2.28) refractive index values at 550 nm are exemplified. Spectra obtained for a typical bare glass substrate are also shown for reference.
Fig. 3
Fig. 3 Results obtained for the CR-39 substrate with hard coat using the TRACK method: (a) T and R spectra measured at an AOI of 10° in p polarized light and modelled data; (b) Difference between experimental and modelled data; (c) Dispersion curves calculated from the parametric model; (d) T and R spectra measured at an AOI of 65° in p polarized light; (e) A spectrum calculated from T and R data; (f) Final dispersion curves of the CR-39 substrate: n is obtained from the parametric model and k is directly calculated from the A spectrum, using n and the film thickness as input parameters.
Fig. 4
Fig. 4 Results obtained for the TiO2 coating on top of the CR-39 substrate with hard coat using the TRACK method: (a) T and R spectra measured at an AOI of 10° in p polarized light and modelled data; (b) Difference between experimental and modelled data; (c) Dispersion curves calculated from the parametric model as well as the discrete point by point fit; (d) T and R spectra measured at an AOI of 65° in p polarized light; (e) A spectra calculated from T and R data for both TiO2-coated and uncoated substrates; (f) Final dispersion curves of the TiO2 coating: n is obtained from the parametric model and k is directly calculated from the A spectrum, using n and the film thickness (392 nm) as input parameters.
Fig. 5
Fig. 5 Non-idealities of a sample Si3N4 coating: (a) Refractive index inhomogeneity along the film thickness evaluated from the modeling of the R and T spectra at AOI=10° and p polarization; (b) Film thickness non-uniformity evidenced by the presence of Newton’s rings visible on the sample surface (dimensions are 50 × 50mm).
Fig. 6
Fig. 6 Results obtained for the non-ideal Si3N4 coating on top of a glass substrate using the TRACK method: (a) T and R spectra measured at an AOI of 10° in p polarized light, and data generated from two models (simple Cauchy/Urbach model and complex general oscillator model including two film non-idealities); (b) Difference between experimental and modelled data for the Cauchy/Urbach and Genosc models; (c) Dispersion curves calculated from the Cauchy/Urbach model and the Genosc model; (d) T and R spectra measured at an AOI of 65° in p polarized light; (e) A spectra calculated from T and R data for both Si3N4-coated and uncoated substrates; (f) Final dispersion curves of the Si3N4 coating: n is obtained from the Cauchy equation, and k is directly calculated from the A spectrum, using n and the film thickness as input parameters.

Tables (2)

Tables Icon

Table 1 Comparison of the absorption and extinction coefficient values obtained at 410 nm and 550 nm for three TiO2 films using the TRACK and LID methods.

Tables Icon

Table 2 Film thickness, refractive index and diffuse transmittance values measured at 410 nm and 550 nm for a bare Gorilla substrate and three TiO2 films deposited during the same run.

Equations (14)

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A ( λ ) = 100 % R ( λ ) T ( λ ) S ( λ )
T = exp ( α t )
with α = 4 π k λ ,
T 1 4 π k t λ
and A 1 T 4 π k t λ .
t λ × 10 3 4 π k .
ε = ε 1 + i ε 2
ε 2 ( E ) = i ε G aussian i = i A i e ( E E i σ i ) 2 A i e ( E + E i σ i ) 2
ε 1 ( E ) = ε inf + A u v E u v 2 E 2 + A i r E i r 2 E 2 + i 2 π P 0 ξ ε G aussian i ( ξ ) ξ 2 E 2 d ξ
n ( λ ) = A C + B C / λ 2 + C C / λ 4 ,
k ( λ ) = A U e B U ( 1 / λ 1 / C U ) ,
ε 2 ( E ) = A T E T C T ( E E T g ) 2 ( E 2 E T 2 ) 2 + C T 2 E 2 1 E E > E T g
ε 2 ( E ) = 0 E E T g
T d [ % ] = ( T 4 T 3 × T 2 / T 1 ) / ( T 1 T 3 ) × 100 ,

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