Abstract

Accurate directional transmittance can reduce uncertainty in parameters regression of optical thin-films. When directional transmittance is measured at large angle of incidence (AOI), a polarizer has to be used to produce linearly polarized light and it also becomes an error source. This study presents a method for accurate measurement of wideband transmittance at large AOI, which is aimed to eliminate the polarization error in measured transmittance at oblique incidence. Using this method, we can measure the directional transmittance with a good precision if a partially polarized incident beam is provided. This method reduces the requirement for the performance of the polarizer, and will find application in the highly integrated spectrophotometers.

© 2013 Optical Society of America

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References

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  1. W. V. Goodell, J. K. Coulter, and P. B. Johnson, “Derivation of optical constants of metals from thin-film measurements at oblique incidence,” Appl. Opt. 11, 643–651 (1972).
    [CrossRef]
  2. 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. T. Hart, F. C. Ho, V. A. Hodgkin, W. P. Klapp, H. A. Macleod, E. Pelletier, and M. K. Purvis, “Multiple determination of the optical constants of thin-film coating materials,” Appl. Opt. 23, 3571–3596 (1984).
    [CrossRef]
  3. J. A. Dobrowolski, F. C. Ho, and A. Waldorf, “Determination of optical constants of thin-film coating materials based on inverse synthesis,” Appl. Opt. 22, 3191–3200 (1983).
    [CrossRef]
  4. T. Kihara and K. Yokomori, “Simultaneous measurement of the refractive index and thickness of thin-films by s-polarized reflectances,” Appl. Opt. 31, 4482–4487 (1992).
    [CrossRef]
  5. K. Lamprecht, W. Papousek, and G. Leising, “Problem of ambiguity in the determination of optical constants of thin absorbing films from spectroscopic reflectance and transmittance measurements,” Appl. Opt. 36, 6364–6371 (1997).
    [CrossRef]
  6. S. Nevas, F. Manoocheri, E. Ikonen, A. V. Tikhonravov, M. A. Kokarev, and M. K. Trubetskov, “Optical metrology of thin-films using high-accuracy spectro-photometric measurements with oblique angles of incidence,” Proc. SPIE 5250, 234–242 (2004).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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2012

2010

2008

C. Amra, M. Zerrad, L. Siozade, G. Georges, and C. Deumié, “Partial polarization of light induced by random defects at surfaces or bulks,” Opt. Express 16, 10372–10383 (2008).
[CrossRef]

P. A. van Nijnatten, “Optical analysis of coatings by variable angle spectrophotometry,” Thin Solid Films 516, 4553–4557 (2008).
[CrossRef]

2006

2004

S. Nevas, F. Manoocheri, E. Ikonen, A. V. Tikhonravov, M. A. Kokarev, and M. K. Trubetskov, “Optical metrology of thin-films using high-accuracy spectro-photometric measurements with oblique angles of incidence,” Proc. SPIE 5250, 234–242 (2004).
[CrossRef]

2003

P. A. Van Nijnatten, “An automated directional reflectance/transmittance analyzer for coating analysis,” Thin Solid Films 442, 74–79 (2003).
[CrossRef]

2001

M. G. Hutchins, A. J. Topping, C. Anderson, F. Olive, P. Van Nijnatten, P. Polato, A. Roos, and M. Rubin, “Measurement and prediction of angle-dependent optical properties of coated glass products: results of an inter-laboratory comparison of spectral transmittance and reflectance,” Thin Solid Films 392, 269–275 (2001).
[CrossRef]

1997

1993

M. G. Hutchins and P. Ageorges, “Angular-dependent spectral optical properties of architectural glazings: results of an interlaboratory comparison of measurements,” Proc. SPIE 2017, 13–24 (1993).
[CrossRef]

1992

1984

1983

1972

Ageorges, P.

M. G. Hutchins and P. Ageorges, “Angular-dependent spectral optical properties of architectural glazings: results of an interlaboratory comparison of measurements,” Proc. SPIE 2017, 13–24 (1993).
[CrossRef]

Amotchkina, T. V.

Amra, C.

Anderson, C.

M. G. Hutchins, A. J. Topping, C. Anderson, F. Olive, P. Van Nijnatten, P. Polato, A. Roos, and M. Rubin, “Measurement and prediction of angle-dependent optical properties of coated glass products: results of an inter-laboratory comparison of spectral transmittance and reflectance,” Thin Solid Films 392, 269–275 (2001).
[CrossRef]

Arndt, D. P.

Azzam, R. M. A.

Bass, M.

M. Bass, Handbook of Optics, Volume I (McGraw-Hill, 2010).

Bennett, J. M.

Borgogno, J. P.

Carniglia, C. K.

Case, W. E.

Collett, E.

D. Goldstein and E. Collett, Polarized Light (Marcel Dekker, 2003).

Coulter, J. K.

Deumié, C.

Dobrowolski, J. A.

Francis, R.

Gao, L.

Georges, G.

Gibson, U. J.

Goldstein, D.

D. Goldstein and E. Collett, Polarized Light (Marcel Dekker, 2003).

Goodell, W. V.

Hart, T. T.

Ho, F. C.

Hodgkin, V. A.

Hutchins, M. G.

M. G. Hutchins, A. J. Topping, C. Anderson, F. Olive, P. Van Nijnatten, P. Polato, A. Roos, and M. Rubin, “Measurement and prediction of angle-dependent optical properties of coated glass products: results of an inter-laboratory comparison of spectral transmittance and reflectance,” Thin Solid Films 392, 269–275 (2001).
[CrossRef]

M. G. Hutchins and P. Ageorges, “Angular-dependent spectral optical properties of architectural glazings: results of an interlaboratory comparison of measurements,” Proc. SPIE 2017, 13–24 (1993).
[CrossRef]

Ikonen, E.

A. Lamminpää, S. Nevas, F. Manoocheri, and E. Ikonen, “Characterization of thin-films based on reflectance and transmittance measurements at oblique angles of incidence,” Appl. Opt. 45, 1392–1396 (2006).
[CrossRef]

S. Nevas, F. Manoocheri, E. Ikonen, A. V. Tikhonravov, M. A. Kokarev, and M. K. Trubetskov, “Optical metrology of thin-films using high-accuracy spectro-photometric measurements with oblique angles of incidence,” Proc. SPIE 5250, 234–242 (2004).
[CrossRef]

Janicki, V.

Johnson, P. B.

Kang, C.

A. F. Ryuichi Shintani and C. Kang, Polarized Light (Atomic Energy, 1994).

Kihara, T.

Klapp, W. P.

Kokarev, M. A.

S. Nevas, F. Manoocheri, E. Ikonen, A. V. Tikhonravov, M. A. Kokarev, and M. K. Trubetskov, “Optical metrology of thin-films using high-accuracy spectro-photometric measurements with oblique angles of incidence,” Proc. SPIE 5250, 234–242 (2004).
[CrossRef]

Lamminpää, A.

Lamprecht, K.

Leising, G.

Lemarchand, F.

Lequime, M.

Macleod, H. A.

Manoocheri, F.

A. Lamminpää, S. Nevas, F. Manoocheri, and E. Ikonen, “Characterization of thin-films based on reflectance and transmittance measurements at oblique angles of incidence,” Appl. Opt. 45, 1392–1396 (2006).
[CrossRef]

S. Nevas, F. Manoocheri, E. Ikonen, A. V. Tikhonravov, M. A. Kokarev, and M. K. Trubetskov, “Optical metrology of thin-films using high-accuracy spectro-photometric measurements with oblique angles of incidence,” Proc. SPIE 5250, 234–242 (2004).
[CrossRef]

Nevas, S.

A. Lamminpää, S. Nevas, F. Manoocheri, and E. Ikonen, “Characterization of thin-films based on reflectance and transmittance measurements at oblique angles of incidence,” Appl. Opt. 45, 1392–1396 (2006).
[CrossRef]

S. Nevas, F. Manoocheri, E. Ikonen, A. V. Tikhonravov, M. A. Kokarev, and M. K. Trubetskov, “Optical metrology of thin-films using high-accuracy spectro-photometric measurements with oblique angles of incidence,” Proc. SPIE 5250, 234–242 (2004).
[CrossRef]

Olive, F.

M. G. Hutchins, A. J. Topping, C. Anderson, F. Olive, P. Van Nijnatten, P. Polato, A. Roos, and M. Rubin, “Measurement and prediction of angle-dependent optical properties of coated glass products: results of an inter-laboratory comparison of spectral transmittance and reflectance,” Thin Solid Films 392, 269–275 (2001).
[CrossRef]

Papousek, W.

Pelletier, E.

Pervak, V.

Polato, P.

M. G. Hutchins, A. J. Topping, C. Anderson, F. Olive, P. Van Nijnatten, P. Polato, A. Roos, and M. Rubin, “Measurement and prediction of angle-dependent optical properties of coated glass products: results of an inter-laboratory comparison of spectral transmittance and reflectance,” Thin Solid Films 392, 269–275 (2001).
[CrossRef]

Purvis, M. K.

Roos, A.

M. G. Hutchins, A. J. Topping, C. Anderson, F. Olive, P. Van Nijnatten, P. Polato, A. Roos, and M. Rubin, “Measurement and prediction of angle-dependent optical properties of coated glass products: results of an inter-laboratory comparison of spectral transmittance and reflectance,” Thin Solid Films 392, 269–275 (2001).
[CrossRef]

Rubin, M.

M. G. Hutchins, A. J. Topping, C. Anderson, F. Olive, P. Van Nijnatten, P. Polato, A. Roos, and M. Rubin, “Measurement and prediction of angle-dependent optical properties of coated glass products: results of an inter-laboratory comparison of spectral transmittance and reflectance,” Thin Solid Films 392, 269–275 (2001).
[CrossRef]

Ryuichi Shintani, A. F.

A. F. Ryuichi Shintani and C. Kang, Polarized Light (Atomic Energy, 1994).

Sancho-Parramon, J.

Siozade, L.

Soriano, G.

Sorrentini, J.

Tikhonravov, A. V.

A. V. Tikhonravov, T. V. Amotchkina, M. K. Trubetskov, R. Francis, V. Janicki, J. Sancho-Parramon, H. Zorc, and V. Pervak, “Optical characterization and reverse engineering based on multiangle spectroscopy,” Appl. Opt. 51, 245–254 (2012).
[CrossRef]

S. Nevas, F. Manoocheri, E. Ikonen, A. V. Tikhonravov, M. A. Kokarev, and M. K. Trubetskov, “Optical metrology of thin-films using high-accuracy spectro-photometric measurements with oblique angles of incidence,” Proc. SPIE 5250, 234–242 (2004).
[CrossRef]

Topping, A. J.

M. G. Hutchins, A. J. Topping, C. Anderson, F. Olive, P. Van Nijnatten, P. Polato, A. Roos, and M. Rubin, “Measurement and prediction of angle-dependent optical properties of coated glass products: results of an inter-laboratory comparison of spectral transmittance and reflectance,” Thin Solid Films 392, 269–275 (2001).
[CrossRef]

Trubetskov, M. K.

A. V. Tikhonravov, T. V. Amotchkina, M. K. Trubetskov, R. Francis, V. Janicki, J. Sancho-Parramon, H. Zorc, and V. Pervak, “Optical characterization and reverse engineering based on multiangle spectroscopy,” Appl. Opt. 51, 245–254 (2012).
[CrossRef]

S. Nevas, F. Manoocheri, E. Ikonen, A. V. Tikhonravov, M. A. Kokarev, and M. K. Trubetskov, “Optical metrology of thin-films using high-accuracy spectro-photometric measurements with oblique angles of incidence,” Proc. SPIE 5250, 234–242 (2004).
[CrossRef]

Van Nijnatten, P.

M. G. Hutchins, A. J. Topping, C. Anderson, F. Olive, P. Van Nijnatten, P. Polato, A. Roos, and M. Rubin, “Measurement and prediction of angle-dependent optical properties of coated glass products: results of an inter-laboratory comparison of spectral transmittance and reflectance,” Thin Solid Films 392, 269–275 (2001).
[CrossRef]

van Nijnatten, P. A.

P. A. van Nijnatten, “Optical analysis of coatings by variable angle spectrophotometry,” Thin Solid Films 516, 4553–4557 (2008).
[CrossRef]

P. A. Van Nijnatten, “An automated directional reflectance/transmittance analyzer for coating analysis,” Thin Solid Films 442, 74–79 (2003).
[CrossRef]

Waldorf, A.

Yokomori, K.

Zerrad, M.

Zorc, H.

Appl. Opt.

W. V. Goodell, J. K. Coulter, and P. B. Johnson, “Derivation of optical constants of metals from thin-film measurements at oblique incidence,” Appl. Opt. 11, 643–651 (1972).
[CrossRef]

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

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. T. Hart, F. C. Ho, V. A. Hodgkin, W. P. Klapp, H. A. Macleod, E. Pelletier, and M. K. Purvis, “Multiple determination of the optical constants of thin-film coating materials,” Appl. Opt. 23, 3571–3596 (1984).
[CrossRef]

T. Kihara and K. Yokomori, “Simultaneous measurement of the refractive index and thickness of thin-films by s-polarized reflectances,” Appl. Opt. 31, 4482–4487 (1992).
[CrossRef]

K. Lamprecht, W. Papousek, and G. Leising, “Problem of ambiguity in the determination of optical constants of thin absorbing films from spectroscopic reflectance and transmittance measurements,” Appl. Opt. 36, 6364–6371 (1997).
[CrossRef]

A. Lamminpää, S. Nevas, F. Manoocheri, and E. Ikonen, “Characterization of thin-films based on reflectance and transmittance measurements at oblique angles of incidence,” Appl. Opt. 45, 1392–1396 (2006).
[CrossRef]

A. V. Tikhonravov, T. V. Amotchkina, M. K. Trubetskov, R. Francis, V. Janicki, J. Sancho-Parramon, H. Zorc, and V. Pervak, “Optical characterization and reverse engineering based on multiangle spectroscopy,” Appl. Opt. 51, 245–254 (2012).
[CrossRef]

Opt. Express

Proc. SPIE

S. Nevas, F. Manoocheri, E. Ikonen, A. V. Tikhonravov, M. A. Kokarev, and M. K. Trubetskov, “Optical metrology of thin-films using high-accuracy spectro-photometric measurements with oblique angles of incidence,” Proc. SPIE 5250, 234–242 (2004).
[CrossRef]

M. G. Hutchins and P. Ageorges, “Angular-dependent spectral optical properties of architectural glazings: results of an interlaboratory comparison of measurements,” Proc. SPIE 2017, 13–24 (1993).
[CrossRef]

Thin Solid Films

M. G. Hutchins, A. J. Topping, C. Anderson, F. Olive, P. Van Nijnatten, P. Polato, A. Roos, and M. Rubin, “Measurement and prediction of angle-dependent optical properties of coated glass products: results of an inter-laboratory comparison of spectral transmittance and reflectance,” Thin Solid Films 392, 269–275 (2001).
[CrossRef]

P. A. van Nijnatten, “Optical analysis of coatings by variable angle spectrophotometry,” Thin Solid Films 516, 4553–4557 (2008).
[CrossRef]

P. A. Van Nijnatten, “An automated directional reflectance/transmittance analyzer for coating analysis,” Thin Solid Films 442, 74–79 (2003).
[CrossRef]

Other

M. Bass, Handbook of Optics, Volume I (McGraw-Hill, 2010).

A. F. Ryuichi Shintani and C. Kang, Polarized Light (Atomic Energy, 1994).

D. Goldstein and E. Collett, Polarized Light (Marcel Dekker, 2003).

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Figures (4)

Fig. 1.
Fig. 1.

Definition of the Stokes vectors of the incidence and output light beam S and S, and the Mueller matrix of the sample M.

Fig. 2.
Fig. 2.

Schema of measurement of the (a) horizontal and (b) vertical transmittances. Θ is the AOI.

Fig. 3.
Fig. 3.

Comparison of measurement results of the new and traditional methods: transmittances of (a) the 1064AR and (c) the 1064PBS at 45° are measured with the traditional method, and transmittances of (b) the AR and (d) the PBS at 45° are measured with the new method.

Fig. 4.
Fig. 4.

p factor used to measure the transmittance of 1064AR and 1064PBS.

Equations (12)

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

S=MS,
S=(S0,S1,S2,S3),
S=(S0,S1,S2,S3).
M=12(Tx+TyTxTy00TxTyTx+Ty00002TxTycosΔ2TxTysinΔ002TxTysinΔ2TxTycosΔ),
{Tx=TPTy=TS;
{Tx=TSTy=TP.
Tm=S0S0.
Thm=(TS+TP)+(TSTP)S1S0,
Tvm=(TS+TP)(TSTP)S1S0,
{TS=12[(Thm+Tvm)+1p(ThmTvm)]TP=12[(Thm+Tvm)1p(ThmTvm)],
p=S1/S0.
p=ThmTvmTSTP=ThmTvmTScTPc,

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