Abstract

A non-invasive method for measuring the refractive index, extinction coefficient and film thickness of absorptive thin films using spectral-domain optical coherent tomography is proposed, analyzed and experimentally demonstrated. Such an optical system employing a normal-incident beam of light exhibits a high spatial resolution. There are no mechanical moving parts involved for the measurement except the transversal scanning module for the measurement at various transversal locations. The method was experimentally demonstrated on two absorptive thin-film samples coated on transparent glass substrates. The refractive index and extinction coefficient spectra from 510 to 580 nm wavelength range and film thickness were simultaneously measured. The results are presented and discussed.

© 2014 Optical Society of America

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2011

2010

2009

2008

A. Dubois, J. Moreau, C. Boccara, “Spectroscopic ultrahigh-resolution full-field optical coherence microscopy,” Opt. Express 16(21), 17082–17091 (2008).
[CrossRef] [PubMed]

J. N. Hilfiker, N. Singh, T. Tiwald, D. Convey, S. M. Smith, J. H. Baker, H. G. Tompkins, “Survey of methods to characterize thin absorbing films with spectroscopic ellipsometry,” Thin Solid Films 516(22), 7979–7989 (2008).
[CrossRef]

2006

2005

2003

2001

2000

A. Knüttel, M. Boehlau-Godau, “Spatially confined and temporally resolved refractive index and scattering evaluation in human skin performed with optical coherence tomography,” J. Biomed. Opt. 5(1), 83–92 (2000).
[CrossRef] [PubMed]

U. Morgner, W. Drexler, F. X. Kärtner, X. D. Li, C. Pitris, E. P. Ippen, J. G. Fujimoto, “Spectroscopic optical coherence tomography,” Opt. Lett. 25(2), 111–113 (2000).
[CrossRef] [PubMed]

1998

F. Yang, M. Tabet, W. A. McGahan, “Characterizing optical properties of red, green, and blue color filters for automated film-thickness measurement,” Proc. SPIE 3332, 403–410 (1998).
[CrossRef]

1995

1994

T. R. Judge, P. J. Bryanston-Cross, “A review of phase unwrapping techniques in fringe analysis,” Opt. Lasers Eng. 21(4), 199–239 (1994).
[CrossRef]

1991

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, J. G. Fujimoto, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

1984

1983

1976

J. C. Manifacier, J. Gasiot, J. P. Fillard, “A simple method for the determination of the optical constants n, k and the thickness of a weakly absorbing thin film,” J. Phys. E Sci. Instrum. 9(11), 1002–1004 (1976).
[CrossRef]

Alexandrov, S.

Armstrong, J.

Azzam, R. M. A.

Baker, J. H.

J. N. Hilfiker, N. Singh, T. Tiwald, D. Convey, S. M. Smith, J. H. Baker, H. G. Tompkins, “Survey of methods to characterize thin absorbing films with spectroscopic ellipsometry,” Thin Solid Films 516(22), 7979–7989 (2008).
[CrossRef]

Boccara, C.

Boehlau-Godau, M.

A. Knüttel, M. Boehlau-Godau, “Spatially confined and temporally resolved refractive index and scattering evaluation in human skin performed with optical coherence tomography,” J. Biomed. Opt. 5(1), 83–92 (2000).
[CrossRef] [PubMed]

Boppart, S. A.

Bouma, B. E.

Brezinski, M. E.

Bryanston-Cross, P. J.

T. R. Judge, P. J. Bryanston-Cross, “A review of phase unwrapping techniques in fringe analysis,” Opt. Lasers Eng. 21(4), 199–239 (1994).
[CrossRef]

Cang, H.

Cense, B.

Chang, W.

C. C. Tsai, T. H. Chen, Y. S. Lin, Y. T. Wang, W. Chang, K. Y. Hsu, Y. H. Chang, P. K. Hsu, D. Y. Jheng, K. Y. Huang, E. Sun, S. L. Huang, “Ce3+:YAG double-clad crystal-fiber-based optical coherence tomography on fish cornea,” Opt. Lett. 35(6), 811–813 (2010).
[CrossRef] [PubMed]

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, J. G. Fujimoto, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

Chang, Y. H.

Chen, J.

Chen, T. H.

Cheng, Y. Y.

Convey, D.

J. N. Hilfiker, N. Singh, T. Tiwald, D. Convey, S. M. Smith, J. H. Baker, H. G. Tompkins, “Survey of methods to characterize thin absorbing films with spectroscopic ellipsometry,” Thin Solid Films 516(22), 7979–7989 (2008).
[CrossRef]

de Boer, J. F.

Donati, S.

Drexler, W.

Dubois, A.

Fathi, M. T.

Fercher, A. F.

Fillard, J. P.

J. C. Manifacier, J. Gasiot, J. P. Fillard, “A simple method for the determination of the optical constants n, k and the thickness of a weakly absorbing thin film,” J. Phys. E Sci. Instrum. 9(11), 1002–1004 (1976).
[CrossRef]

Flotte, T.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, J. G. Fujimoto, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

Fujimoto, J. G.

Gasiot, J.

J. C. Manifacier, J. Gasiot, J. P. Fillard, “A simple method for the determination of the optical constants n, k and the thickness of a weakly absorbing thin film,” J. Phys. E Sci. Instrum. 9(11), 1002–1004 (1976).
[CrossRef]

Gregory, K.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, J. G. Fujimoto, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

Hee, M. R.

G. J. Tearney, M. E. Brezinski, J. F. Southern, B. E. Bouma, M. R. Hee, J. G. Fujimoto, “Determination of the refractive index of highly scattering human tissue by optical coherence tomography,” Opt. Lett. 20(21), 2258–2260 (1995).
[CrossRef] [PubMed]

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, J. G. Fujimoto, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

Hendargo, H. C.

Hilfiker, J. N.

J. N. Hilfiker, N. Singh, T. Tiwald, D. Convey, S. M. Smith, J. H. Baker, H. G. Tompkins, “Survey of methods to characterize thin absorbing films with spectroscopic ellipsometry,” Thin Solid Films 516(22), 7979–7989 (2008).
[CrossRef]

Hillman, T.

Hitzenberger, C. K.

Ho, T. S.

Ho, Y.

Hsu, K. Y.

Hsu, P. K.

Huang, D.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, J. G. Fujimoto, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

Huang, K. Y.

Huang, P. L.

Huang, S. L.

Ippen, E. P.

Izatt, J. A.

Jheng, D. Y.

Judge, T. R.

T. R. Judge, P. J. Bryanston-Cross, “A review of phase unwrapping techniques in fringe analysis,” Opt. Lasers Eng. 21(4), 199–239 (1994).
[CrossRef]

Kärtner, F. X.

Knüttel, A.

A. Knüttel, M. Boehlau-Godau, “Spatially confined and temporally resolved refractive index and scattering evaluation in human skin performed with optical coherence tomography,” J. Biomed. Opt. 5(1), 83–92 (2000).
[CrossRef] [PubMed]

Kung, A. H.

Leitgeb, R.

Li, X.

Li, X. D.

Li, Z. Y.

Lin, C. P.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, J. G. Fujimoto, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

Lin, Y. S.

Luo, W.

Manifacier, J. C.

J. C. Manifacier, J. Gasiot, J. P. Fillard, “A simple method for the determination of the optical constants n, k and the thickness of a weakly absorbing thin film,” J. Phys. E Sci. Instrum. 9(11), 1002–1004 (1976).
[CrossRef]

McGahan, W. A.

F. Yang, M. Tabet, W. A. McGahan, “Characterizing optical properties of red, green, and blue color filters for automated film-thickness measurement,” Proc. SPIE 3332, 403–410 (1998).
[CrossRef]

Moreau, J.

Morgner, U.

Park, B. H.

Pei, S. C.

Pierce, M. C.

Pitris, C.

Puliafito, C. A.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, J. G. Fujimoto, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

Ralston, T. S.

Sampson, D.

Schuman, J. S.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, J. G. Fujimoto, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

Shepherd, N.

Silva, K. K. M. B.

Singh, N.

J. N. Hilfiker, N. Singh, T. Tiwald, D. Convey, S. M. Smith, J. H. Baker, H. G. Tompkins, “Survey of methods to characterize thin absorbing films with spectroscopic ellipsometry,” Thin Solid Films 516(22), 7979–7989 (2008).
[CrossRef]

Smith, S. M.

J. N. Hilfiker, N. Singh, T. Tiwald, D. Convey, S. M. Smith, J. H. Baker, H. G. Tompkins, “Survey of methods to characterize thin absorbing films with spectroscopic ellipsometry,” Thin Solid Films 516(22), 7979–7989 (2008).
[CrossRef]

Southern, J. F.

Sticker, M.

Stinson, W. G.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, J. G. Fujimoto, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

Sun, E.

Sun, T.

Swanson, E. A.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, J. G. Fujimoto, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

Tabet, M.

F. Yang, M. Tabet, W. A. McGahan, “Characterizing optical properties of red, green, and blue color filters for automated film-thickness measurement,” Proc. SPIE 3332, 403–410 (1998).
[CrossRef]

Tan, W.

Tearney, G. J.

Tiwald, T.

J. N. Hilfiker, N. Singh, T. Tiwald, D. Convey, S. M. Smith, J. H. Baker, H. G. Tompkins, “Survey of methods to characterize thin absorbing films with spectroscopic ellipsometry,” Thin Solid Films 516(22), 7979–7989 (2008).
[CrossRef]

Tompkins, H. G.

J. N. Hilfiker, N. Singh, T. Tiwald, D. Convey, S. M. Smith, J. H. Baker, H. G. Tompkins, “Survey of methods to characterize thin absorbing films with spectroscopic ellipsometry,” Thin Solid Films 516(22), 7979–7989 (2008).
[CrossRef]

Tsai, C. C.

Tsuzuki, T.

Vinegoni, C.

Wang, Y. T.

Wiley, B. J.

Wyant, J. C.

Xia, Y.

Xu, C.

Yang, F.

F. Yang, M. Tabet, W. A. McGahan, “Characterizing optical properties of red, green, and blue color filters for automated film-thickness measurement,” Proc. SPIE 3332, 403–410 (1998).
[CrossRef]

Zhao, M.

Zvyagin, A.

Appl. Opt.

J. Biomed. Opt.

A. Knüttel, M. Boehlau-Godau, “Spatially confined and temporally resolved refractive index and scattering evaluation in human skin performed with optical coherence tomography,” J. Biomed. Opt. 5(1), 83–92 (2000).
[CrossRef] [PubMed]

J. Opt. Soc. Am.

J. Phys. E Sci. Instrum.

J. C. Manifacier, J. Gasiot, J. P. Fillard, “A simple method for the determination of the optical constants n, k and the thickness of a weakly absorbing thin film,” J. Phys. E Sci. Instrum. 9(11), 1002–1004 (1976).
[CrossRef]

Opt. Express

Opt. Lasers Eng.

T. R. Judge, P. J. Bryanston-Cross, “A review of phase unwrapping techniques in fringe analysis,” Opt. Lasers Eng. 21(4), 199–239 (1994).
[CrossRef]

Opt. Lett.

C. C. Tsai, T. H. Chen, Y. S. Lin, Y. T. Wang, W. Chang, K. Y. Hsu, Y. H. Chang, P. K. Hsu, D. Y. Jheng, K. Y. Huang, E. Sun, S. L. Huang, “Ce3+:YAG double-clad crystal-fiber-based optical coherence tomography on fish cornea,” Opt. Lett. 35(6), 811–813 (2010).
[CrossRef] [PubMed]

C. K. Hitzenberger, M. Sticker, R. Leitgeb, A. F. Fercher, “Differential phase measurements in low-coherence interferometry without 2π ambiguity,” Opt. Lett. 26(23), 1864–1866 (2001).
[CrossRef] [PubMed]

M. T. Fathi, S. Donati, “Thickness measurement of transparent plates by a self-mixing interferometer,” Opt. Lett. 35(11), 1844–1846 (2010).
[CrossRef] [PubMed]

G. J. Tearney, M. E. Brezinski, J. F. Southern, B. E. Bouma, M. R. Hee, J. G. Fujimoto, “Determination of the refractive index of highly scattering human tissue by optical coherence tomography,” Opt. Lett. 20(21), 2258–2260 (1995).
[CrossRef] [PubMed]

J. F. de Boer, B. Cense, B. H. Park, M. C. Pierce, G. J. Tearney, B. E. Bouma, “Improved signal-to-noise ratio in spectral-domain compared with time-domain optical coherence tomography,” Opt. Lett. 28(21), 2067–2069 (2003).
[CrossRef] [PubMed]

U. Morgner, W. Drexler, F. X. Kärtner, X. D. Li, C. Pitris, E. P. Ippen, J. G. Fujimoto, “Spectroscopic optical coherence tomography,” Opt. Lett. 25(2), 111–113 (2000).
[CrossRef] [PubMed]

H. Cang, T. Sun, Z. Y. Li, J. Chen, B. J. Wiley, Y. Xia, X. Li, “Gold nanocages as contrast agents for spectroscopic optical coherence tomography,” Opt. Lett. 30(22), 3048–3050 (2005).
[CrossRef] [PubMed]

C. Xu, C. Vinegoni, T. S. Ralston, W. Luo, W. Tan, S. A. Boppart, “Spectroscopic spectral-domain optical coherence microscopy,” Opt. Lett. 31(8), 1079–1081 (2006).
[CrossRef] [PubMed]

Proc. SPIE

F. Yang, M. Tabet, W. A. McGahan, “Characterizing optical properties of red, green, and blue color filters for automated film-thickness measurement,” Proc. SPIE 3332, 403–410 (1998).
[CrossRef]

Science

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, J. G. Fujimoto, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

Thin Solid Films

J. N. Hilfiker, N. Singh, T. Tiwald, D. Convey, S. M. Smith, J. H. Baker, H. G. Tompkins, “Survey of methods to characterize thin absorbing films with spectroscopic ellipsometry,” Thin Solid Films 516(22), 7979–7989 (2008).
[CrossRef]

Other

P. Yeh, Optical Waves in Layered Media (John Wiley, 1998), Chap. 4.

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Figures (8)

Fig. 1
Fig. 1

The thin film sample scheme.

Fig. 2
Fig. 2

(a) Ce:YAG DCF fluorescence spectrum. (b) SD-OCT setup.

Fig. 3
Fig. 3

Transmission spectra. (a) Sample 1. (b) Sample 2.

Fig. 4
Fig. 4

Axial scan and calculated spectral attributes. (a) Axial scan of Sample 1. (b) Axial scan of Sample 2. (c) Calculated spectral attribute A, B and C of sample 1. (d) Calculated spectral attribute A, B and C of sample 2.

Fig. 5
Fig. 5

MSE versus m plot. The m is equal to zero if Cexp is within the principal interval [-π,π] at 545 nm. The insets show the zoomed portions of the figures around the minimum of MSE. (a) Sample 1. (b) Sample 2.

Fig. 6
Fig. 6

The derived optical properties. From left to right: refractive index, extinction coefficient, uniqueness test of film thickness. (a) Sample 1. (b) Sample 2.

Fig. 7
Fig. 7

Cross-sectional tomographic images of the thin film samples measured with SD-OCT in the substrate-incident scheme. The figures show tomographic images within 20 μm (axial) X 5 mm (lateral) area. The figures are plotted in logarithmic scale and stretched in the longitudinal direction. Light is incident from the top of figures. (a) Sample 1. (b) Sample 2.

Fig. 8
Fig. 8

Comparison of the derived transmittance based on SD-OCT data (with a 50-nm standard deviation of optical thickness) and the value measured with commercial transmittance spectrometer. Black solid line: derived from the optical constants measured with the OCT. Red dash line: measured with transmittance spectrometer. (a) Sample 1. (b) Sample 2.

Equations (10)

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

S = a s I s + a r r I r + 2 η a s a r I s I r r cos ϕ
S i nter = 2 η a s a r I s I r e i ϕ r G r
S int e r = G ( r f r o n t + t f r o n t t f r o n t r r e a r exp [ i 4 π ( n + i k ) f l / c ] 1 - r f r o n t r r e a r exp [ i 4 π ( n + i k ) f l / c ] )
A = G | r f r o n t |
B = G | t f r o n t t f r o n t r r e a r | exp ( 4 π k f l / c )
C = ( t f r o n t t f r o n t r r e a r r f r o n t ) + 4 π n f l / c
( δ n δ k δ l ) = ( A / n A / k A / l B / n B / k B / l C / n C / k C / l ) 1 ( A exp A B exp B C exp C )
C exp ( m ) = C u n w r a p p e d + 2 π m
M S E ( m ) = { 1 N j = 1 N [ ( A exp j A j A exp j ) 2 + ( B exp j B j B exp j ) 2 + ( C exp j C j C exp j ( m ) ) 2 ] } 1 2
T = | t s u b s t r a t e t f r o n t t r e a r exp [ i 2 π ( n + i k ) f l / c ] 1 r f r o n t r r e a r exp [ i 4 π ( n + i k ) f l / c ] | 2

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