Abstract

A new method for measuring simultaneously the thickness and the refractive index of a transparent plate is proposed. The method is based on a simple, variable lateral-shear, wavelength-scanning interferometer. To achieve highly accurate measurements of both refractive index n and thickness d we use several means to determine these two quantities. We finely tune a distributed-feedback diode laser light source to introduce a phase shift into the detected signal, whereas we make the sample rotate to produce variable lateral shearing. Phase shifting permits precise determination of the optical thickness, nd, whereas refractive index n is obtained from the retrieved phase of the overall interference signal for all incidence angles.

© 2003 Optical Society of America

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References

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  1. T. Fukano, I. Yamaguchi, “Simultaneous measurement of thicknesses and refractive indices of multiple layers by a low-coherence confocal interference microscope,” Opt. Lett. 21, 1942–1944 (1996).
    [CrossRef]
  2. 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, 2258–2260 (1995).
    [CrossRef] [PubMed]
  3. M. Haruna, M. Ohmi, T. Mitsuyama, H. Tajiri, H. Maruyama, M. Hashimoto, “Simultaneous measurement of the phase and group indices and the thickness of transparent plates by low-coherence interferometry,” Opt. Lett. 23, 966–968 (1998).
    [CrossRef]
  4. H. Maruyama, S. Inoue, T. Mitsuyama, M. Ohmi, M. Haruna, “Low-coherence interferometer system for the simultaneous measurement of refractive index and thickness,” Appl. Opt. 41, 1315–1322 (2002).
    [CrossRef] [PubMed]
  5. T. Fukano, I. Yamaguchi, “Separation of measurement of the refractive index and the geometrical thickness by use of a wavelength-scanning interferometer with a confocal microscope,” Appl. Opt. 38, 4065–4073 (1999).
    [CrossRef]
  6. D. Bhattacharyya, A. Ray, B. K. Dutta, P. N. Ghosh, “Direct measurement on transparent plates by using Fizeau interferometry,” Opt. Laser Technol. 34, 93–96 (2002).
    [CrossRef]
  7. J. C. Martinez-Anton, E. Bernabeu, “Simultaneous determination of film thickness and refractive index by interferential spectrogoniometry,” Opt. Commun. 132, 321–328 (1996).
    [CrossRef]
  8. J. C. Wyant, “A simple interferometric OTF instrument,” Opt. Commun. 19, 120–122 (1976).
    [CrossRef]
  9. D. Malacara, ed. Optical Shop Testing (Wiley, New York, 1990).
  10. S. De Nicola, P. Ferraro, A. Finizio, P. De Natale, S. Grilli, G. Pierattini, “A Mach-Zehender interferometric system for measuring the refractive indices of uniaxial crystals,” Opt. Commun. 202, 9–15 (2002).
    [CrossRef]
  11. M. Musso, R. Aschauer, A. Asenbaum, C. Vasi, E. Milhelm, “Interferometric determination of refractive index of liquid sulphur dioxide,” Meas. Sci. Technol. 11, 1714–1720 (2000).
    [CrossRef]
  12. R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977), p. 356.
  13. We have adopted the Curve Fitting Toolbox of Matlab 6.5 (Release 13).
  14. T. Kreis, in Holographic Interferometry, P. K. Rastogi, ed. (Springer-Verlag, Berlin, 1994), p. 200.

2002 (3)

D. Bhattacharyya, A. Ray, B. K. Dutta, P. N. Ghosh, “Direct measurement on transparent plates by using Fizeau interferometry,” Opt. Laser Technol. 34, 93–96 (2002).
[CrossRef]

S. De Nicola, P. Ferraro, A. Finizio, P. De Natale, S. Grilli, G. Pierattini, “A Mach-Zehender interferometric system for measuring the refractive indices of uniaxial crystals,” Opt. Commun. 202, 9–15 (2002).
[CrossRef]

H. Maruyama, S. Inoue, T. Mitsuyama, M. Ohmi, M. Haruna, “Low-coherence interferometer system for the simultaneous measurement of refractive index and thickness,” Appl. Opt. 41, 1315–1322 (2002).
[CrossRef] [PubMed]

2000 (1)

M. Musso, R. Aschauer, A. Asenbaum, C. Vasi, E. Milhelm, “Interferometric determination of refractive index of liquid sulphur dioxide,” Meas. Sci. Technol. 11, 1714–1720 (2000).
[CrossRef]

1999 (1)

1998 (1)

1996 (2)

T. Fukano, I. Yamaguchi, “Simultaneous measurement of thicknesses and refractive indices of multiple layers by a low-coherence confocal interference microscope,” Opt. Lett. 21, 1942–1944 (1996).
[CrossRef]

J. C. Martinez-Anton, E. Bernabeu, “Simultaneous determination of film thickness and refractive index by interferential spectrogoniometry,” Opt. Commun. 132, 321–328 (1996).
[CrossRef]

1995 (1)

1976 (1)

J. C. Wyant, “A simple interferometric OTF instrument,” Opt. Commun. 19, 120–122 (1976).
[CrossRef]

Aschauer, R.

M. Musso, R. Aschauer, A. Asenbaum, C. Vasi, E. Milhelm, “Interferometric determination of refractive index of liquid sulphur dioxide,” Meas. Sci. Technol. 11, 1714–1720 (2000).
[CrossRef]

Asenbaum, A.

M. Musso, R. Aschauer, A. Asenbaum, C. Vasi, E. Milhelm, “Interferometric determination of refractive index of liquid sulphur dioxide,” Meas. Sci. Technol. 11, 1714–1720 (2000).
[CrossRef]

Azzam, R. M. A.

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977), p. 356.

Bashara, N. M.

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977), p. 356.

Bernabeu, E.

J. C. Martinez-Anton, E. Bernabeu, “Simultaneous determination of film thickness and refractive index by interferential spectrogoniometry,” Opt. Commun. 132, 321–328 (1996).
[CrossRef]

Bhattacharyya, D.

D. Bhattacharyya, A. Ray, B. K. Dutta, P. N. Ghosh, “Direct measurement on transparent plates by using Fizeau interferometry,” Opt. Laser Technol. 34, 93–96 (2002).
[CrossRef]

Bouma, B. E.

Brezinski, M. E.

De Natale, P.

S. De Nicola, P. Ferraro, A. Finizio, P. De Natale, S. Grilli, G. Pierattini, “A Mach-Zehender interferometric system for measuring the refractive indices of uniaxial crystals,” Opt. Commun. 202, 9–15 (2002).
[CrossRef]

De Nicola, S.

S. De Nicola, P. Ferraro, A. Finizio, P. De Natale, S. Grilli, G. Pierattini, “A Mach-Zehender interferometric system for measuring the refractive indices of uniaxial crystals,” Opt. Commun. 202, 9–15 (2002).
[CrossRef]

Dutta, B. K.

D. Bhattacharyya, A. Ray, B. K. Dutta, P. N. Ghosh, “Direct measurement on transparent plates by using Fizeau interferometry,” Opt. Laser Technol. 34, 93–96 (2002).
[CrossRef]

Ferraro, P.

S. De Nicola, P. Ferraro, A. Finizio, P. De Natale, S. Grilli, G. Pierattini, “A Mach-Zehender interferometric system for measuring the refractive indices of uniaxial crystals,” Opt. Commun. 202, 9–15 (2002).
[CrossRef]

Finizio, A.

S. De Nicola, P. Ferraro, A. Finizio, P. De Natale, S. Grilli, G. Pierattini, “A Mach-Zehender interferometric system for measuring the refractive indices of uniaxial crystals,” Opt. Commun. 202, 9–15 (2002).
[CrossRef]

Fujimoto, J. G.

Fukano, T.

Ghosh, P. N.

D. Bhattacharyya, A. Ray, B. K. Dutta, P. N. Ghosh, “Direct measurement on transparent plates by using Fizeau interferometry,” Opt. Laser Technol. 34, 93–96 (2002).
[CrossRef]

Grilli, S.

S. De Nicola, P. Ferraro, A. Finizio, P. De Natale, S. Grilli, G. Pierattini, “A Mach-Zehender interferometric system for measuring the refractive indices of uniaxial crystals,” Opt. Commun. 202, 9–15 (2002).
[CrossRef]

Haruna, M.

Hashimoto, M.

Hee, M. R.

Inoue, S.

Kreis, T.

T. Kreis, in Holographic Interferometry, P. K. Rastogi, ed. (Springer-Verlag, Berlin, 1994), p. 200.

Martinez-Anton, J. C.

J. C. Martinez-Anton, E. Bernabeu, “Simultaneous determination of film thickness and refractive index by interferential spectrogoniometry,” Opt. Commun. 132, 321–328 (1996).
[CrossRef]

Maruyama, H.

Milhelm, E.

M. Musso, R. Aschauer, A. Asenbaum, C. Vasi, E. Milhelm, “Interferometric determination of refractive index of liquid sulphur dioxide,” Meas. Sci. Technol. 11, 1714–1720 (2000).
[CrossRef]

Mitsuyama, T.

Musso, M.

M. Musso, R. Aschauer, A. Asenbaum, C. Vasi, E. Milhelm, “Interferometric determination of refractive index of liquid sulphur dioxide,” Meas. Sci. Technol. 11, 1714–1720 (2000).
[CrossRef]

Ohmi, M.

Pierattini, G.

S. De Nicola, P. Ferraro, A. Finizio, P. De Natale, S. Grilli, G. Pierattini, “A Mach-Zehender interferometric system for measuring the refractive indices of uniaxial crystals,” Opt. Commun. 202, 9–15 (2002).
[CrossRef]

Ray, A.

D. Bhattacharyya, A. Ray, B. K. Dutta, P. N. Ghosh, “Direct measurement on transparent plates by using Fizeau interferometry,” Opt. Laser Technol. 34, 93–96 (2002).
[CrossRef]

Southern, J. F.

Tajiri, H.

Tearney, G. J.

Vasi, C.

M. Musso, R. Aschauer, A. Asenbaum, C. Vasi, E. Milhelm, “Interferometric determination of refractive index of liquid sulphur dioxide,” Meas. Sci. Technol. 11, 1714–1720 (2000).
[CrossRef]

Wyant, J. C.

J. C. Wyant, “A simple interferometric OTF instrument,” Opt. Commun. 19, 120–122 (1976).
[CrossRef]

Yamaguchi, I.

Appl. Opt. (2)

Meas. Sci. Technol. (1)

M. Musso, R. Aschauer, A. Asenbaum, C. Vasi, E. Milhelm, “Interferometric determination of refractive index of liquid sulphur dioxide,” Meas. Sci. Technol. 11, 1714–1720 (2000).
[CrossRef]

Opt. Commun. (3)

J. C. Martinez-Anton, E. Bernabeu, “Simultaneous determination of film thickness and refractive index by interferential spectrogoniometry,” Opt. Commun. 132, 321–328 (1996).
[CrossRef]

J. C. Wyant, “A simple interferometric OTF instrument,” Opt. Commun. 19, 120–122 (1976).
[CrossRef]

S. De Nicola, P. Ferraro, A. Finizio, P. De Natale, S. Grilli, G. Pierattini, “A Mach-Zehender interferometric system for measuring the refractive indices of uniaxial crystals,” Opt. Commun. 202, 9–15 (2002).
[CrossRef]

Opt. Laser Technol. (1)

D. Bhattacharyya, A. Ray, B. K. Dutta, P. N. Ghosh, “Direct measurement on transparent plates by using Fizeau interferometry,” Opt. Laser Technol. 34, 93–96 (2002).
[CrossRef]

Opt. Lett. (3)

Other (4)

D. Malacara, ed. Optical Shop Testing (Wiley, New York, 1990).

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977), p. 356.

We have adopted the Curve Fitting Toolbox of Matlab 6.5 (Release 13).

T. Kreis, in Holographic Interferometry, P. K. Rastogi, ed. (Springer-Verlag, Berlin, 1994), p. 200.

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Figures (7)

Fig. 1
Fig. 1

Experimental setup for determining both refractive indices and thicknesses of transparent plates: DFB, distributed feedback.

Fig. 2
Fig. 2

Experimental interferometric signal versus wavelength λ and rotation angle θ for a Si sample.

Fig. 3
Fig. 3

Experimental (circles) and fitted (solid curve) intensity curves for normal incidence (θ = 0) for a Si sample.

Fig. 4
Fig. 4

(a) Experimental signal and (b) corresponding cosine of the retrieved phase at a fixed wavelength (1535.68 nm).

Fig. 5
Fig. 5

Experimental (circles) and fitted (solid curve) intensity curves for normal incidence (θ = 0) for a LiNbO3 sample.

Fig. 6
Fig. 6

Calculated sensitivity of phase change δφ(θ) = (∂φ/∂nn of the interferometric signal corresponding to the refractive change δn = 0.0001 for a Si sample.

Fig. 7
Fig. 7

Density plot of experimental interferometric signals as function of wavelength λ and rotation angle θ for (a) a Si sample and (b) a LiNbO3 sample. These signals were discarded because external effects perturbed the rotation period, as is clearly illustrated by local discontinuities in the pattern.

Equations (6)

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

Iθ=I0+γ cos4πndλ1-sin2 θn21/2,
Δϕθ=4πndλΔλλ1-sin2 θn21/2,
Iθ=0λA+m=13 Bm cosm Cλ+D,
Inpθ=I0+γ cos4πnodλ1-sin2 θnp21/2, p=o, e
4πndΔλMax/λ2π.
dmin=λ2/4nΔλMax.

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