Abstract

We describe a low-coherence interferometric technique for simultaneous measurement of geometric thickness and group refractive index of highly dispersive samples. The technique is immune to the dispersion-induced asymmetry of the interferograms, thus overcoming limitations associated with some other low-coherence approaches to this simultaneous measurement. We use the experimental configuration of a tandem interferometer, with the samples to be characterized placed in an air gap in one arm of the measurement interferometer. Unambiguous, dispersion-insensitive measurements of critical group-delay imbalances in the measurement interferometer are determined from the optical frequency dependence of interferogram phases, by means of dispersive Fourier transform spectrometry. Sample thickness and group refractive index are calculated from these group delays. A thickness measurement precision of 0.2 µm and group index measurement accuracy of 5 parts in 105 across a wavelength range of 150 nm have been achieved for BK7 and fused-silica glass samples in the thickness range 2000 to 6000 µm.

© 2000 Optical Society of America

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  1. M. D. Hopler, J. R. Rogers, “Interferometric measurement of group and phase refractive index,” Appl. Opt. 30, 735–744 (1991).
    [CrossRef] [PubMed]
  2. S. Diddams, J.-C. Diels, “Dispersion measurements with white-light interferometry,” J. Opt. Soc. Am. B 13, 1120–1129 (1996).
    [CrossRef]
  3. U. Schnell, R. Dandliker, S. Gray, “Dispersive white-light inteferometry for absolute distance measurement with dielectric multilayer systems on the target,” Opt. Lett. 21, 528–530 (1996).
    [CrossRef] [PubMed]
  4. R. C. Youngquist, S. Carr, D. E. N. Davies, “Optical coherence domain reflectometry: a new optical evaluation technique,” Opt. Lett. 12, 158–160 (1987).
    [CrossRef] [PubMed]
  5. F. Lexer, C. K. Hitzenberger, A. F. Fercher, M. Kulhavy, “Wavelength-tuning interferometry of intraocular distances,” Appl. Opt. 36, 6548–6553 (1997).
    [CrossRef]
  6. Y. Rao, D. A. Jackson, “Recent progress in fibre optic low-coherence interferometry,” Meas. Sci. Technol. 7, 981–999 (1996).
    [CrossRef]
  7. W. V. Sorin, S. Venkatesh, B. L. Heffner, “Optical monitoring of film thickness using low-coherence reflectometry,” in Proceedings of the Ninth International Conference on Optical Fiber Sensors OFS’9, A. Scheggi, R. Th. Kersten, eds., Firenze, Italy, 4–6 May1993, pp. 566–569.
  8. T. P. Newson, F. Farahi, J. D. C. Jones, D. A. Jackson, “Combined interferometric and polarimetric fibre optic sensor with a short coherence length source,” Opt. Commun. 68, 161–165 (1988).
    [CrossRef]
  9. A. S. Gerges, F. Farahi, T. P. Newson, J. D. C. Jones, D. A. Jackson, “Interferometric fibre-optic sensor using a short coherence length source,” Electron Lett. 23, 1110–1111 (1987).
    [CrossRef]
  10. R. Dandliker, E. Zimmerman, G. Frosio, “Electronically scanned white-light interferometry: a novel noise-resistant signal processing,” Opt. Lett. 17, 679–681 (1992).
    [CrossRef] [PubMed]
  11. W. Urbanczyk, W. J. Bock, “Analysis of dispersion effects for white-light interferometric fiber-optic sensors,” Appl. Opt. 33, 124–129 (1994).
    [CrossRef] [PubMed]
  12. D. A. Flavin, R. McBride, J. D. C. Jones, “Interferometric fiber-optic sensing based on the modulation of group delay and first order dispersion: application to strain-temperature measurand,” J. Lightwave Technol. 13, 1314–1323 (1995).
    [CrossRef]
  13. B. L. Danielson, C. Y. Boisrobert, “Absolute optical ranging using low coherence interferometry,” Appl. Opt. 30, 2975–2979 (1991).
    [CrossRef] [PubMed]
  14. V. N. Kumar, D. N. Rao, “Using interference in the frequency domain for precise determination of thickness and refractive indices of normal dispersive materials,” J. Opt. Soc. Am. B 12, 1559–1563 (1995).
    [CrossRef]
  15. 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] [PubMed]
  16. M. Haruna, M. Ohmi, T. Mitsuyama, H. Tajiri, H. Maruyama, “Simultaneous measurement of the phase and group indices and thickness of transparent plates by low-coherence interferometry,” Opt. Lett. 23, 966–968 (1998).
    [CrossRef]
  17. W. V. Sorin, D. F. Gray, “Simultaneous thickness and group index measurement using optical low-coherence reflectometry,” IEEE Photon. Technol. Lett. 4, 105–107 (1992).
    [CrossRef]
  18. D. A. Jackson, J. D. C. Jones, Optical Fiber Sensors (Artech House, Norwood, Mass., 1989), Vol. 2, pp. 329–380.
  19. D. A. Flavin, R. McBride, J. D. C. Jones, “Demodulation of polarimetric fibre sensors by dispersive Fourier transform spectroscopy,” Opt. Commun. 156, 367–373 (1998).
    [CrossRef]
  20. J. E. Chamberlain, The Principles of Interferometric Spectroscopy (Wiley, Chichester, UK1979).
  21. K. B. Rochford, S. D. Dyer, “Demultiplexing of interferometrically interrogated fiber Bragg grating sensors using Hilbert transform processing,” J. Lightwave Technol. 17, 831–836 (1999).
    [CrossRef]
  22. D. A. Flavin, R. McBride, J. D. C. Jones, “Short-scan interferometric interrogation and multiplexing of fibre Bragg grating sensors,” Opt. Commun. 170, 347–353 (1999).
    [CrossRef]
  23. L. Thevenaz, J.-P. Pellaux, J.-P. Von Der Weid, “All-fiber interferometer for chromatic dispersion measurements,” J. Lightwave Technol. 6, 1–7 (1988).
    [CrossRef]

1999

K. B. Rochford, S. D. Dyer, “Demultiplexing of interferometrically interrogated fiber Bragg grating sensors using Hilbert transform processing,” J. Lightwave Technol. 17, 831–836 (1999).
[CrossRef]

D. A. Flavin, R. McBride, J. D. C. Jones, “Short-scan interferometric interrogation and multiplexing of fibre Bragg grating sensors,” Opt. Commun. 170, 347–353 (1999).
[CrossRef]

1998

M. Haruna, M. Ohmi, T. Mitsuyama, H. Tajiri, H. Maruyama, “Simultaneous measurement of the phase and group indices and thickness of transparent plates by low-coherence interferometry,” Opt. Lett. 23, 966–968 (1998).
[CrossRef]

D. A. Flavin, R. McBride, J. D. C. Jones, “Demodulation of polarimetric fibre sensors by dispersive Fourier transform spectroscopy,” Opt. Commun. 156, 367–373 (1998).
[CrossRef]

1997

1996

1995

D. A. Flavin, R. McBride, J. D. C. Jones, “Interferometric fiber-optic sensing based on the modulation of group delay and first order dispersion: application to strain-temperature measurand,” J. Lightwave Technol. 13, 1314–1323 (1995).
[CrossRef]

V. N. Kumar, D. N. Rao, “Using interference in the frequency domain for precise determination of thickness and refractive indices of normal dispersive materials,” J. Opt. Soc. Am. B 12, 1559–1563 (1995).
[CrossRef]

1994

1992

W. V. Sorin, D. F. Gray, “Simultaneous thickness and group index measurement using optical low-coherence reflectometry,” IEEE Photon. Technol. Lett. 4, 105–107 (1992).
[CrossRef]

R. Dandliker, E. Zimmerman, G. Frosio, “Electronically scanned white-light interferometry: a novel noise-resistant signal processing,” Opt. Lett. 17, 679–681 (1992).
[CrossRef] [PubMed]

1991

1988

T. P. Newson, F. Farahi, J. D. C. Jones, D. A. Jackson, “Combined interferometric and polarimetric fibre optic sensor with a short coherence length source,” Opt. Commun. 68, 161–165 (1988).
[CrossRef]

L. Thevenaz, J.-P. Pellaux, J.-P. Von Der Weid, “All-fiber interferometer for chromatic dispersion measurements,” J. Lightwave Technol. 6, 1–7 (1988).
[CrossRef]

1987

A. S. Gerges, F. Farahi, T. P. Newson, J. D. C. Jones, D. A. Jackson, “Interferometric fibre-optic sensor using a short coherence length source,” Electron Lett. 23, 1110–1111 (1987).
[CrossRef]

R. C. Youngquist, S. Carr, D. E. N. Davies, “Optical coherence domain reflectometry: a new optical evaluation technique,” Opt. Lett. 12, 158–160 (1987).
[CrossRef] [PubMed]

Bock, W. J.

Boisrobert, C. Y.

Carr, S.

Chamberlain, J. E.

J. E. Chamberlain, The Principles of Interferometric Spectroscopy (Wiley, Chichester, UK1979).

Dandliker, R.

Danielson, B. L.

Davies, D. E. N.

Diddams, S.

Diels, J.-C.

Dyer, S. D.

Farahi, F.

T. P. Newson, F. Farahi, J. D. C. Jones, D. A. Jackson, “Combined interferometric and polarimetric fibre optic sensor with a short coherence length source,” Opt. Commun. 68, 161–165 (1988).
[CrossRef]

A. S. Gerges, F. Farahi, T. P. Newson, J. D. C. Jones, D. A. Jackson, “Interferometric fibre-optic sensor using a short coherence length source,” Electron Lett. 23, 1110–1111 (1987).
[CrossRef]

Fercher, A. F.

Flavin, D. A.

D. A. Flavin, R. McBride, J. D. C. Jones, “Short-scan interferometric interrogation and multiplexing of fibre Bragg grating sensors,” Opt. Commun. 170, 347–353 (1999).
[CrossRef]

D. A. Flavin, R. McBride, J. D. C. Jones, “Demodulation of polarimetric fibre sensors by dispersive Fourier transform spectroscopy,” Opt. Commun. 156, 367–373 (1998).
[CrossRef]

D. A. Flavin, R. McBride, J. D. C. Jones, “Interferometric fiber-optic sensing based on the modulation of group delay and first order dispersion: application to strain-temperature measurand,” J. Lightwave Technol. 13, 1314–1323 (1995).
[CrossRef]

Frosio, G.

Fukano, T.

Gerges, A. S.

A. S. Gerges, F. Farahi, T. P. Newson, J. D. C. Jones, D. A. Jackson, “Interferometric fibre-optic sensor using a short coherence length source,” Electron Lett. 23, 1110–1111 (1987).
[CrossRef]

Gray, D. F.

W. V. Sorin, D. F. Gray, “Simultaneous thickness and group index measurement using optical low-coherence reflectometry,” IEEE Photon. Technol. Lett. 4, 105–107 (1992).
[CrossRef]

Gray, S.

Haruna, M.

Heffner, B. L.

W. V. Sorin, S. Venkatesh, B. L. Heffner, “Optical monitoring of film thickness using low-coherence reflectometry,” in Proceedings of the Ninth International Conference on Optical Fiber Sensors OFS’9, A. Scheggi, R. Th. Kersten, eds., Firenze, Italy, 4–6 May1993, pp. 566–569.

Hitzenberger, C. K.

Hopler, M. D.

Jackson, D. A.

Y. Rao, D. A. Jackson, “Recent progress in fibre optic low-coherence interferometry,” Meas. Sci. Technol. 7, 981–999 (1996).
[CrossRef]

T. P. Newson, F. Farahi, J. D. C. Jones, D. A. Jackson, “Combined interferometric and polarimetric fibre optic sensor with a short coherence length source,” Opt. Commun. 68, 161–165 (1988).
[CrossRef]

A. S. Gerges, F. Farahi, T. P. Newson, J. D. C. Jones, D. A. Jackson, “Interferometric fibre-optic sensor using a short coherence length source,” Electron Lett. 23, 1110–1111 (1987).
[CrossRef]

D. A. Jackson, J. D. C. Jones, Optical Fiber Sensors (Artech House, Norwood, Mass., 1989), Vol. 2, pp. 329–380.

Jones, J. D. C.

D. A. Flavin, R. McBride, J. D. C. Jones, “Short-scan interferometric interrogation and multiplexing of fibre Bragg grating sensors,” Opt. Commun. 170, 347–353 (1999).
[CrossRef]

D. A. Flavin, R. McBride, J. D. C. Jones, “Demodulation of polarimetric fibre sensors by dispersive Fourier transform spectroscopy,” Opt. Commun. 156, 367–373 (1998).
[CrossRef]

D. A. Flavin, R. McBride, J. D. C. Jones, “Interferometric fiber-optic sensing based on the modulation of group delay and first order dispersion: application to strain-temperature measurand,” J. Lightwave Technol. 13, 1314–1323 (1995).
[CrossRef]

T. P. Newson, F. Farahi, J. D. C. Jones, D. A. Jackson, “Combined interferometric and polarimetric fibre optic sensor with a short coherence length source,” Opt. Commun. 68, 161–165 (1988).
[CrossRef]

A. S. Gerges, F. Farahi, T. P. Newson, J. D. C. Jones, D. A. Jackson, “Interferometric fibre-optic sensor using a short coherence length source,” Electron Lett. 23, 1110–1111 (1987).
[CrossRef]

D. A. Jackson, J. D. C. Jones, Optical Fiber Sensors (Artech House, Norwood, Mass., 1989), Vol. 2, pp. 329–380.

Kulhavy, M.

Kumar, V. N.

Lexer, F.

Maruyama, H.

McBride, R.

D. A. Flavin, R. McBride, J. D. C. Jones, “Short-scan interferometric interrogation and multiplexing of fibre Bragg grating sensors,” Opt. Commun. 170, 347–353 (1999).
[CrossRef]

D. A. Flavin, R. McBride, J. D. C. Jones, “Demodulation of polarimetric fibre sensors by dispersive Fourier transform spectroscopy,” Opt. Commun. 156, 367–373 (1998).
[CrossRef]

D. A. Flavin, R. McBride, J. D. C. Jones, “Interferometric fiber-optic sensing based on the modulation of group delay and first order dispersion: application to strain-temperature measurand,” J. Lightwave Technol. 13, 1314–1323 (1995).
[CrossRef]

Mitsuyama, T.

Newson, T. P.

T. P. Newson, F. Farahi, J. D. C. Jones, D. A. Jackson, “Combined interferometric and polarimetric fibre optic sensor with a short coherence length source,” Opt. Commun. 68, 161–165 (1988).
[CrossRef]

A. S. Gerges, F. Farahi, T. P. Newson, J. D. C. Jones, D. A. Jackson, “Interferometric fibre-optic sensor using a short coherence length source,” Electron Lett. 23, 1110–1111 (1987).
[CrossRef]

Ohmi, M.

Pellaux, J.-P.

L. Thevenaz, J.-P. Pellaux, J.-P. Von Der Weid, “All-fiber interferometer for chromatic dispersion measurements,” J. Lightwave Technol. 6, 1–7 (1988).
[CrossRef]

Rao, D. N.

Rao, Y.

Y. Rao, D. A. Jackson, “Recent progress in fibre optic low-coherence interferometry,” Meas. Sci. Technol. 7, 981–999 (1996).
[CrossRef]

Rochford, K. B.

Rogers, J. R.

Schnell, U.

Sorin, W. V.

W. V. Sorin, D. F. Gray, “Simultaneous thickness and group index measurement using optical low-coherence reflectometry,” IEEE Photon. Technol. Lett. 4, 105–107 (1992).
[CrossRef]

W. V. Sorin, S. Venkatesh, B. L. Heffner, “Optical monitoring of film thickness using low-coherence reflectometry,” in Proceedings of the Ninth International Conference on Optical Fiber Sensors OFS’9, A. Scheggi, R. Th. Kersten, eds., Firenze, Italy, 4–6 May1993, pp. 566–569.

Tajiri, H.

Thevenaz, L.

L. Thevenaz, J.-P. Pellaux, J.-P. Von Der Weid, “All-fiber interferometer for chromatic dispersion measurements,” J. Lightwave Technol. 6, 1–7 (1988).
[CrossRef]

Urbanczyk, W.

Venkatesh, S.

W. V. Sorin, S. Venkatesh, B. L. Heffner, “Optical monitoring of film thickness using low-coherence reflectometry,” in Proceedings of the Ninth International Conference on Optical Fiber Sensors OFS’9, A. Scheggi, R. Th. Kersten, eds., Firenze, Italy, 4–6 May1993, pp. 566–569.

Von Der Weid, J.-P.

L. Thevenaz, J.-P. Pellaux, J.-P. Von Der Weid, “All-fiber interferometer for chromatic dispersion measurements,” J. Lightwave Technol. 6, 1–7 (1988).
[CrossRef]

Yamaguchi, I.

Youngquist, R. C.

Zimmerman, E.

Appl. Opt.

Electron Lett.

A. S. Gerges, F. Farahi, T. P. Newson, J. D. C. Jones, D. A. Jackson, “Interferometric fibre-optic sensor using a short coherence length source,” Electron Lett. 23, 1110–1111 (1987).
[CrossRef]

IEEE Photon. Technol. Lett.

W. V. Sorin, D. F. Gray, “Simultaneous thickness and group index measurement using optical low-coherence reflectometry,” IEEE Photon. Technol. Lett. 4, 105–107 (1992).
[CrossRef]

J. Lightwave Technol.

D. A. Flavin, R. McBride, J. D. C. Jones, “Interferometric fiber-optic sensing based on the modulation of group delay and first order dispersion: application to strain-temperature measurand,” J. Lightwave Technol. 13, 1314–1323 (1995).
[CrossRef]

K. B. Rochford, S. D. Dyer, “Demultiplexing of interferometrically interrogated fiber Bragg grating sensors using Hilbert transform processing,” J. Lightwave Technol. 17, 831–836 (1999).
[CrossRef]

L. Thevenaz, J.-P. Pellaux, J.-P. Von Der Weid, “All-fiber interferometer for chromatic dispersion measurements,” J. Lightwave Technol. 6, 1–7 (1988).
[CrossRef]

J. Opt. Soc. Am. B

Meas. Sci. Technol.

Y. Rao, D. A. Jackson, “Recent progress in fibre optic low-coherence interferometry,” Meas. Sci. Technol. 7, 981–999 (1996).
[CrossRef]

Opt. Commun.

T. P. Newson, F. Farahi, J. D. C. Jones, D. A. Jackson, “Combined interferometric and polarimetric fibre optic sensor with a short coherence length source,” Opt. Commun. 68, 161–165 (1988).
[CrossRef]

D. A. Flavin, R. McBride, J. D. C. Jones, “Short-scan interferometric interrogation and multiplexing of fibre Bragg grating sensors,” Opt. Commun. 170, 347–353 (1999).
[CrossRef]

D. A. Flavin, R. McBride, J. D. C. Jones, “Demodulation of polarimetric fibre sensors by dispersive Fourier transform spectroscopy,” Opt. Commun. 156, 367–373 (1998).
[CrossRef]

Opt. Lett.

Other

D. A. Jackson, J. D. C. Jones, Optical Fiber Sensors (Artech House, Norwood, Mass., 1989), Vol. 2, pp. 329–380.

W. V. Sorin, S. Venkatesh, B. L. Heffner, “Optical monitoring of film thickness using low-coherence reflectometry,” in Proceedings of the Ninth International Conference on Optical Fiber Sensors OFS’9, A. Scheggi, R. Th. Kersten, eds., Firenze, Italy, 4–6 May1993, pp. 566–569.

J. E. Chamberlain, The Principles of Interferometric Spectroscopy (Wiley, Chichester, UK1979).

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Figures (6)

Fig. 1
Fig. 1

Generic optical fiber Michelson measurement interferometer for thickness or index measurement. S, target sample; M1, M2, mirrors.

Fig. 2
Fig. 2

Full tandem Michelson interferometer. P1, P2, P3, P4, fiber interferometer ports; DC, fiber directional coupler; PC, polarization controller; L1, L2, and L3, microscope objectives; AG1, AG2, air gaps; S, target sample; M1, M2, M3, and M4, mirrors; BS, beam splitter; CTS, computer-controlled translation stage; D1, D2 photodiode detectors.

Fig. 3
Fig. 3

Tungsten source interferograms: I c r ), the central interferogram; I m1 r ), I m2 r ), I m3 r ), and I m4 r ), the four measurement interferograms.

Fig. 4
Fig. 4

SLD source interferograms: I c r ), the central interferogram; I m1 r ), I m2 r ), I m3 r ), and I m4 r ), the four measurement interferograms.

Fig. 5
Fig. 5

Measured spectra and phases for measurement interferogram I m3 r ). (a) Recovered tungsten and He–Ne power spectra; (b) unwrapped phase and fit to phase corresponding to the range of meaningful source spectral frequencies for the tungsten interferogram; (c) recovered power spectra for the SLD and the He–Ne sources; (d) phase and phase fit for the range of SLD source spectral frequencies.

Fig. 6
Fig. 6

Index measurements over the extended wavelength range. The dots indicate the measured values for the 4.141-mm BK7 glass sample; the curve represents calculated values with the manufacturer’s dispersion equation.

Tables (1)

Tables Icon

Table 1 Measured Group-Delay Differences, Geometric Thicknesses, and Group Refractive Indices (λ0 = 833.47 nm)

Equations (10)

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

Iosτr=Icτr+Im+τr+Im-τr=I0Reγ˜cτr+12 γ˜m+τr+12 γ˜m-τr,
γ˜cτr=- Gωexp-iωτrdω.
γ˜mτr=-Gωexp-iϕmωexp-iωτrdω,
ϕmω=arg FImτr,
ϕω=ϕω0+ω-ω0dϕω0dω+higher-order dispersive terms.
τmω0=dϕmω0dω.
Φmω=ϕmω1, ϕmω2, , ϕmωn.
Δ1τω0=τm2ω0-τm1ω0,  Δ2τω0=τm4ω0-τm3ω0.
Δ1τω0=2zNω0c,  Δ2τω0=2zNω0-Naω0c,
z=c2Naω0Δ1τω0-Δ2τω0,  Nω0=Naω0Δ1τω0Δ1τω0-Δ2τω0.

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