Abstract

An improved system for the separate measurement of the refractive index and the geometrical thickness that constitutes a hybrid configuration of a confocal microscope and a wavelength-scanning heterodyne interferometer with a laser diode is presented. The optical path difference can be measured in less than 1 s, which is 10 times quicker than with the low-coherence interferometry previously used, and with a resolution of 10 µm with a fixed reference mirror. Separate measurement of the refractive index and the geometrical thickness of glass plates was demonstrated by use of the arrangement in place of the low-coherence interferometer used previously.

© 1999 Optical Society of America

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References

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  1. T. Tsuruta, Y. Ichihara, “Accurate measurement of lens thickness by using white-light fringes,” in Proceedings of the International Commission for Optics Conference (Japan Society of Applied Physics, Tokyo, 1974), pp. 369–372.
  2. B. L. Danielson, C. Y. Boisrobert, “Absolute optical ranging using low coherence interferometry,” Appl. Opt. 30, 2976–2979 (1991).
    [CrossRef]
  3. C. J. R. Sheppard, T. J. Connolly, J. Lee, C. J. Cogswell, “Confocal imaging of a stratified medium,” Appl. Opt. 33, 631–640 (1994).
    [CrossRef] [PubMed]
  4. T. Fukano, I. Yamaguchi, “Measurement of layer thickness by a laser confocal microscope,” in Proceedings of the Fifteenth Meeting on Lightwave Sensing Technology (Japanese Society of Lightwave Sensing Technology, Japan Society of Applied Physics, Tokyo, 1995), pp. 91–98.
  5. P. A. Flournoy, R. W. McClure, G. Wyntjes, “White-light interferometric thickness gauge,” Appl. Opt. 11, 1907–1915 (1972).
    [CrossRef] [PubMed]
  6. 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]
  7. 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]
  8. N. Sakai, S. Ohkubo, A. Takayanagi, N. Umeda, “Simultaneous measurement of thickness and refractive index of crystalline quartz using low coherence interferometry,” in Proceedings of the Twentieth Meeting of Japan Society for Laser Microscopy (Japan Society for Laser Microscopy, Tokyo, 1997), pp. 59–65.
  9. S. Y. El-Zaiat, “Measuring the thickness and refractive index of a thick transparent plate by an unexpanded laser beam,” Opt. Laser Technol. 29, 63–65 (1997).
    [CrossRef]
  10. 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]
  11. M. Ohmi, T. Shiraishi, H. Tajiri, M. Haruna, “Simultaneous measurement of refractive index and thickness of transparent plates by low coherence interferometry,” Opt. Rev. 4, 507–515 (1997).
    [CrossRef]
  12. 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]
  13. H. Kikuta, K. Iwata, R. Nagata, “Distance measurement by the wavelength shift of laser diode light,” Appl. Opt. 25, 2976–2980 (1986).
    [CrossRef] [PubMed]
  14. E. Fischer, E. Dalhoff, S. Heim, U. Hofbauerr, H. Tiziani, “Absolute interferometric distance measurement using a FM-demodulation technique,” Appl. Opt. 34, 5589–5594 (1995).
    [CrossRef] [PubMed]
  15. M. Takeda, H. Yamamoto, “Fourier-transform speckle profilometry: three-dimensional shape measurements of diffuse objects with large height steps and/or spatially isolated surfaces,” Appl. Opt. 33, 7829–7837 (1994).
    [CrossRef] [PubMed]
  16. T. H. Barnes, T. Eiju, K. Matsuda, “Rough surface profile measurement using speckle optical frequency-domain reflectometry with an external cavity tunable diode laser,” Optik 103, 93–100 (1996).
  17. S. Kuwamura, I. Yamaguchi, “Wavelength scanning profilometry for real-time surface shape measurement,” Appl. Opt. 36, 4473–4482 (1997).
    [CrossRef] [PubMed]
  18. H. J. Tiziani, B. Franze, P. Haible, “Wavelength-shift speckle interferometry for absolute profilometry using a mode-hop free external cavity diode laser,” J. Mod. Opt. 44, 1485–1496 (1997).
    [CrossRef]
  19. F. Lexer, C. K. Hitzenberger, A. F. Fercher, M. Kulhavy, “Wavelength-tuning interferometry of intraocular distances,” Appl. Opt. 36, 6548–6553 (1997).
    [CrossRef]
  20. S. R. Chinn, E. A. Swanson, J. G. Fujimoto, “Optical coherence tomography using a frequency-tunable optical source,” Opt. Lett. 22, 340–342 (1997).
    [CrossRef] [PubMed]
  21. M. Suematsu, M. Takeda, “Wavelength-shift interferometry for distance measurements using the Fourier transform technique for fringe analysis,” Appl. Opt. 30, 4046–4055 (1991).
    [CrossRef] [PubMed]
  22. 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, 1178–1181 (1991).
    [CrossRef] [PubMed]
  23. W. Drexler, C. K. Hitzenberger, H. Sattmann, A. F. Fercher, “Measurement of the thickness of fundus layers by partial coherence tomography,” Opt. Eng. 34, 701–710 (1995).
    [CrossRef]
  24. J. Ballif, R. Gianotti, Ph. Chavanne, R. Wälti, R. P. Salathé, “Rapid and scalable scans at 21 m/s in optical low-coherence reflectometry,” Opt. Lett. 22, 757–759 (1997).
    [CrossRef] [PubMed]

1998 (1)

1997 (7)

S. Kuwamura, I. Yamaguchi, “Wavelength scanning profilometry for real-time surface shape measurement,” Appl. Opt. 36, 4473–4482 (1997).
[CrossRef] [PubMed]

H. J. Tiziani, B. Franze, P. Haible, “Wavelength-shift speckle interferometry for absolute profilometry using a mode-hop free external cavity diode laser,” J. Mod. Opt. 44, 1485–1496 (1997).
[CrossRef]

F. Lexer, C. K. Hitzenberger, A. F. Fercher, M. Kulhavy, “Wavelength-tuning interferometry of intraocular distances,” Appl. Opt. 36, 6548–6553 (1997).
[CrossRef]

S. R. Chinn, E. A. Swanson, J. G. Fujimoto, “Optical coherence tomography using a frequency-tunable optical source,” Opt. Lett. 22, 340–342 (1997).
[CrossRef] [PubMed]

S. Y. El-Zaiat, “Measuring the thickness and refractive index of a thick transparent plate by an unexpanded laser beam,” Opt. Laser Technol. 29, 63–65 (1997).
[CrossRef]

M. Ohmi, T. Shiraishi, H. Tajiri, M. Haruna, “Simultaneous measurement of refractive index and thickness of transparent plates by low coherence interferometry,” Opt. Rev. 4, 507–515 (1997).
[CrossRef]

J. Ballif, R. Gianotti, Ph. Chavanne, R. Wälti, R. P. Salathé, “Rapid and scalable scans at 21 m/s in optical low-coherence reflectometry,” Opt. Lett. 22, 757–759 (1997).
[CrossRef] [PubMed]

1996 (2)

T. H. Barnes, T. Eiju, K. Matsuda, “Rough surface profile measurement using speckle optical frequency-domain reflectometry with an external cavity tunable diode laser,” Optik 103, 93–100 (1996).

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]

1995 (3)

1994 (2)

1992 (1)

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]

1991 (3)

B. L. Danielson, C. Y. Boisrobert, “Absolute optical ranging using low coherence interferometry,” Appl. Opt. 30, 2976–2979 (1991).
[CrossRef]

M. Suematsu, M. Takeda, “Wavelength-shift interferometry for distance measurements using the Fourier transform technique for fringe analysis,” Appl. Opt. 30, 4046–4055 (1991).
[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, 1178–1181 (1991).
[CrossRef] [PubMed]

1986 (1)

1972 (1)

Ballif, J.

Barnes, T. H.

T. H. Barnes, T. Eiju, K. Matsuda, “Rough surface profile measurement using speckle optical frequency-domain reflectometry with an external cavity tunable diode laser,” Optik 103, 93–100 (1996).

Boisrobert, C. Y.

B. L. Danielson, C. Y. Boisrobert, “Absolute optical ranging using low coherence interferometry,” Appl. Opt. 30, 2976–2979 (1991).
[CrossRef]

Bouma, B. E.

Brezinski, M. E.

Chang, W.

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, 1178–1181 (1991).
[CrossRef] [PubMed]

Chavanne, Ph.

Chinn, S. R.

Cogswell, C. J.

Connolly, T. J.

Dalhoff, E.

Danielson, B. L.

B. L. Danielson, C. Y. Boisrobert, “Absolute optical ranging using low coherence interferometry,” Appl. Opt. 30, 2976–2979 (1991).
[CrossRef]

Drexler, W.

W. Drexler, C. K. Hitzenberger, H. Sattmann, A. F. Fercher, “Measurement of the thickness of fundus layers by partial coherence tomography,” Opt. Eng. 34, 701–710 (1995).
[CrossRef]

Eiju, T.

T. H. Barnes, T. Eiju, K. Matsuda, “Rough surface profile measurement using speckle optical frequency-domain reflectometry with an external cavity tunable diode laser,” Optik 103, 93–100 (1996).

El-Zaiat, S. Y.

S. Y. El-Zaiat, “Measuring the thickness and refractive index of a thick transparent plate by an unexpanded laser beam,” Opt. Laser Technol. 29, 63–65 (1997).
[CrossRef]

Fercher, A. F.

F. Lexer, C. K. Hitzenberger, A. F. Fercher, M. Kulhavy, “Wavelength-tuning interferometry of intraocular distances,” Appl. Opt. 36, 6548–6553 (1997).
[CrossRef]

W. Drexler, C. K. Hitzenberger, H. Sattmann, A. F. Fercher, “Measurement of the thickness of fundus layers by partial coherence tomography,” Opt. Eng. 34, 701–710 (1995).
[CrossRef]

Fischer, E.

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, 1178–1181 (1991).
[CrossRef] [PubMed]

Flournoy, P. A.

Franze, B.

H. J. Tiziani, B. Franze, P. Haible, “Wavelength-shift speckle interferometry for absolute profilometry using a mode-hop free external cavity diode laser,” J. Mod. Opt. 44, 1485–1496 (1997).
[CrossRef]

Fujimoto, J. G.

Fukano, T.

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]

T. Fukano, I. Yamaguchi, “Measurement of layer thickness by a laser confocal microscope,” in Proceedings of the Fifteenth Meeting on Lightwave Sensing Technology (Japanese Society of Lightwave Sensing Technology, Japan Society of Applied Physics, Tokyo, 1995), pp. 91–98.

Gianotti, R.

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]

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, 1178–1181 (1991).
[CrossRef] [PubMed]

Haible, P.

H. J. Tiziani, B. Franze, P. Haible, “Wavelength-shift speckle interferometry for absolute profilometry using a mode-hop free external cavity diode laser,” J. Mod. Opt. 44, 1485–1496 (1997).
[CrossRef]

Haruna, M.

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]

M. Ohmi, T. Shiraishi, H. Tajiri, M. Haruna, “Simultaneous measurement of refractive index and thickness of transparent plates by low coherence interferometry,” Opt. Rev. 4, 507–515 (1997).
[CrossRef]

Hashimoto, M.

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, 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, 1178–1181 (1991).
[CrossRef] [PubMed]

Heim, S.

Hitzenberger, C. K.

F. Lexer, C. K. Hitzenberger, A. F. Fercher, M. Kulhavy, “Wavelength-tuning interferometry of intraocular distances,” Appl. Opt. 36, 6548–6553 (1997).
[CrossRef]

W. Drexler, C. K. Hitzenberger, H. Sattmann, A. F. Fercher, “Measurement of the thickness of fundus layers by partial coherence tomography,” Opt. Eng. 34, 701–710 (1995).
[CrossRef]

Hofbauerr, U.

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, 1178–1181 (1991).
[CrossRef] [PubMed]

Ichihara, Y.

T. Tsuruta, Y. Ichihara, “Accurate measurement of lens thickness by using white-light fringes,” in Proceedings of the International Commission for Optics Conference (Japan Society of Applied Physics, Tokyo, 1974), pp. 369–372.

Iwata, K.

Kikuta, H.

Kulhavy, M.

Kuwamura, S.

Lee, J.

Lexer, F.

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, 1178–1181 (1991).
[CrossRef] [PubMed]

Maruyama, H.

Matsuda, K.

T. H. Barnes, T. Eiju, K. Matsuda, “Rough surface profile measurement using speckle optical frequency-domain reflectometry with an external cavity tunable diode laser,” Optik 103, 93–100 (1996).

McClure, R. W.

Mitsuyama, T.

Nagata, R.

Ohkubo, S.

N. Sakai, S. Ohkubo, A. Takayanagi, N. Umeda, “Simultaneous measurement of thickness and refractive index of crystalline quartz using low coherence interferometry,” in Proceedings of the Twentieth Meeting of Japan Society for Laser Microscopy (Japan Society for Laser Microscopy, Tokyo, 1997), pp. 59–65.

Ohmi, M.

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]

M. Ohmi, T. Shiraishi, H. Tajiri, M. Haruna, “Simultaneous measurement of refractive index and thickness of transparent plates by low coherence interferometry,” Opt. Rev. 4, 507–515 (1997).
[CrossRef]

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, 1178–1181 (1991).
[CrossRef] [PubMed]

Sakai, N.

N. Sakai, S. Ohkubo, A. Takayanagi, N. Umeda, “Simultaneous measurement of thickness and refractive index of crystalline quartz using low coherence interferometry,” in Proceedings of the Twentieth Meeting of Japan Society for Laser Microscopy (Japan Society for Laser Microscopy, Tokyo, 1997), pp. 59–65.

Salathé, R. P.

Sattmann, H.

W. Drexler, C. K. Hitzenberger, H. Sattmann, A. F. Fercher, “Measurement of the thickness of fundus layers by partial coherence tomography,” Opt. Eng. 34, 701–710 (1995).
[CrossRef]

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, 1178–1181 (1991).
[CrossRef] [PubMed]

Sheppard, C. J. R.

Shiraishi, T.

M. Ohmi, T. Shiraishi, H. Tajiri, M. Haruna, “Simultaneous measurement of refractive index and thickness of transparent plates by low coherence interferometry,” Opt. Rev. 4, 507–515 (1997).
[CrossRef]

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]

Southern, J. F.

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, 1178–1181 (1991).
[CrossRef] [PubMed]

Suematsu, M.

Swanson, E. A.

S. R. Chinn, E. A. Swanson, J. G. Fujimoto, “Optical coherence tomography using a frequency-tunable optical source,” Opt. Lett. 22, 340–342 (1997).
[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, 1178–1181 (1991).
[CrossRef] [PubMed]

Tajiri, H.

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]

M. Ohmi, T. Shiraishi, H. Tajiri, M. Haruna, “Simultaneous measurement of refractive index and thickness of transparent plates by low coherence interferometry,” Opt. Rev. 4, 507–515 (1997).
[CrossRef]

Takayanagi, A.

N. Sakai, S. Ohkubo, A. Takayanagi, N. Umeda, “Simultaneous measurement of thickness and refractive index of crystalline quartz using low coherence interferometry,” in Proceedings of the Twentieth Meeting of Japan Society for Laser Microscopy (Japan Society for Laser Microscopy, Tokyo, 1997), pp. 59–65.

Takeda, M.

Tearney, G. J.

Tiziani, H.

Tiziani, H. J.

H. J. Tiziani, B. Franze, P. Haible, “Wavelength-shift speckle interferometry for absolute profilometry using a mode-hop free external cavity diode laser,” J. Mod. Opt. 44, 1485–1496 (1997).
[CrossRef]

Tsuruta, T.

T. Tsuruta, Y. Ichihara, “Accurate measurement of lens thickness by using white-light fringes,” in Proceedings of the International Commission for Optics Conference (Japan Society of Applied Physics, Tokyo, 1974), pp. 369–372.

Umeda, N.

N. Sakai, S. Ohkubo, A. Takayanagi, N. Umeda, “Simultaneous measurement of thickness and refractive index of crystalline quartz using low coherence interferometry,” in Proceedings of the Twentieth Meeting of Japan Society for Laser Microscopy (Japan Society for Laser Microscopy, Tokyo, 1997), pp. 59–65.

Wälti, R.

Wyntjes, G.

Yamaguchi, I.

S. Kuwamura, I. Yamaguchi, “Wavelength scanning profilometry for real-time surface shape measurement,” Appl. Opt. 36, 4473–4482 (1997).
[CrossRef] [PubMed]

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]

T. Fukano, I. Yamaguchi, “Measurement of layer thickness by a laser confocal microscope,” in Proceedings of the Fifteenth Meeting on Lightwave Sensing Technology (Japanese Society of Lightwave Sensing Technology, Japan Society of Applied Physics, Tokyo, 1995), pp. 91–98.

Yamamoto, H.

Appl. Opt. (9)

P. A. Flournoy, R. W. McClure, G. Wyntjes, “White-light interferometric thickness gauge,” Appl. Opt. 11, 1907–1915 (1972).
[CrossRef] [PubMed]

B. L. Danielson, C. Y. Boisrobert, “Absolute optical ranging using low coherence interferometry,” Appl. Opt. 30, 2976–2979 (1991).
[CrossRef]

C. J. R. Sheppard, T. J. Connolly, J. Lee, C. J. Cogswell, “Confocal imaging of a stratified medium,” Appl. Opt. 33, 631–640 (1994).
[CrossRef] [PubMed]

H. Kikuta, K. Iwata, R. Nagata, “Distance measurement by the wavelength shift of laser diode light,” Appl. Opt. 25, 2976–2980 (1986).
[CrossRef] [PubMed]

E. Fischer, E. Dalhoff, S. Heim, U. Hofbauerr, H. Tiziani, “Absolute interferometric distance measurement using a FM-demodulation technique,” Appl. Opt. 34, 5589–5594 (1995).
[CrossRef] [PubMed]

M. Takeda, H. Yamamoto, “Fourier-transform speckle profilometry: three-dimensional shape measurements of diffuse objects with large height steps and/or spatially isolated surfaces,” Appl. Opt. 33, 7829–7837 (1994).
[CrossRef] [PubMed]

S. Kuwamura, I. Yamaguchi, “Wavelength scanning profilometry for real-time surface shape measurement,” Appl. Opt. 36, 4473–4482 (1997).
[CrossRef] [PubMed]

F. Lexer, C. K. Hitzenberger, A. F. Fercher, M. Kulhavy, “Wavelength-tuning interferometry of intraocular distances,” Appl. Opt. 36, 6548–6553 (1997).
[CrossRef]

M. Suematsu, M. Takeda, “Wavelength-shift interferometry for distance measurements using the Fourier transform technique for fringe analysis,” Appl. Opt. 30, 4046–4055 (1991).
[CrossRef] [PubMed]

IEEE Photon. Technol. Lett. (1)

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. Mod. Opt. (1)

H. J. Tiziani, B. Franze, P. Haible, “Wavelength-shift speckle interferometry for absolute profilometry using a mode-hop free external cavity diode laser,” J. Mod. Opt. 44, 1485–1496 (1997).
[CrossRef]

Opt. Eng. (1)

W. Drexler, C. K. Hitzenberger, H. Sattmann, A. F. Fercher, “Measurement of the thickness of fundus layers by partial coherence tomography,” Opt. Eng. 34, 701–710 (1995).
[CrossRef]

Opt. Laser Technol. (1)

S. Y. El-Zaiat, “Measuring the thickness and refractive index of a thick transparent plate by an unexpanded laser beam,” Opt. Laser Technol. 29, 63–65 (1997).
[CrossRef]

Opt. Lett. (5)

Opt. Rev. (1)

M. Ohmi, T. Shiraishi, H. Tajiri, M. Haruna, “Simultaneous measurement of refractive index and thickness of transparent plates by low coherence interferometry,” Opt. Rev. 4, 507–515 (1997).
[CrossRef]

Optik (1)

T. H. Barnes, T. Eiju, K. Matsuda, “Rough surface profile measurement using speckle optical frequency-domain reflectometry with an external cavity tunable diode laser,” Optik 103, 93–100 (1996).

Science (1)

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, 1178–1181 (1991).
[CrossRef] [PubMed]

Other (3)

T. Tsuruta, Y. Ichihara, “Accurate measurement of lens thickness by using white-light fringes,” in Proceedings of the International Commission for Optics Conference (Japan Society of Applied Physics, Tokyo, 1974), pp. 369–372.

T. Fukano, I. Yamaguchi, “Measurement of layer thickness by a laser confocal microscope,” in Proceedings of the Fifteenth Meeting on Lightwave Sensing Technology (Japanese Society of Lightwave Sensing Technology, Japan Society of Applied Physics, Tokyo, 1995), pp. 91–98.

N. Sakai, S. Ohkubo, A. Takayanagi, N. Umeda, “Simultaneous measurement of thickness and refractive index of crystalline quartz using low coherence interferometry,” in Proceedings of the Twentieth Meeting of Japan Society for Laser Microscopy (Japan Society for Laser Microscopy, Tokyo, 1997), pp. 59–65.

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Figures (7)

Fig. 1
Fig. 1

Fundamental principle of the separation of the refractive index n and the geometrical thickness d. The focus is onto (a) the front surface and (b) the rear surface of the sample. The sample movement for the focal shift is denoted by Δz, and the resultant increment of the OPD is Δl. (c) Shift of the marginal rays caused by the focal shift.

Fig. 2
Fig. 2

Schematic diagram of the experimental setup and the measurement system. LD, laser diode; L, lens; M, mirror; BS, beam splitter; FS, frequency shifter; PBS, polarizing beam splitter; AOM, acousto-optic modulator; QWP, quarter-wave plate for 690 nm; OL, objective lens; RM, reference mirror; POL, polarizer; IF, interference filter for 625 (IF1) and 700 (IF2) nm; PD, photodetector; PMT, photomultiplier tube; FG, function generator; HPF, high-pass filter; ZCC, zero-cross comparator; LPF, low-pass filter; AMP, amplifier; PC, phase comparator; LIA, lock-in amplifier.

Fig. 3
Fig. 3

Example of the interference signal. The reference beat signal at 100 kHz is generated by the He–Ne laser. The interference beat signal is detected by the PMT. In this signal both amplitude and phase modulation, which are caused by the intensity and the frequency modulation of the LD, respectively, are superimposed.

Fig. 4
Fig. 4

Measured amplitude (circles) and phase (squares) of the output signal of the phase comparator with mirror displacement: (a) long-range (10-mm) scanning with an increment of 500 µm and (b) short-range scanning with an increment of 50 µm around zero OPD in (a). The measurement was repeated 30 times at each position.

Fig. 5
Fig. 5

Examples of the signal for a glass plate. Confocal signals obtained from sample scanning observed at stage (3) in Fig. 2.

Fig. 6
Fig. 6

Signals fed to the phase comparator at 1 and 2 in Fig. 5. The upper traces are the reference signals generated by the He–Ne laser observed at stage (2) in Fig. 2. The oscilloscope was triggered by these signals. The lower traces are the phase-modulated signals observed at stage (1) in Fig. 2 after reshaping.

Fig. 7
Fig. 7

Schematic diagram of the wavelength scanning interferometer with dispersive material that has a geometrical thickness d and a refractive index n(λ) at the wavelength λ. TL, tunable laser; BS, beam splitter; RM, reference mirror; DM, dispersive material; PD, photodetector. The terms l 1 and l 2 represent the reference-arm length and the length between the BS and the front surface of the DM, respectively.

Tables (1)

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Table 1 Measured Results for the Refractive Index and the Geometrical Thickness Compared with Catalog Values

Equations (18)

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n sin θ=sin θ0=NA,
d tan θ=Δz tan θ0.
Δl=nd-Δz,
n2=12NA2+NA4+41-NA21+ΔlΔz21/2,
d=Δl+Δzn.
Δφ=2πLc Δν,
νt=ν0+Δν cos2πfmt+ϕ,
It=I0+ΔI cos2πfbt+φ1+φ2t,
φ1=2πν0Lc,
φ2t=2πLΔνcos2πfmt+ϕc,
L1=2l2-l1,
L2=2l2+nλd-l1=L1+2nλd,
φ=2π Lλ.
Δφ=λλ+Δλφλdλ.
Δφ1=λλ+Δλ-2π L1λ2dλ=2πL11λ+Δλ-1λ,
Δφ2=λλ+Δλ-2π L1λ2+4πd λnλλdλ=2πL11λ+Δλ-1λ+4πdnλ+Δλλ+Δλ-nλ1λ,
Δφ1=-2πL1Δλλ2,
Δφ2=Δφ1-4πdnλΔλλ2,

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