Abstract

We have developed a low-coherence interferometer system used for the simultaneous measurement of refractive index n and thickness t of transparent plates. Both the phase index n p and group index n g can be determined automatically in a wide thickness range of from 10 µm to a few millimeters. Two unique techniques are presented to measure n p, n g, and t simultaneously. One allows us to determine n p, n g, and t accurately by using a special sample holder, in which the measurement accuracy is 0.3% for the thickness t above 0.1 mm. In the other technique the chromatic dispersion δn of index is approximately expressed as a function of (n p - 1) on the basis of measured values of n p and n g for a variety of materials, and then the simultaneous measurement is performed with a normal sample holder. In addition, a measurement accuracy of less than 1% is achieved even when the sample is as thin as 20 µm. The measurement time is also 3 min or more.

© 2002 Optical Society of America

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References

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  1. P. A. Flournoy, R. W. McClure, G. Wyntjes, “White-light interferometric thickness gauge,” Appl. Opt. 11, 1907–1915 (1972).
    [CrossRef] [PubMed]
  2. B. W. Weinstein, “White-light interferometric measurement of the wall thickness of hollow glass microspheres,” J. Appl. Phys. 46, 5305–5306 (1975).
    [CrossRef]
  3. K. Takada, I. Yokohama, K. Chida, J. Noda, “New measurement system for fault location in optical waveguide devices based on an interferometric technique,” Appl. Opt. 26, 1603–1606 (1987).
    [CrossRef] [PubMed]
  4. R. C. Youngquist, S. Carr, D. E. N. Davis, “Optical coherence-domain reflectmetry:a new optical evaluation technique,” Opt. Lett. 12, 158–160 (1987).
    [CrossRef] [PubMed]
  5. H. H. Gilgen, R. P. Novak, R. P. Salathe, W. Hodel, P. Beaud, “Submillimeter optical reflectmetry,” J. Lightwave Technol. 7, 1225–1233 (1989).
    [CrossRef]
  6. 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]
  7. E. A. Swanson, J. A. Izatt, M. R. Hee, D. Huang, C. P. Lin, J. S. Schuman, C. A. Puliafito, J. G. Fujimoto, “In vivo retinal imaging by optical coherence tomography,” Opt. Lett. 18, 1864–1866 (1993).
    [CrossRef] [PubMed]
  8. 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, 2258–2261 (1995).
    [CrossRef] [PubMed]
  9. T. Fukano, I. Yamaguchi, “Simultaneous measurement of thickness and refractive indices of multiple layers by a low-coherence confocal microscope,” Opt. Lett. 21, 1942–1944 (1996).
    [CrossRef] [PubMed]
  10. 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]
  11. M. Haruna, M. Ohmi, T. Mitsuyama, H. Tajiri, H. Maruyama, M. Hashimoto, “Simultaneous measurement of the phase and group indices and thickness of transparent plates by low-coherence interferometry,” Opt. Lett. 23, 966–968 (1998).
    [CrossRef]
  12. H. Maruyama, T. Mitsuyama, M. Ohmi, M. Haruna, “Simultaneous measurement of refractive index and thickness by low coherence interferometry considering chromatic dispersion of index,” Opt. Rev. 7, 468–472 (2000).
    [CrossRef]
  13. S. Inoue, H. Maruyama, T. Mitsuyama, M. Ohmi, K. Ihara, M. Haruna, “A low-coherence interferometer system for simultaneous measurement of refractive index and thickness ranging from 20 µm to a few millimeters,” in 13th International Conference on Optical Fiber Sensors, B. Kim, K. Hotate, eds., Proc. SPIE3746, 26–29 (1999).
  14. H. Maruyama, S. Inoue, M. Ohmi, K. Ihara, S. Nakagawa, M. Haruna, “A practical measurement system for determination of refractive index and thickness using the low coherence interferometry,” in Proceedings of the International Conference on Optical Engineering for Sensing and Nanotechnology, I. Yamaguchi, ed., Proc. SPIE3740, 26–29 (1999).
    [CrossRef]
  15. For fused quartz and sapphire, see K. Kudo, Figures and Tables of the Basic Study of Spectroscopy (Kyouritsu-Shuppan, Tokyo, 1972), pp. 190 and 280; for LiNbO3 and LiTaO3, see C. J. G. Kirkby, Properties of Lithium Niobate (Institution of Electrical Engineers, London, 1989), Sec. 5.1; for BaCD14 and FD60 optical glass, see optical glass J9206-1A005D, in the HOYA Catalog (HOYA, Tokyo, 1992).

2000 (1)

H. Maruyama, T. Mitsuyama, M. Ohmi, M. Haruna, “Simultaneous measurement of refractive index and thickness by low coherence interferometry considering chromatic dispersion of index,” Opt. Rev. 7, 468–472 (2000).
[CrossRef]

1998 (1)

1997 (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]

1996 (1)

1995 (1)

1993 (1)

1991 (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]

1989 (1)

H. H. Gilgen, R. P. Novak, R. P. Salathe, W. Hodel, P. Beaud, “Submillimeter optical reflectmetry,” J. Lightwave Technol. 7, 1225–1233 (1989).
[CrossRef]

1987 (2)

1975 (1)

B. W. Weinstein, “White-light interferometric measurement of the wall thickness of hollow glass microspheres,” J. Appl. Phys. 46, 5305–5306 (1975).
[CrossRef]

1972 (1)

Beaud, P.

H. H. Gilgen, R. P. Novak, R. P. Salathe, W. Hodel, P. Beaud, “Submillimeter optical reflectmetry,” J. Lightwave Technol. 7, 1225–1233 (1989).
[CrossRef]

Bouma, B. E.

Brezinski, M. E.

Carr, S.

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]

Chida, K.

Davis, D. E. N.

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.

Fujimoto, J. G.

Fukano, T.

Gilgen, H. H.

H. H. Gilgen, R. P. Novak, R. P. Salathe, W. Hodel, P. Beaud, “Submillimeter optical reflectmetry,” J. Lightwave Technol. 7, 1225–1233 (1989).
[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]

Haruna, M.

H. Maruyama, T. Mitsuyama, M. Ohmi, M. Haruna, “Simultaneous measurement of refractive index and thickness by low coherence interferometry considering chromatic dispersion of index,” Opt. Rev. 7, 468–472 (2000).
[CrossRef]

M. Haruna, M. Ohmi, T. Mitsuyama, H. Tajiri, H. Maruyama, M. Hashimoto, “Simultaneous measurement of the phase and group indices and 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]

S. Inoue, H. Maruyama, T. Mitsuyama, M. Ohmi, K. Ihara, M. Haruna, “A low-coherence interferometer system for simultaneous measurement of refractive index and thickness ranging from 20 µm to a few millimeters,” in 13th International Conference on Optical Fiber Sensors, B. Kim, K. Hotate, eds., Proc. SPIE3746, 26–29 (1999).

H. Maruyama, S. Inoue, M. Ohmi, K. Ihara, S. Nakagawa, M. Haruna, “A practical measurement system for determination of refractive index and thickness using the low coherence interferometry,” in Proceedings of the International Conference on Optical Engineering for Sensing and Nanotechnology, I. Yamaguchi, ed., Proc. SPIE3740, 26–29 (1999).
[CrossRef]

Hashimoto, M.

Hee, M. R.

Hodel, W.

H. H. Gilgen, R. P. Novak, R. P. Salathe, W. Hodel, P. Beaud, “Submillimeter optical reflectmetry,” J. Lightwave Technol. 7, 1225–1233 (1989).
[CrossRef]

Huang, D.

E. A. Swanson, J. A. Izatt, M. R. Hee, D. Huang, C. P. Lin, J. S. Schuman, C. A. Puliafito, J. G. Fujimoto, “In vivo retinal imaging by optical coherence tomography,” Opt. Lett. 18, 1864–1866 (1993).
[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]

Ihara, K.

S. Inoue, H. Maruyama, T. Mitsuyama, M. Ohmi, K. Ihara, M. Haruna, “A low-coherence interferometer system for simultaneous measurement of refractive index and thickness ranging from 20 µm to a few millimeters,” in 13th International Conference on Optical Fiber Sensors, B. Kim, K. Hotate, eds., Proc. SPIE3746, 26–29 (1999).

H. Maruyama, S. Inoue, M. Ohmi, K. Ihara, S. Nakagawa, M. Haruna, “A practical measurement system for determination of refractive index and thickness using the low coherence interferometry,” in Proceedings of the International Conference on Optical Engineering for Sensing and Nanotechnology, I. Yamaguchi, ed., Proc. SPIE3740, 26–29 (1999).
[CrossRef]

Inoue, S.

H. Maruyama, S. Inoue, M. Ohmi, K. Ihara, S. Nakagawa, M. Haruna, “A practical measurement system for determination of refractive index and thickness using the low coherence interferometry,” in Proceedings of the International Conference on Optical Engineering for Sensing and Nanotechnology, I. Yamaguchi, ed., Proc. SPIE3740, 26–29 (1999).
[CrossRef]

S. Inoue, H. Maruyama, T. Mitsuyama, M. Ohmi, K. Ihara, M. Haruna, “A low-coherence interferometer system for simultaneous measurement of refractive index and thickness ranging from 20 µm to a few millimeters,” in 13th International Conference on Optical Fiber Sensors, B. Kim, K. Hotate, eds., Proc. SPIE3746, 26–29 (1999).

Izatt, J. A.

Kudo, K.

For fused quartz and sapphire, see K. Kudo, Figures and Tables of the Basic Study of Spectroscopy (Kyouritsu-Shuppan, Tokyo, 1972), pp. 190 and 280; for LiNbO3 and LiTaO3, see C. J. G. Kirkby, Properties of Lithium Niobate (Institution of Electrical Engineers, London, 1989), Sec. 5.1; for BaCD14 and FD60 optical glass, see optical glass J9206-1A005D, in the HOYA Catalog (HOYA, Tokyo, 1992).

Lin, C. P.

E. A. Swanson, J. A. Izatt, M. R. Hee, D. Huang, C. P. Lin, J. S. Schuman, C. A. Puliafito, J. G. Fujimoto, “In vivo retinal imaging by optical coherence tomography,” Opt. Lett. 18, 1864–1866 (1993).
[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]

Maruyama, H.

H. Maruyama, T. Mitsuyama, M. Ohmi, M. Haruna, “Simultaneous measurement of refractive index and thickness by low coherence interferometry considering chromatic dispersion of index,” Opt. Rev. 7, 468–472 (2000).
[CrossRef]

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

H. Maruyama, S. Inoue, M. Ohmi, K. Ihara, S. Nakagawa, M. Haruna, “A practical measurement system for determination of refractive index and thickness using the low coherence interferometry,” in Proceedings of the International Conference on Optical Engineering for Sensing and Nanotechnology, I. Yamaguchi, ed., Proc. SPIE3740, 26–29 (1999).
[CrossRef]

S. Inoue, H. Maruyama, T. Mitsuyama, M. Ohmi, K. Ihara, M. Haruna, “A low-coherence interferometer system for simultaneous measurement of refractive index and thickness ranging from 20 µm to a few millimeters,” in 13th International Conference on Optical Fiber Sensors, B. Kim, K. Hotate, eds., Proc. SPIE3746, 26–29 (1999).

McClure, R. W.

Mitsuyama, T.

H. Maruyama, T. Mitsuyama, M. Ohmi, M. Haruna, “Simultaneous measurement of refractive index and thickness by low coherence interferometry considering chromatic dispersion of index,” Opt. Rev. 7, 468–472 (2000).
[CrossRef]

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

S. Inoue, H. Maruyama, T. Mitsuyama, M. Ohmi, K. Ihara, M. Haruna, “A low-coherence interferometer system for simultaneous measurement of refractive index and thickness ranging from 20 µm to a few millimeters,” in 13th International Conference on Optical Fiber Sensors, B. Kim, K. Hotate, eds., Proc. SPIE3746, 26–29 (1999).

Nakagawa, S.

H. Maruyama, S. Inoue, M. Ohmi, K. Ihara, S. Nakagawa, M. Haruna, “A practical measurement system for determination of refractive index and thickness using the low coherence interferometry,” in Proceedings of the International Conference on Optical Engineering for Sensing and Nanotechnology, I. Yamaguchi, ed., Proc. SPIE3740, 26–29 (1999).
[CrossRef]

Noda, J.

Novak, R. P.

H. H. Gilgen, R. P. Novak, R. P. Salathe, W. Hodel, P. Beaud, “Submillimeter optical reflectmetry,” J. Lightwave Technol. 7, 1225–1233 (1989).
[CrossRef]

Ohmi, M.

H. Maruyama, T. Mitsuyama, M. Ohmi, M. Haruna, “Simultaneous measurement of refractive index and thickness by low coherence interferometry considering chromatic dispersion of index,” Opt. Rev. 7, 468–472 (2000).
[CrossRef]

M. Haruna, M. Ohmi, T. Mitsuyama, H. Tajiri, H. Maruyama, M. Hashimoto, “Simultaneous measurement of the phase and group indices and 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]

S. Inoue, H. Maruyama, T. Mitsuyama, M. Ohmi, K. Ihara, M. Haruna, “A low-coherence interferometer system for simultaneous measurement of refractive index and thickness ranging from 20 µm to a few millimeters,” in 13th International Conference on Optical Fiber Sensors, B. Kim, K. Hotate, eds., Proc. SPIE3746, 26–29 (1999).

H. Maruyama, S. Inoue, M. Ohmi, K. Ihara, S. Nakagawa, M. Haruna, “A practical measurement system for determination of refractive index and thickness using the low coherence interferometry,” in Proceedings of the International Conference on Optical Engineering for Sensing and Nanotechnology, I. Yamaguchi, ed., Proc. SPIE3740, 26–29 (1999).
[CrossRef]

Puliafito, C. A.

E. A. Swanson, J. A. Izatt, M. R. Hee, D. Huang, C. P. Lin, J. S. Schuman, C. A. Puliafito, J. G. Fujimoto, “In vivo retinal imaging by optical coherence tomography,” Opt. Lett. 18, 1864–1866 (1993).
[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]

Salathe, R. P.

H. H. Gilgen, R. P. Novak, R. P. Salathe, W. Hodel, P. Beaud, “Submillimeter optical reflectmetry,” J. Lightwave Technol. 7, 1225–1233 (1989).
[CrossRef]

Schuman, J. S.

E. A. Swanson, J. A. Izatt, M. R. Hee, D. Huang, C. P. Lin, J. S. Schuman, C. A. Puliafito, J. G. Fujimoto, “In vivo retinal imaging by optical coherence tomography,” Opt. Lett. 18, 1864–1866 (1993).
[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]

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]

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]

Swanson, E. A.

E. A. Swanson, J. A. Izatt, M. R. Hee, D. Huang, C. P. Lin, J. S. Schuman, C. A. Puliafito, J. G. Fujimoto, “In vivo retinal imaging by optical coherence tomography,” Opt. Lett. 18, 1864–1866 (1993).
[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 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]

Takada, K.

Tearney, G. J.

Weinstein, B. W.

B. W. Weinstein, “White-light interferometric measurement of the wall thickness of hollow glass microspheres,” J. Appl. Phys. 46, 5305–5306 (1975).
[CrossRef]

Wyntjes, G.

Yamaguchi, I.

Yokohama, I.

Youngquist, R. C.

Appl. Opt. (2)

J. Appl. Phys. (1)

B. W. Weinstein, “White-light interferometric measurement of the wall thickness of hollow glass microspheres,” J. Appl. Phys. 46, 5305–5306 (1975).
[CrossRef]

J. Lightwave Technol. (1)

H. H. Gilgen, R. P. Novak, R. P. Salathe, W. Hodel, P. Beaud, “Submillimeter optical reflectmetry,” J. Lightwave Technol. 7, 1225–1233 (1989).
[CrossRef]

Opt. Lett. (5)

Opt. Rev. (2)

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]

H. Maruyama, T. Mitsuyama, M. Ohmi, M. Haruna, “Simultaneous measurement of refractive index and thickness by low coherence interferometry considering chromatic dispersion of index,” Opt. Rev. 7, 468–472 (2000).
[CrossRef]

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)

S. Inoue, H. Maruyama, T. Mitsuyama, M. Ohmi, K. Ihara, M. Haruna, “A low-coherence interferometer system for simultaneous measurement of refractive index and thickness ranging from 20 µm to a few millimeters,” in 13th International Conference on Optical Fiber Sensors, B. Kim, K. Hotate, eds., Proc. SPIE3746, 26–29 (1999).

H. Maruyama, S. Inoue, M. Ohmi, K. Ihara, S. Nakagawa, M. Haruna, “A practical measurement system for determination of refractive index and thickness using the low coherence interferometry,” in Proceedings of the International Conference on Optical Engineering for Sensing and Nanotechnology, I. Yamaguchi, ed., Proc. SPIE3740, 26–29 (1999).
[CrossRef]

For fused quartz and sapphire, see K. Kudo, Figures and Tables of the Basic Study of Spectroscopy (Kyouritsu-Shuppan, Tokyo, 1972), pp. 190 and 280; for LiNbO3 and LiTaO3, see C. J. G. Kirkby, Properties of Lithium Niobate (Institution of Electrical Engineers, London, 1989), Sec. 5.1; for BaCD14 and FD60 optical glass, see optical glass J9206-1A005D, in the HOYA Catalog (HOYA, Tokyo, 1992).

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Figures (11)

Fig. 1
Fig. 1

Configuration of the simultaneous measurement of n and t; two focusing states are schematically shown. BS, beam splitter; PD, photodiode.

Fig. 2
Fig. 2

Special sample holder for the measurement of n p , n g , and t.

Fig. 3
Fig. 3

Experimental result of the relation between δn and (n p - 1): ●, solid; ■, liquid.

Fig. 4
Fig. 4

Automatic measurement system for refractive index and thickness using low-coherence interferometry. A/D, analog to digital; PD, photodiode; BPF, band-pass filter.

Fig. 5
Fig. 5

Displayed measurement result of n p , n g , and t using the special sample holder when a Z-cut sapphire plate was used as the sample.

Fig. 6
Fig. 6

Displayed measurement result of n p , t, and δn using the normal sample holder when a polymer plate was used as the sample.

Fig. 7
Fig. 7

Envelopes of interference fringes for front and rear reflection planes when a X-cut LiNbO3 plate was used as the sample.

Fig. 8
Fig. 8

Displayed measurement result of n p , t, and δn using the normal sample holder when a nearly 20-µm-thick fused-quartz film was used as the sample with a resolution of 1 µm.

Fig. 9
Fig. 9

Displayed measurement result of n p , t, and δn using the normal holder after five repeats of the alternate scanning with a resolution of 0.08 µm when a nearly 20-µm-thick fused-quartz film was used as the sample.

Fig. 10
Fig. 10

Measurement result for polymer wrapping film, where only the envelope having the maximum peak is drawn for each reflection plane.

Fig. 11
Fig. 11

Envelopes of interference fringes for each plane when a multilayer sample (9GB type of DVD-ROM) was used as the sample.

Tables (2)

Tables Icon

Table 1 System Specification and Performance for the Simultaneous Measurement of n and t

Tables Icon

Table 2 Experimental Results of the Simultaneous Measurement of n p , n g , and t by Using the Automatic Measurement System at λ = 850 nm

Equations (12)

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

Δz=t 1-ζ2np2-ζ2 or np=ζ2+1-ζ2tΔz2,
ΔL+Δz=ng×t or ng=ΔL+Δzt.
t=g0-g1+g2.
ng=np1+δn,
δn= λcnpdnpdλλc=ng-npnp,
δn=anp-1b,
a=0.024,b=1.69 for solid,a=0.046,b=1.535 for liquid.
np2=12ζ2+ ζ4+41-ζ21+ΔLΔz21-2δn
t=ΔL+Δznp1+δn.
np1+ΔLΔz.
δna 1+ΔLΔz-1b,
ζ=t2-np2Δz2t2-Δz2.

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