Abstract

We propose a variable-path interferometric technique for the measurement of the absolute refractive index of optical glasses. We use two interferometers to decide the ratio between changes in the optical path in a prism-shaped sample glass and in air resulting from displacement of the sample. The method allows precise measurements to be made without prior knowledge of the properties of the sample. The combined standard uncertainty of the proposed method is 1.6×106.

© 2009 Optical Society of America

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References

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  1. M. Daimon and A. Masumura, “High-accuracy measurements of the refractive index and its temperature coefficient of calcium fluoride in a wide wavelength range from 138 to 2326 nm,” Appl. Opt. 41, 5275-5281 (2002).
    [CrossRef] [PubMed]
  2. J. H. Burnett, R. Gupta, and U. Griesmann, “Absolute refractive indices and thermal coefficients of CaF2, SrF2, BaF2, and LiF near 157 nm,” Appl. Opt. 41, 2508-2513 (2002).
    [CrossRef] [PubMed]
  3. A. J. Werner, “Methods in high precision refractometry of optical glasses,” Appl. Opt. 7, 837-843 (1968).
    [CrossRef] [PubMed]
  4. A. Hirai and H. Matsumoto, “Measurement of group refractive index wavelength dependence using a low-coherence tandem interferometer,” Appl. Opt. 45, 5614-5620 (2006).
    [CrossRef] [PubMed]
  5. D. F. Murphy and D. A. Flavin, “Dispersion-insensitive measurement of thickness and group refractive index by low-coherence interferometry,” Appl. Opt. 39, 4607-4615 (2000).
    [CrossRef]
  6. M. Haruna, M. Ohmi, T. Mitsuyama, H. Tajiri, H. Maruyama, and 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]
  7. H. Delbarre, C. Przygodzki, M. Tassou, and D. Boucher, “High-precision index measurement in anisotropic crystals using white-light spectral interferometry,” Appl. Phys. B 70, 45-51(2000).
    [CrossRef]
  8. J. Zhang, Z. H. Lu, B. Menegozzi, and L. J. Wang, “Application of frequency combs in the measurement of the refractive index of air,” Rev. Sci. Instrum. 77, 083104 (2006).
    [CrossRef]
  9. K. Fujii, E. R. Williams, R. L. Steiner, and D. B. Newell, “A new refractometer by combining a variable length vacuum cell and a double-pass Michelson interferometer,” IEEE Trans. Instrum. Meas. 46, 191-195 (1997).
    [CrossRef]
  10. Y. Yeh, “Simultaneous measurement of refractive index and thickness of birefringent wave plate,” Appl. Opt. 47, 1457-1464 (2008).
    [CrossRef] [PubMed]
  11. M. Galli, F. Marabelli, and G. Guizzetti, “Direct measurement of refractive-index dispersion of transparent media by white-light interferometry,” Appl. Opt. 42, 3910-3914 (2003).
    [CrossRef] [PubMed]
  12. P. E. Ciddor, “Refractive index of air: new equations for the visible and near infrared,” Appl. Opt. 35, 1566-1573(1996).
    [CrossRef] [PubMed]
  13. T. Keem, S. Gonda, I. Misumi, Q. Huang, and T. Kurosawa, “Removing nonlinearity of a homodyne interferometer by adjusting the gains of its quadrature detector systems,” Appl. Opt. 43, 2443-2448 (2004).
    [CrossRef] [PubMed]

2008

2006

J. Zhang, Z. H. Lu, B. Menegozzi, and L. J. Wang, “Application of frequency combs in the measurement of the refractive index of air,” Rev. Sci. Instrum. 77, 083104 (2006).
[CrossRef]

A. Hirai and H. Matsumoto, “Measurement of group refractive index wavelength dependence using a low-coherence tandem interferometer,” Appl. Opt. 45, 5614-5620 (2006).
[CrossRef] [PubMed]

2004

2003

2002

2000

D. F. Murphy and D. A. Flavin, “Dispersion-insensitive measurement of thickness and group refractive index by low-coherence interferometry,” Appl. Opt. 39, 4607-4615 (2000).
[CrossRef]

H. Delbarre, C. Przygodzki, M. Tassou, and D. Boucher, “High-precision index measurement in anisotropic crystals using white-light spectral interferometry,” Appl. Phys. B 70, 45-51(2000).
[CrossRef]

1998

1997

K. Fujii, E. R. Williams, R. L. Steiner, and D. B. Newell, “A new refractometer by combining a variable length vacuum cell and a double-pass Michelson interferometer,” IEEE Trans. Instrum. Meas. 46, 191-195 (1997).
[CrossRef]

1996

1968

Boucher, D.

H. Delbarre, C. Przygodzki, M. Tassou, and D. Boucher, “High-precision index measurement in anisotropic crystals using white-light spectral interferometry,” Appl. Phys. B 70, 45-51(2000).
[CrossRef]

Burnett, J. H.

Ciddor, P. E.

Daimon, M.

Delbarre, H.

H. Delbarre, C. Przygodzki, M. Tassou, and D. Boucher, “High-precision index measurement in anisotropic crystals using white-light spectral interferometry,” Appl. Phys. B 70, 45-51(2000).
[CrossRef]

Flavin, D. A.

Fujii, K.

K. Fujii, E. R. Williams, R. L. Steiner, and D. B. Newell, “A new refractometer by combining a variable length vacuum cell and a double-pass Michelson interferometer,” IEEE Trans. Instrum. Meas. 46, 191-195 (1997).
[CrossRef]

Galli, M.

Gonda, S.

Griesmann, U.

Guizzetti, G.

Gupta, R.

Haruna, M.

Hashimoto, M.

Hirai, A.

Huang, Q.

Keem, T.

Kurosawa, T.

Lu, Z. H.

J. Zhang, Z. H. Lu, B. Menegozzi, and L. J. Wang, “Application of frequency combs in the measurement of the refractive index of air,” Rev. Sci. Instrum. 77, 083104 (2006).
[CrossRef]

Marabelli, F.

Maruyama, H.

Masumura, A.

Matsumoto, H.

Menegozzi, B.

J. Zhang, Z. H. Lu, B. Menegozzi, and L. J. Wang, “Application of frequency combs in the measurement of the refractive index of air,” Rev. Sci. Instrum. 77, 083104 (2006).
[CrossRef]

Misumi, I.

Mitsuyama, T.

Murphy, D. F.

Newell, D. B.

K. Fujii, E. R. Williams, R. L. Steiner, and D. B. Newell, “A new refractometer by combining a variable length vacuum cell and a double-pass Michelson interferometer,” IEEE Trans. Instrum. Meas. 46, 191-195 (1997).
[CrossRef]

Ohmi, M.

Przygodzki, C.

H. Delbarre, C. Przygodzki, M. Tassou, and D. Boucher, “High-precision index measurement in anisotropic crystals using white-light spectral interferometry,” Appl. Phys. B 70, 45-51(2000).
[CrossRef]

Steiner, R. L.

K. Fujii, E. R. Williams, R. L. Steiner, and D. B. Newell, “A new refractometer by combining a variable length vacuum cell and a double-pass Michelson interferometer,” IEEE Trans. Instrum. Meas. 46, 191-195 (1997).
[CrossRef]

Tajiri, H.

Tassou, M.

H. Delbarre, C. Przygodzki, M. Tassou, and D. Boucher, “High-precision index measurement in anisotropic crystals using white-light spectral interferometry,” Appl. Phys. B 70, 45-51(2000).
[CrossRef]

Wang, L. J.

J. Zhang, Z. H. Lu, B. Menegozzi, and L. J. Wang, “Application of frequency combs in the measurement of the refractive index of air,” Rev. Sci. Instrum. 77, 083104 (2006).
[CrossRef]

Werner, A. J.

Williams, E. R.

K. Fujii, E. R. Williams, R. L. Steiner, and D. B. Newell, “A new refractometer by combining a variable length vacuum cell and a double-pass Michelson interferometer,” IEEE Trans. Instrum. Meas. 46, 191-195 (1997).
[CrossRef]

Yeh, Y.

Zhang, J.

J. Zhang, Z. H. Lu, B. Menegozzi, and L. J. Wang, “Application of frequency combs in the measurement of the refractive index of air,” Rev. Sci. Instrum. 77, 083104 (2006).
[CrossRef]

Appl. Opt.

M. Daimon and A. Masumura, “High-accuracy measurements of the refractive index and its temperature coefficient of calcium fluoride in a wide wavelength range from 138 to 2326 nm,” Appl. Opt. 41, 5275-5281 (2002).
[CrossRef] [PubMed]

J. H. Burnett, R. Gupta, and U. Griesmann, “Absolute refractive indices and thermal coefficients of CaF2, SrF2, BaF2, and LiF near 157 nm,” Appl. Opt. 41, 2508-2513 (2002).
[CrossRef] [PubMed]

A. J. Werner, “Methods in high precision refractometry of optical glasses,” Appl. Opt. 7, 837-843 (1968).
[CrossRef] [PubMed]

A. Hirai and H. Matsumoto, “Measurement of group refractive index wavelength dependence using a low-coherence tandem interferometer,” Appl. Opt. 45, 5614-5620 (2006).
[CrossRef] [PubMed]

D. F. Murphy and D. A. Flavin, “Dispersion-insensitive measurement of thickness and group refractive index by low-coherence interferometry,” Appl. Opt. 39, 4607-4615 (2000).
[CrossRef]

Y. Yeh, “Simultaneous measurement of refractive index and thickness of birefringent wave plate,” Appl. Opt. 47, 1457-1464 (2008).
[CrossRef] [PubMed]

M. Galli, F. Marabelli, and G. Guizzetti, “Direct measurement of refractive-index dispersion of transparent media by white-light interferometry,” Appl. Opt. 42, 3910-3914 (2003).
[CrossRef] [PubMed]

P. E. Ciddor, “Refractive index of air: new equations for the visible and near infrared,” Appl. Opt. 35, 1566-1573(1996).
[CrossRef] [PubMed]

T. Keem, S. Gonda, I. Misumi, Q. Huang, and T. Kurosawa, “Removing nonlinearity of a homodyne interferometer by adjusting the gains of its quadrature detector systems,” Appl. Opt. 43, 2443-2448 (2004).
[CrossRef] [PubMed]

Appl. Phys. B

H. Delbarre, C. Przygodzki, M. Tassou, and D. Boucher, “High-precision index measurement in anisotropic crystals using white-light spectral interferometry,” Appl. Phys. B 70, 45-51(2000).
[CrossRef]

IEEE Trans. Instrum. Meas.

K. Fujii, E. R. Williams, R. L. Steiner, and D. B. Newell, “A new refractometer by combining a variable length vacuum cell and a double-pass Michelson interferometer,” IEEE Trans. Instrum. Meas. 46, 191-195 (1997).
[CrossRef]

Opt. Lett.

Rev. Sci. Instrum.

J. Zhang, Z. H. Lu, B. Menegozzi, and L. J. Wang, “Application of frequency combs in the measurement of the refractive index of air,” Rev. Sci. Instrum. 77, 083104 (2006).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Principle of the proposed method. Ps, prism under measurement; Pi, incident prism; ML, refractive-index-matching liquid. Interferometer 1 detects the change in the optical path length in Ps ( Δ x 1 ) and interferometer 2 detects the change in the optical path length in air ( Δ x 2 ) generated by translation of Ps. From Δ x 1 , Δ x 2 , and the refractive index of the air, the absolute refractive index of Ps can be calculated by using Eq. (1).

Fig. 2
Fig. 2

Phase calculation procedure from the interferogram. The upper figure shows the intensity of the interferogram and the lower one shows the phase calculated from the interferogram, with a common horizontal axis of time. Δ φ i ( i = 1 , 2 ) in the lower figure is the phase change from the point where the stage starts to the first point where the intensity crosses the zero line of the interferogram. N i ( i = 1 , 2 ) represents the integral number of fringes counted from points where the zero line is crossed. Δ ψ i ( i = 1 , 2 ) is the phase change from the final point where the zero line is crossed to the point where the stage stopped.

Fig. 3
Fig. 3

Experimental setup. Ps, prism under measurement; Pi, incident prism; M, mirror; BS, beam splitter; PD, photodiode; BPF, bandpass filter; W, wedge plate; CCD, charge-coupled device camera. The alignment system is used to maintain a constant separation between Pi and Ps during movement of the stage.

Fig. 4
Fig. 4

Allan standard deviation of phase from the intensity of the interferograms.

Fig. 5
Fig. 5

Results of a series of measurements. The filled circles and error bars represent the average and standard deviations, respectively, of a group of ten measurements. The average for a total of 120 measurements is 1.5154317 (dotted horizontal line). The vertical dotted lines represent removal and resetting of Ps.

Tables (1)

Tables Icon

Table 1 Uncertainty Budget of the Proposed Method a

Equations (3)

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n s = n a ( Δ x 1 / Δ x 2 ) .
Δ x i = λ i ( N i + ϵ i ) / 2 ( i = 1 , 2 ) .
ϵ i = ( Δ φ i + Δ ψ i ) / 2 π ( i = 1 , 2 ) ,

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