Abstract

A prism-pair interferometer for a spectrum lamp was developed for precise measurement of the refractive index of a prism of optical glass. Previously we reported the prism-pair interferometer with a He–Ne laser light source, resulting in a measurement uncertainty of 1.1×106. However, most of the refractive-index values managed by optical glass manufacturers are conventionally measured with spectrum lamps. We have optimized the prism-pair interferometer for spectrum lamps and implemented a signal-processing technique from Fourier-transform spectroscopy. When the refractive index is measured, the wavelength of the spectrum lamp is simultaneously calibrated by part of the interferometer, so that the resulting refractive index is traceable to a national standard of length. The combined standard uncertainty for a refractive index measured with the e-line (546 nm) of a Hg lamp is 6.9×106.

© 2014 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  6. T. J. Quinn, “Practical realization of the definition of the metre, including recommended radiations of other optical frequency standards (2001),” Metrologia 40, 103–133 (2003).
    [CrossRef]
  7. R. J. Bell, Introductory Fourier Transform Spectroscopy (Academic, 1972).
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    [CrossRef]
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    [CrossRef]
  10. R. Schödel, “Chapter 15 Length and Size,” in Handbook of Optical Metrology, T. Yoshizawa, ed. (CRC Press, 2009), pp. 365–390.
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    [CrossRef]
  12. A. V. Zvyagin, I. Eix, and D. D. Sampson, “High-speed, high-sensitivity, gated surface profiling with closed-loop optical coherence topography,” Appl. Opt. 41, 2179–2184 (2002).
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2012 (1)

A. Hirai, Y. Hori, K. Minoshima, M. Pisani, and M. Astrua, “A bilateral comparison of optical glass refractive index between NMIJ and INRiM for the validation of the measuring systems,” Metrologia 49, 283–288 (2012).
[CrossRef]

2011 (1)

2009 (2)

Y. Hori, A. Hirai, K. Minoshima, and H. Matsumoto, “High-accuracy interferometer with a prism pair for measurement of the absolute refractive index of glass,” Appl. Opt. 48, 2045–2050 (2009).
[CrossRef]

J. A. Stone, J. E. Decker, P. Gill, P. Juncar, A. Lewis, G. D. Rovera, and M. Viliesid, “Advice from the CCL on the use of unstabilized lasers as standards of wavelength: the Helium–Neon laser at 633  nm,” Metrologia 46, 11–18 (2009).
[CrossRef]

2003 (1)

T. J. Quinn, “Practical realization of the definition of the metre, including recommended radiations of other optical frequency standards (2001),” Metrologia 40, 103–133 (2003).
[CrossRef]

2002 (3)

1996 (1)

1972 (1)

E. J. G. Engelhard and F. Bayer-Helms, “114Cd and 198Hg hot cathode spectral lamps for interferometry,” Metrologia 8, 91–95 (1972).
[CrossRef]

Astrua, M.

A. Hirai, Y. Hori, K. Minoshima, M. Pisani, and M. Astrua, “A bilateral comparison of optical glass refractive index between NMIJ and INRiM for the validation of the measuring systems,” Metrologia 49, 283–288 (2012).
[CrossRef]

Bayer-Helms, F.

E. J. G. Engelhard and F. Bayer-Helms, “114Cd and 198Hg hot cathode spectral lamps for interferometry,” Metrologia 8, 91–95 (1972).
[CrossRef]

Bell, R. J.

R. J. Bell, Introductory Fourier Transform Spectroscopy (Academic, 1972).

Burnett, J. H.

Ciddor, P. E.

Daimon, M.

Decker, J. E.

J. A. Stone, J. E. Decker, P. Gill, P. Juncar, A. Lewis, G. D. Rovera, and M. Viliesid, “Advice from the CCL on the use of unstabilized lasers as standards of wavelength: the Helium–Neon laser at 633  nm,” Metrologia 46, 11–18 (2009).
[CrossRef]

Eix, I.

Engelhard, E. J. G.

E. J. G. Engelhard and F. Bayer-Helms, “114Cd and 198Hg hot cathode spectral lamps for interferometry,” Metrologia 8, 91–95 (1972).
[CrossRef]

Gill, P.

J. A. Stone, J. E. Decker, P. Gill, P. Juncar, A. Lewis, G. D. Rovera, and M. Viliesid, “Advice from the CCL on the use of unstabilized lasers as standards of wavelength: the Helium–Neon laser at 633  nm,” Metrologia 46, 11–18 (2009).
[CrossRef]

Griesmann, U.

Gupta, R.

Hirai, A.

Hori, Y.

Juncar, P.

J. A. Stone, J. E. Decker, P. Gill, P. Juncar, A. Lewis, G. D. Rovera, and M. Viliesid, “Advice from the CCL on the use of unstabilized lasers as standards of wavelength: the Helium–Neon laser at 633  nm,” Metrologia 46, 11–18 (2009).
[CrossRef]

Lewis, A.

J. A. Stone, J. E. Decker, P. Gill, P. Juncar, A. Lewis, G. D. Rovera, and M. Viliesid, “Advice from the CCL on the use of unstabilized lasers as standards of wavelength: the Helium–Neon laser at 633  nm,” Metrologia 46, 11–18 (2009).
[CrossRef]

Masumura, A.

Matsumoto, H.

Minoshima, K.

Pisani, M.

A. Hirai, Y. Hori, K. Minoshima, M. Pisani, and M. Astrua, “A bilateral comparison of optical glass refractive index between NMIJ and INRiM for the validation of the measuring systems,” Metrologia 49, 283–288 (2012).
[CrossRef]

Quinn, T. J.

T. J. Quinn, “Practical realization of the definition of the metre, including recommended radiations of other optical frequency standards (2001),” Metrologia 40, 103–133 (2003).
[CrossRef]

Rovera, G. D.

J. A. Stone, J. E. Decker, P. Gill, P. Juncar, A. Lewis, G. D. Rovera, and M. Viliesid, “Advice from the CCL on the use of unstabilized lasers as standards of wavelength: the Helium–Neon laser at 633  nm,” Metrologia 46, 11–18 (2009).
[CrossRef]

Sampson, D. D.

Schödel, R.

R. Schödel, “Chapter 15 Length and Size,” in Handbook of Optical Metrology, T. Yoshizawa, ed. (CRC Press, 2009), pp. 365–390.

Stone, J. A.

J. A. Stone, J. E. Decker, P. Gill, P. Juncar, A. Lewis, G. D. Rovera, and M. Viliesid, “Advice from the CCL on the use of unstabilized lasers as standards of wavelength: the Helium–Neon laser at 633  nm,” Metrologia 46, 11–18 (2009).
[CrossRef]

Viliesid, M.

J. A. Stone, J. E. Decker, P. Gill, P. Juncar, A. Lewis, G. D. Rovera, and M. Viliesid, “Advice from the CCL on the use of unstabilized lasers as standards of wavelength: the Helium–Neon laser at 633  nm,” Metrologia 46, 11–18 (2009).
[CrossRef]

Zvyagin, A. V.

Appl. Opt. (6)

Metrologia (4)

E. J. G. Engelhard and F. Bayer-Helms, “114Cd and 198Hg hot cathode spectral lamps for interferometry,” Metrologia 8, 91–95 (1972).
[CrossRef]

J. A. Stone, J. E. Decker, P. Gill, P. Juncar, A. Lewis, G. D. Rovera, and M. Viliesid, “Advice from the CCL on the use of unstabilized lasers as standards of wavelength: the Helium–Neon laser at 633  nm,” Metrologia 46, 11–18 (2009).
[CrossRef]

A. Hirai, Y. Hori, K. Minoshima, M. Pisani, and M. Astrua, “A bilateral comparison of optical glass refractive index between NMIJ and INRiM for the validation of the measuring systems,” Metrologia 49, 283–288 (2012).
[CrossRef]

T. J. Quinn, “Practical realization of the definition of the metre, including recommended radiations of other optical frequency standards (2001),” Metrologia 40, 103–133 (2003).
[CrossRef]

Other (2)

R. J. Bell, Introductory Fourier Transform Spectroscopy (Academic, 1972).

R. Schödel, “Chapter 15 Length and Size,” in Handbook of Optical Metrology, T. Yoshizawa, ed. (CRC Press, 2009), pp. 365–390.

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Figures (6)

Fig. 1.
Fig. 1.

Principle of prism-pair interferometry. Ps, prism under measurement; Pf, fixed prism; ML, refractive-index-matching liquid. (a) Interferometer 1 (Mach–Zehnder type) detects changes in the optical path length inside Ps, represented as (nsna)X, where X is the geometrical displacement of surface α of Ps, ns is the absolute refractive index of Ps, and na is the refractive index of air. (b) Interferometer 2 (Michelson type) detects changes in the optical path length in air, represented as 2naX, generated as a result of translation of Ps. Interferometer 3 is the same as Interferometer 2, but the light source is a He–Ne laser, the signal of which is used as a reference scale for Interferometers 1 and 2 in the process of calculation of ns, as shown in Fig. 4.

Fig. 2.
Fig. 2.

Linear relationship between interference signals: λ1, period of interference signal 1; λ2, period of interference signal 2; λr, known wavelength of the light source of Interferometer 3 in air; N1,2,3, numbers of fringes, including fractions, of interference signals. We can see a simple linear relationship between λ1, λ2, and λr from this figure, as λ1=λr×(N3/N1) and λ2=λr×(N3/N2).

Fig. 3.
Fig. 3.

Experimental setup. Ps, prism under measurement; Pf, fixed prism; BPF, bandpass filter; CL, collimator lens; BS, beam splitter; GP, glass plate; M, mirror; PBS, polarizing beam splitter; QWP, quarter-wave plate; DM, dichroic mirror; PD, photodiode. Interferometer 1 is of Mach–Zehnder type, whereas Interferometers 2 and 3 are of Michelson type. Interference signals from all three interferometers are detected simultaneously and are processed for calculation of the absolute refractive index of Ps(ns) and the wavelength of the Hg lamp source (λ) as shown in Fig. 4.

Fig. 4.
Fig. 4.

Signal processing for measurement of refractive index and wavelength. λ1, period of interference signal 1; λ2, period of interference signal 2; λr, known wavelength of the light source of Interferometer 3 in air. The interference signals for Interferometers 1 and 2 are resampled (square) synchronously at the zero-crossing points of the reference signal (circle). λ1 and λ2 are obtained by Gaussian fitting of the spectra obtained by Fourier transformation of the resampled signals from Interferometers 1 and 2. We can calculate the absolute refractive index of Ps(ns) and the wavelength of the Hg lamp source in vacuum (λ) from Eqs. (6) and (7) by using the value of λ1 and λ2.

Fig. 5.
Fig. 5.

Results of the measurement of the absolute refractive index of Ps(ns). The material of Ps is BSL7Y (OHARA Inc.), and these results are corrected to values at 20.0°C by using the temperature coefficient of BSL7Y. The plots in this figure represent average values of 20 measurements (one set of measurements) and the error bars represent their standard deviation. The average value from a total of 200 measurements is 1.519057; this was confirmed to agree, within our measurement uncertainty, with the result of 1.519061, measured by the minimum-deviation-angle method by OHARA Inc.

Fig. 6.
Fig. 6.

Results of the measurement of the wavelength of the e-line of the Hg lamp in vacuum performed simultaneously with the measurement of the absolute refractive index of Ps, as shown in Fig. 5. The wavelengths shown in this figure are corrected by the so-called pinhole correction represented in Eq. (8). The plots in this figure represent average values from 20 measurements (one set of measurements) and the error bars represent their standard deviation. The average value from a total of 200 measurements is 546.22558 nm, which agrees, within our measurement uncertainty, with the CIPM-recommended value of 546.22705 nm for the e-line of a Hg lamp.

Tables (1)

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Table 1. Uncertainty Budget of the Proposed Methoda

Equations (8)

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λN1=(nsna)X,
λN2=2naX,
λrN3=2na,rX,
λ1=λr×N3N1=2λnsna,
λ2=λr×N3N1=2λna.
ns=(2λ2λ1+1)na.
λ=λ2na.
Δλ=a24f2×λ.

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