Abstract

We present a refractometer that is capable of measuring the refractive index of gases with an unambiguous range of 1.000395 and an uncertainty of 3.14×108 at 633 nm. The measurement range was extended via the combination of the vacuum cells according to the proposed synthetic pseudo-wavelength (SPW) method. The basic principles of the SPW method and the design of the gas refractometer are presented in detail. The performance of the refractometer was verified in the measurements of dry air, nitrogen gas, and ambient air under different environmental conditions. No gas-filling or pumping processes were required during the measurements; so one measurement could be completed within 70 s. Compared with existing refractometers, the method reported here holds advantages in its large unambiguous measuring range, fast speed, high accuracy, and simple instrumentation design.

© 2013 Optical Society of America

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  1. K. P. Birch and M. J. Downs, “An updated Edlén equation for the refractive index of air,” Metrologia 30, 155–162 (1993).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  5. M. Ishige, M. Aketagawa, T. B. Quoc, and Y. Hoshino, “Measurement of air-refractive-index fluctuation from frequency change using a phase modulation homodyne interferometer and an external cavity laser diode,” Meas. Sci. Technol. 20, 084019 (2009).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  13. G. P. Xie, Y. J. Wang, L. J. Reiter, and J. C. Tsai, “High-accuracy absolute measurement of the refractive index of air,” Opt. Eng. 43, 950–953 (2004).
    [CrossRef]
  14. P. J. de Groot, “Extending the unambiguous range of two-color interferometers,” Appl. Opt. 33, 5948–5953 (1994).
    [CrossRef]
  15. S. H. Lu and C. C. Lee, “Measuring large step heights by variable synthetic wavelength interferometry,” Meas. Sci. Technol. 13, 1382–1387 (2002).
    [CrossRef]
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  19. “Evaluation of measurement data—guide to the expression of uncertainty in measurement,” (2008), http://www.iso.org/sites/JCGM/GUM/JCGM100/C045315e-html/C045315e.html?csnumber=50461 .
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2012 (2)

2011 (1)

2009 (1)

M. Ishige, M. Aketagawa, T. B. Quoc, and Y. Hoshino, “Measurement of air-refractive-index fluctuation from frequency change using a phase modulation homodyne interferometer and an external cavity laser diode,” Meas. Sci. Technol. 20, 084019 (2009).
[CrossRef]

2008 (1)

2006 (1)

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]

2005 (1)

2004 (1)

G. P. Xie, Y. J. Wang, L. J. Reiter, and J. C. Tsai, “High-accuracy absolute measurement of the refractive index of air,” Opt. Eng. 43, 950–953 (2004).
[CrossRef]

2002 (2)

L. J. Zeng, I. Fujima, A. Hirai, H. Matsumoto, and S. Iwasaki, “A two-color heterodyne interferometer for measuring the refractive index of air using an optical diffraction grating,” Opt. Commun. 203, 243–247 (2002).
[CrossRef]

S. H. Lu and C. C. Lee, “Measuring large step heights by variable synthetic wavelength interferometry,” Meas. Sci. Technol. 13, 1382–1387 (2002).
[CrossRef]

1998 (1)

G. Bönsch and E. Potulski, “Measurement of the refractive index of air and comparison with modified Edlén’s formulae,” Metrologia 35, 133–139 (1998).
[CrossRef]

1996 (1)

1994 (2)

K. P. Birch and M. J. Downs, “Correction to the updated Edlén equation for the refractive index of air,” Metrologia 31, 315–316 (1994).
[CrossRef]

P. J. de Groot, “Extending the unambiguous range of two-color interferometers,” Appl. Opt. 33, 5948–5953 (1994).
[CrossRef]

1993 (1)

K. P. Birch and M. J. Downs, “An updated Edlén equation for the refractive index of air,” Metrologia 30, 155–162 (1993).
[CrossRef]

1991 (1)

1966 (1)

1965 (1)

J. Terrien, “An air refractometer for interference length metrology,” Metrologia 1, 80–83 (1965).
[CrossRef]

Aketagawa, M.

M. Ishige, M. Aketagawa, T. B. Quoc, and Y. Hoshino, “Measurement of air-refractive-index fluctuation from frequency change using a phase modulation homodyne interferometer and an external cavity laser diode,” Meas. Sci. Technol. 20, 084019 (2009).
[CrossRef]

Aleksoff, C.

Birch, K. P.

K. P. Birch and M. J. Downs, “Correction to the updated Edlén equation for the refractive index of air,” Metrologia 31, 315–316 (1994).
[CrossRef]

K. P. Birch and M. J. Downs, “An updated Edlén equation for the refractive index of air,” Metrologia 30, 155–162 (1993).
[CrossRef]

K. P. Birch, “Precise determination of refractometric parameters for atmospheric gases,” J. Opt. Soc. Am. A 8, 647–651 (1991).
[CrossRef]

Bönsch, G.

G. Bönsch and E. Potulski, “Measurement of the refractive index of air and comparison with modified Edlén’s formulae,” Metrologia 35, 133–139 (1998).
[CrossRef]

Chen, Q. H.

Ciddor, P. E.

de Groot, P. J.

Downs, M. J.

K. P. Birch and M. J. Downs, “Correction to the updated Edlén equation for the refractive index of air,” Metrologia 31, 315–316 (1994).
[CrossRef]

K. P. Birch and M. J. Downs, “An updated Edlén equation for the refractive index of air,” Metrologia 30, 155–162 (1993).
[CrossRef]

Egan, P.

Fujima, I.

L. J. Zeng, I. Fujima, A. Hirai, H. Matsumoto, and S. Iwasaki, “A two-color heterodyne interferometer for measuring the refractive index of air using an optical diffraction grating,” Opt. Commun. 203, 243–247 (2002).
[CrossRef]

Hirai, A.

L. J. Zeng, I. Fujima, A. Hirai, H. Matsumoto, and S. Iwasaki, “A two-color heterodyne interferometer for measuring the refractive index of air using an optical diffraction grating,” Opt. Commun. 203, 243–247 (2002).
[CrossRef]

Hoshino, Y.

M. Ishige, M. Aketagawa, T. B. Quoc, and Y. Hoshino, “Measurement of air-refractive-index fluctuation from frequency change using a phase modulation homodyne interferometer and an external cavity laser diode,” Meas. Sci. Technol. 20, 084019 (2009).
[CrossRef]

Ishige, M.

M. Ishige, M. Aketagawa, T. B. Quoc, and Y. Hoshino, “Measurement of air-refractive-index fluctuation from frequency change using a phase modulation homodyne interferometer and an external cavity laser diode,” Meas. Sci. Technol. 20, 084019 (2009).
[CrossRef]

Iwasaki, S.

L. J. Zeng, I. Fujima, A. Hirai, H. Matsumoto, and S. Iwasaki, “A two-color heterodyne interferometer for measuring the refractive index of air using an optical diffraction grating,” Opt. Commun. 203, 243–247 (2002).
[CrossRef]

Khanna, B. N.

Lee, C. C.

S. H. Lu and C. C. Lee, “Measuring large step heights by variable synthetic wavelength interferometry,” Meas. Sci. Technol. 13, 1382–1387 (2002).
[CrossRef]

Lu, S. H.

S. H. Lu and C. C. Lee, “Measuring large step heights by variable synthetic wavelength interferometry,” Meas. Sci. Technol. 13, 1382–1387 (2002).
[CrossRef]

Lu, Z. H.

Luo, H. F.

Matsumoto, H.

L. J. Zeng, I. Fujima, A. Hirai, H. Matsumoto, and S. Iwasaki, “A two-color heterodyne interferometer for measuring the refractive index of air using an optical diffraction grating,” Opt. Commun. 203, 243–247 (2002).
[CrossRef]

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]

Ni, J.

Peck, R.

Potulski, E.

G. Bönsch and E. Potulski, “Measurement of the refractive index of air and comparison with modified Edlén’s formulae,” Metrologia 35, 133–139 (1998).
[CrossRef]

Quoc, T. B.

M. Ishige, M. Aketagawa, T. B. Quoc, and Y. Hoshino, “Measurement of air-refractive-index fluctuation from frequency change using a phase modulation homodyne interferometer and an external cavity laser diode,” Meas. Sci. Technol. 20, 084019 (2009).
[CrossRef]

Reiter, L. J.

G. P. Xie, Y. J. Wang, L. J. Reiter, and J. C. Tsai, “High-accuracy absolute measurement of the refractive index of air,” Opt. Eng. 43, 950–953 (2004).
[CrossRef]

Stone, J. A.

Terrien, J.

J. Terrien, “An air refractometer for interference length metrology,” Metrologia 1, 80–83 (1965).
[CrossRef]

Tsai, J. C.

G. P. Xie, Y. J. Wang, L. J. Reiter, and J. C. Tsai, “High-accuracy absolute measurement of the refractive index of air,” Opt. Eng. 43, 950–953 (2004).
[CrossRef]

Wang, F.

Wang, L. J.

Wang, S. M.

Wang, Y. J.

G. P. Xie, Y. J. Wang, L. J. Reiter, and J. C. Tsai, “High-accuracy absolute measurement of the refractive index of air,” Opt. Eng. 43, 950–953 (2004).
[CrossRef]

Weber, M. J.

M. J. Weber, Handbook of Optical Materials (CRC Press, 2003), p. 445.

Xie, G. P.

G. P. Xie, Y. J. Wang, L. J. Reiter, and J. C. Tsai, “High-accuracy absolute measurement of the refractive index of air,” Opt. Eng. 43, 950–953 (2004).
[CrossRef]

Yu, H.

Zeng, L. J.

L. J. Zeng, I. Fujima, A. Hirai, H. Matsumoto, and S. Iwasaki, “A two-color heterodyne interferometer for measuring the refractive index of air using an optical diffraction grating,” Opt. Commun. 203, 243–247 (2002).
[CrossRef]

Zhang, J.

Appl. Opt. (5)

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

Meas. Sci. Technol. (2)

M. Ishige, M. Aketagawa, T. B. Quoc, and Y. Hoshino, “Measurement of air-refractive-index fluctuation from frequency change using a phase modulation homodyne interferometer and an external cavity laser diode,” Meas. Sci. Technol. 20, 084019 (2009).
[CrossRef]

S. H. Lu and C. C. Lee, “Measuring large step heights by variable synthetic wavelength interferometry,” Meas. Sci. Technol. 13, 1382–1387 (2002).
[CrossRef]

Metrologia (4)

G. Bönsch and E. Potulski, “Measurement of the refractive index of air and comparison with modified Edlén’s formulae,” Metrologia 35, 133–139 (1998).
[CrossRef]

J. Terrien, “An air refractometer for interference length metrology,” Metrologia 1, 80–83 (1965).
[CrossRef]

K. P. Birch and M. J. Downs, “An updated Edlén equation for the refractive index of air,” Metrologia 30, 155–162 (1993).
[CrossRef]

K. P. Birch and M. J. Downs, “Correction to the updated Edlén equation for the refractive index of air,” Metrologia 31, 315–316 (1994).
[CrossRef]

Opt. Commun. (1)

L. J. Zeng, I. Fujima, A. Hirai, H. Matsumoto, and S. Iwasaki, “A two-color heterodyne interferometer for measuring the refractive index of air using an optical diffraction grating,” Opt. Commun. 203, 243–247 (2002).
[CrossRef]

Opt. Eng. (1)

G. P. Xie, Y. J. Wang, L. J. Reiter, and J. C. Tsai, “High-accuracy absolute measurement of the refractive index of air,” Opt. Eng. 43, 950–953 (2004).
[CrossRef]

Opt. Lett. (2)

Rev. Sci. Instrum. (1)

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]

Other (2)

M. J. Weber, Handbook of Optical Materials (CRC Press, 2003), p. 445.

“Evaluation of measurement data—guide to the expression of uncertainty in measurement,” (2008), http://www.iso.org/sites/JCGM/GUM/JCGM100/C045315e-html/C045315e.html?csnumber=50461 .

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Figures (7)

Fig. 1.
Fig. 1.

Measurement principle of the gas refractometer. He–Ne laser, laser with two orthogonally linear polarized frequency components f1 and f2, where the subscripts p and s indicate that the polarization direction of f1 and f2 are parallel and perpendicular to the paper, respectively. M, plane beam splitter; QWP, quarter-wave plate; T, vacuum cell; CC, corner cube; PBS, polarized beam splitter; M1, reflector; D1, D2, photo detectors; PM, phase meter. Gas with refractive index of n is filled in the chamber before measurement.

Fig. 2.
Fig. 2.

SPW chain organized using three vacuum cells. Symbol λji represents the SPWs, where j indicates the SPW’s order and i indicates the cell’s number.

Fig. 3.
Fig. 3.

Example of length design for the vacuum cell. (a) Length of L12L2+L3 restricted by the expected measurement range according to Eq. (9a). (b) Length of L1L2 restricted by the maximum measurement range according to Eq. (9b). (c) Length of L1L2 restricted by the measurement uncertainty according to Eq. (9c). (d) Length of L1 restricted by the expected uncertainty according to Eq. (9d).

Fig. 4.
Fig. 4.

Optical setup of gas refractometer. He–Ne laser, laser with two orthogonally linear polarized frequency components f1 and f2; M, plane beam splitter; QWP, quarter-wave plate; T1, T2 and T3, vacuum cells; CC, corner cube; PBS, polarized beam splitter; M1, reflector; D1, D2, photodetectors; PM, phase meter. Photograph of a vacuum cell is also shown.

Fig. 5.
Fig. 5.

Experimental results of the refractive index of dry air under different environmental conditions. (a) Comparison of experimental and reference data of dry air. Dashed circle with arrow indicates the corresponding y axis of the data curve. (b) Pressure and temperature data in the measurements.

Fig. 6.
Fig. 6.

Experimental results of the refractive index of nitrogen gas with different environmental conditions. (a) Comparison of experimental and reference data of nitrogen gas. Dashed circle with arrow indicates the corresponding y axis of the data curve. (b) Pressure and temperature data in the measurements.

Fig. 7.
Fig. 7.

Long-term measurement of the refractive index of ambient gas at 633 nm for about 16 h. (a) Experimental and reference data of ambient air. (b) Difference between experimental and reference data.

Tables (1)

Tables Icon

Table 1. Calibration Results for the Thermometer, Pressure Gauge, Hygrometer, and Vacuum Gauge

Equations (30)

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

I1=I01cos(2πΔft+Δφ0+Δφ)I2=I02cos(2πΔft+Δφ0Δφ)},
Δφ=2π×2(n1)Lλ,
2Δφ2π=N+ε=4(n1)Lλ,
n1=λs(N+ε),
n1=λs1(N1+ε1),
n1=λs2(N2+ε2),
n1=Λs(ΔN+Δε),
Nj1=INT((nj1)λj1εj1+12),j=1,2,,
u(nj1)<12λj1u(nj11),
λ4(L12L2+L3)(nmax1),
u(n21)<12×λ4(L1L2)u(n11),
u(n11)<12×λ4L1u(n01),
u(n01)u0.
u(n1)n1=[(u(ε01)N01+ε01)2+(u(L1)L1)2+(u(λ)λ)2]1/2,
n1=λj(Nj+εj)=λj1(Nj1+εj1)=
nj1=λjεj,
Nj1=(nj1)λj1εj1±[u(nj1)λj1+u(nj11)λj1].
0<[u(nj1)λj1+u(nj11)λj1]<12,
0<±[u(nj1)λj1+u(nj11)λj1]+12<1.
Nj1<(nj1)λj1εj1+12<Nj1+1.
u(nj1)nj1=[(u(εj1)Nj1+εj1)2+(u(λj1)λj1)2]1/2,j=0,1,2.
ε01=ε1,ε02=ε2,ε03=ε3,
ε11=ε1ε2,
ε21=ε12ε2+ε3,
u(ε01)=u(p),
u(ε11)=2·u(p),
u(ε21)=6·u(p).
u(λ01)λ01=u(L1)L1=1L1u(L),
u(λ11)λ11=u(L1L2)L1L2=2L1L2u(L),
u(λ21)λ21=u(L12L2+L3)L12L2+L3=6L12L2+L3u(L).

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