Abstract

We present a method of measuring the refractive index of dry gases absolutely at 632.8nm wavelength using a Fabry–Perot cavity with an expanded uncertainty of <3×109 (coverage factor k=2). The main contribution to this uncertainty is how well vacuum-to-atmosphere compression effects (physical length variation) in the cavities can be corrected. This paper describes the technique and reports reference values for the refractive indices of nitrogen and argon gases at 100kPa and 20°C with an expanded uncertainty of <9×109 (coverage factor k=2), with the additional and larger part of this uncertainty coming from the pressure and temperature measurement.

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  1. B. Edlén, “The refractive index of air,” Metrologia 2, 71–80(1966).
    [CrossRef]
  2. K. P. Birch and M. J. Downs, “An updated Edlén equation for the refractive index of air,” Metrologia 30, 155–162 (1993).
    [CrossRef]
  3. P. E. Ciddor, “Refractive index of air: new equations for the visible and near infrared,” Appl. Opt. 35, 1566–1573 (1996).
    [CrossRef] [PubMed]
  4. G. Bönsch and E. Potulski, “Measurement of the refractive index of air and comparison with modified Edlén’s formulae,” Metrologia 35, 133 (1998).
    [CrossRef]
  5. J. A. Stone and J. H. Zimmerman, “Refractive index of air calculator,” http://emtoolbox.nist.gov/Wavelength/Abstract.asp.
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    [CrossRef]
  14. Any mention of commercial products is for information only; it does not imply recommendation or endorsement by NIST nor does it imply that the products mentioned are necessarily the best available for the purpose.
  15. L. Marmet, A. A. Madej, K. J. Siemsen, J. E. Bernard, and B. G. Whitford, “Precision frequency measurement of the S1/2−D25/22 transition of Sr+ with a 674 nm diode laser locked to an ultrastable cavity,” IEEE Trans. Instrum. Meas. 46, 169–173 (1997).
    [CrossRef]
  16. A. Takahashi, “Long-term dimensional stability and longitudinal uniformity of line scales made of glass ceramics,” Meas. Sci. Technol. 21, 105301 (2010).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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  22. H. J. Achtermann, G. Magnus, and T. K. Bose, “Refractivity virial coefficients of gaseous CH4, C2H4, C2H6, CO2, SF6, H2, N2, He, and Ar,” J. Chem. Phys. 94, 5669–5684 (1991).
    [CrossRef]
  23. K. P. Birch, “Precise determination of refractometric parameters for atmospheric gases,” J. Opt. Soc. Am. A 8, 647–651(1991).
    [CrossRef]
  24. W. Hou and R. Thalmann, “Accurate measurement of the refractive index of air,” Measurement 13, 307–314 (1994).
    [CrossRef]
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2011 (1)

P. Egan and J. A. Stone, “Temperature stabilization system with millikelvin gradients for air refractometry measurements below the 10−8 level,” NCSLI Measure: J. Measure Sci. 6, 40–46 (2011).

2010 (1)

A. Takahashi, “Long-term dimensional stability and longitudinal uniformity of line scales made of glass ceramics,” Meas. Sci. Technol. 21, 105301 (2010).
[CrossRef]

2009 (1)

2005 (2)

2004 (1)

J. A. Stone and A. Stejskal, “Using helium as a standard of refractive index: correcting errors in a gas refractometer,” Metrologia 41, 189–197 (2004).
[CrossRef]

2000 (1)

1999 (1)

J. S. Beers and W. B. Penzes, “The NIST length scale interferometer,” J. Res. Natl. Inst. Stand. Technol. 104, 225–252(1999).

1998 (2)

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

N. Khélifa, H. Fang, J. Xu, P. Juncar, and M. Himbert, “Refractometer for tracking changes in the refractive index of air near 780 nm,” Appl. Opt. 37, 156–161 (1998).
[CrossRef]

1997 (3)

M. L. Eickhoff and J. L. Hall, “Real-time precision refractometry: new approaches,” Appl. Opt. 36, 1223–1234 (1997).
[CrossRef] [PubMed]

T. Doiron and J. Stoup, “Uncertainty and dimensional calibrations,” J. Res. Natl. Inst. Stand. Technol. 102, 647–676 (1997).

L. Marmet, A. A. Madej, K. J. Siemsen, J. E. Bernard, and B. G. Whitford, “Precision frequency measurement of the S1/2−D25/22 transition of Sr+ with a 674 nm diode laser locked to an ultrastable cavity,” IEEE Trans. Instrum. Meas. 46, 169–173 (1997).
[CrossRef]

1996 (1)

1994 (1)

W. Hou and R. Thalmann, “Accurate measurement of the refractive index of air,” Measurement 13, 307–314 (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 (2)

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

H. J. Achtermann, G. Magnus, and T. K. Bose, “Refractivity virial coefficients of gaseous CH4, C2H4, C2H6, CO2, SF6, H2, N2, He, and Ar,” J. Chem. Phys. 94, 5669–5684 (1991).
[CrossRef]

1987 (1)

1985 (2)

1966 (1)

B. Edlén, “The refractive index of air,” Metrologia 2, 71–80(1966).
[CrossRef]

Achtermann, H. J.

H. J. Achtermann, G. Magnus, and T. K. Bose, “Refractivity virial coefficients of gaseous CH4, C2H4, C2H6, CO2, SF6, H2, N2, He, and Ar,” J. Chem. Phys. 94, 5669–5684 (1991).
[CrossRef]

Andersson, M.

Beers, J. S.

J. S. Beers and W. B. Penzes, “The NIST length scale interferometer,” J. Res. Natl. Inst. Stand. Technol. 104, 225–252(1999).

Bernard, J. E.

L. Marmet, A. A. Madej, K. J. Siemsen, J. E. Bernard, and B. G. Whitford, “Precision frequency measurement of the S1/2−D25/22 transition of Sr+ with a 674 nm diode laser locked to an ultrastable cavity,” IEEE Trans. Instrum. Meas. 46, 169–173 (1997).
[CrossRef]

Birch, K. P.

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 (1998).
[CrossRef]

Bose, T. K.

H. J. Achtermann, G. Magnus, and T. K. Bose, “Refractivity virial coefficients of gaseous CH4, C2H4, C2H6, CO2, SF6, H2, N2, He, and Ar,” J. Chem. Phys. 94, 5669–5684 (1991).
[CrossRef]

Ciddor, P. E.

Doiron, T.

T. Doiron and J. Stoup, “Uncertainty and dimensional calibrations,” J. Res. Natl. Inst. Stand. Technol. 102, 647–676 (1997).

Downs, M. J.

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

Dymond, J. D.

J. D. Dymond, K. N. Marsh, R. C. Wilhoit, and K. C. Wong, “Virial coefficients of pure gases and mixtures,” in Landolt–Börnstein: Group IV Physical Chemistry (Springer–Verlag, 2002), Vol. 21A.

Edlén, B.

B. Edlén, “The refractive index of air,” Metrologia 2, 71–80(1966).
[CrossRef]

Egan, P.

P. Egan and J. A. Stone, “Temperature stabilization system with millikelvin gradients for air refractometry measurements below the 10−8 level,” NCSLI Measure: J. Measure Sci. 6, 40–46 (2011).

Eickhoff, M. L.

Eliasson, L.

Estler, W. T.

Fang, H.

Fox, R. W.

Hall, J. L.

Himbert, M.

Hollberg, L.

Hou, W.

W. Hou and R. Thalmann, “Accurate measurement of the refractive index of air,” Measurement 13, 307–314 (1994).
[CrossRef]

Juncar, P.

Khélifa, N.

Lawall, J. R.

Lichten, W.

Madej, A. A.

L. Marmet, A. A. Madej, K. J. Siemsen, J. E. Bernard, and B. G. Whitford, “Precision frequency measurement of the S1/2−D25/22 transition of Sr+ with a 674 nm diode laser locked to an ultrastable cavity,” IEEE Trans. Instrum. Meas. 46, 169–173 (1997).
[CrossRef]

Magnus, G.

H. J. Achtermann, G. Magnus, and T. K. Bose, “Refractivity virial coefficients of gaseous CH4, C2H4, C2H6, CO2, SF6, H2, N2, He, and Ar,” J. Chem. Phys. 94, 5669–5684 (1991).
[CrossRef]

Marmet, L.

L. Marmet, A. A. Madej, K. J. Siemsen, J. E. Bernard, and B. G. Whitford, “Precision frequency measurement of the S1/2−D25/22 transition of Sr+ with a 674 nm diode laser locked to an ultrastable cavity,” IEEE Trans. Instrum. Meas. 46, 169–173 (1997).
[CrossRef]

Marsh, K. N.

J. D. Dymond, K. N. Marsh, R. C. Wilhoit, and K. C. Wong, “Virial coefficients of pure gases and mixtures,” in Landolt–Börnstein: Group IV Physical Chemistry (Springer–Verlag, 2002), Vol. 21A.

Newbury, N. R.

Pendrill, L. R.

Penzes, W. B.

J. S. Beers and W. B. Penzes, “The NIST length scale interferometer,” J. Res. Natl. Inst. Stand. Technol. 104, 225–252(1999).

Potulski, E.

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

Siemsen, K. J.

L. Marmet, A. A. Madej, K. J. Siemsen, J. E. Bernard, and B. G. Whitford, “Precision frequency measurement of the S1/2−D25/22 transition of Sr+ with a 674 nm diode laser locked to an ultrastable cavity,” IEEE Trans. Instrum. Meas. 46, 169–173 (1997).
[CrossRef]

Stejskal, A.

J. A. Stone and A. Stejskal, “Using helium as a standard of refractive index: correcting errors in a gas refractometer,” Metrologia 41, 189–197 (2004).
[CrossRef]

Stone, J. A.

P. Egan and J. A. Stone, “Temperature stabilization system with millikelvin gradients for air refractometry measurements below the 10−8 level,” NCSLI Measure: J. Measure Sci. 6, 40–46 (2011).

J. A. Stone and A. Stejskal, “Using helium as a standard of refractive index: correcting errors in a gas refractometer,” Metrologia 41, 189–197 (2004).
[CrossRef]

J. A. Stone and J. H. Zimmerman, “Refractive index of air calculator,” http://emtoolbox.nist.gov/Wavelength/Abstract.asp.

Stoup, J.

T. Doiron and J. Stoup, “Uncertainty and dimensional calibrations,” J. Res. Natl. Inst. Stand. Technol. 102, 647–676 (1997).

Takahashi, A.

A. Takahashi, “Long-term dimensional stability and longitudinal uniformity of line scales made of glass ceramics,” Meas. Sci. Technol. 21, 105301 (2010).
[CrossRef]

Taubman, M. S.

Thalmann, R.

W. Hou and R. Thalmann, “Accurate measurement of the refractive index of air,” Measurement 13, 307–314 (1994).
[CrossRef]

Washburn, B. R.

Whitford, B. G.

L. Marmet, A. A. Madej, K. J. Siemsen, J. E. Bernard, and B. G. Whitford, “Precision frequency measurement of the S1/2−D25/22 transition of Sr+ with a 674 nm diode laser locked to an ultrastable cavity,” IEEE Trans. Instrum. Meas. 46, 169–173 (1997).
[CrossRef]

Wilhoit, R. C.

J. D. Dymond, K. N. Marsh, R. C. Wilhoit, and K. C. Wong, “Virial coefficients of pure gases and mixtures,” in Landolt–Börnstein: Group IV Physical Chemistry (Springer–Verlag, 2002), Vol. 21A.

Wong, K. C.

J. D. Dymond, K. N. Marsh, R. C. Wilhoit, and K. C. Wong, “Virial coefficients of pure gases and mixtures,” in Landolt–Börnstein: Group IV Physical Chemistry (Springer–Verlag, 2002), Vol. 21A.

Xu, J.

Zimmerman, J. H.

J. A. Stone and J. H. Zimmerman, “Refractive index of air calculator,” http://emtoolbox.nist.gov/Wavelength/Abstract.asp.

Appl. Opt. (6)

IEEE Trans. Instrum. Meas. (1)

L. Marmet, A. A. Madej, K. J. Siemsen, J. E. Bernard, and B. G. Whitford, “Precision frequency measurement of the S1/2−D25/22 transition of Sr+ with a 674 nm diode laser locked to an ultrastable cavity,” IEEE Trans. Instrum. Meas. 46, 169–173 (1997).
[CrossRef]

J. Chem. Phys. (1)

H. J. Achtermann, G. Magnus, and T. K. Bose, “Refractivity virial coefficients of gaseous CH4, C2H4, C2H6, CO2, SF6, H2, N2, He, and Ar,” J. Chem. Phys. 94, 5669–5684 (1991).
[CrossRef]

J. Opt. Soc. Am. A (3)

J. Res. Natl. Inst. Stand. Technol. (2)

T. Doiron and J. Stoup, “Uncertainty and dimensional calibrations,” J. Res. Natl. Inst. Stand. Technol. 102, 647–676 (1997).

J. S. Beers and W. B. Penzes, “The NIST length scale interferometer,” J. Res. Natl. Inst. Stand. Technol. 104, 225–252(1999).

Meas. Sci. Technol. (1)

A. Takahashi, “Long-term dimensional stability and longitudinal uniformity of line scales made of glass ceramics,” Meas. Sci. Technol. 21, 105301 (2010).
[CrossRef]

Measurement (1)

W. Hou and R. Thalmann, “Accurate measurement of the refractive index of air,” Measurement 13, 307–314 (1994).
[CrossRef]

Metrologia (4)

J. A. Stone and A. Stejskal, “Using helium as a standard of refractive index: correcting errors in a gas refractometer,” Metrologia 41, 189–197 (2004).
[CrossRef]

B. Edlén, “The refractive index of air,” Metrologia 2, 71–80(1966).
[CrossRef]

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

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

NCSLI Measure: J. Measure Sci. (1)

P. Egan and J. A. Stone, “Temperature stabilization system with millikelvin gradients for air refractometry measurements below the 10−8 level,” NCSLI Measure: J. Measure Sci. 6, 40–46 (2011).

Opt. Express (1)

Opt. Lett. (1)

Other (3)

J. D. Dymond, K. N. Marsh, R. C. Wilhoit, and K. C. Wong, “Virial coefficients of pure gases and mixtures,” in Landolt–Börnstein: Group IV Physical Chemistry (Springer–Verlag, 2002), Vol. 21A.

J. A. Stone and J. H. Zimmerman, “Refractive index of air calculator,” http://emtoolbox.nist.gov/Wavelength/Abstract.asp.

Any mention of commercial products is for information only; it does not imply recommendation or endorsement by NIST nor does it imply that the products mentioned are necessarily the best available for the purpose.

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Figures (4)

Fig. 1
Fig. 1

Optical setup for refractometry (only one laser system is shown). Components include: thermally tunable helium–neon laser (He–Ne), isolators (iso), polarizing beamsplitter (pbs), acoustooptic modulator (aom), mirrors (m), lenses (pcx, bcx), fiber coupler/collimator (fc), polarization-maintaining single-mode fiber (pm-smf), nonpolarizing beamsplitters (bs), 100 kHz photodetectors (pd), and 1 GHz avalanche photodetector (apd). End-on photograph of longer FP cavity also shown.

Fig. 2
Fig. 2

Temperature, pressure, and (density corrected) frequency dynamics for a helium correction of the long ULE cavity.

Fig. 3
Fig. 3

Absolute resonant frequency (density corrected) of the short cavity, and beat frequency between two cavities, after charging to 100 kPa nitrogen.

Fig. 4
Fig. 4

Disagreement in the refractive index of air between the cavities as a function of relative humidity.

Tables (2)

Tables Icon

Table 1 Refractometer Uncertainties and Relative Error in Determining Refractive Index n Using Eq. (2) with the Long Cavity

Tables Icon

Table 2 Derived Reference Values for the Refractivities of Nitrogen and Argon for p = 100 kPa , T = 20 ° C , and λ = 633 nm

Equations (5)

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

ν = c 2 n L [ m + Φ ( L ) π ϕ R ( ν ) 2 π ] ,
n 1 = ( ν i ν f ) ( 1 + ε α ) + Δ m c 2 L i + ε d ν f + n L i L f L i ,
n L i L f L i Δ L L = Δ p 3 K .
ν corr = ν meas + ν nom [ p p nom · T nom T 1 ] ( n nom 1 ) ,
f f = f i + ( Δ m long c 2 L i long Δ m short c 2 L i short ) 1 + Δ n n i ,

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