Abstract

We report precision measurements of the refractive indices of dry air, N2, O2, Ar, and CO2, performed by using a frequency comb as the light source in a Mach–Zehnder interferometer setup. Improved dispersion formulas for all gases are derived with a sensitivity level of 109. These results are valid for a wavelength range from 740 to 860nm and are in good agreement with measurements from other groups.

© 2008 Optical Society of America

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References

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  1. N. Bobroff, “Recent advances in displacement measuring interferometry,” Meas. Sci. Technol. 4, 907-926 (1993).
    [CrossRef]
  2. W. C. Swann and N. R. Newbury, “Frequency-resolved coherent lidar using a femtosecond fiber laser,” Opt. Lett. 31, 826-828 (2006).
    [CrossRef] [PubMed]
  3. J. Zhang, Z. H. Lu, and L. J. Wang, “Precision measurement of the refractive index of air with frequency combs,” Opt. Lett. 30, 3314-3316 (2005).
    [CrossRef]
  4. 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]
  5. J. Zhang, Z. H. Lu, and L. J. Wang, “Precision measurement of the refractive index of carbon dioxide with a frequency comb,” Opt. Lett. 32, 3212-3214 (2007).
    [CrossRef] [PubMed]
  6. A. Couairon, J. Biegert, C. P. Hauri, W. Kornelis, F. W. Helbing, U. Keller, and A. Mysyrowicz, “Self-compression of ultra-short laser pulses down to one optical cycle by filamentation,” J. Mod. Opt. 53, 75-85 (2006).
    [CrossRef]
  7. K. P. Birch, M. J. Downs, and D. H. Ferriss, “Optical path length changes induced in cell windows and solid etalons by evacuation,” J. Phys. E 21, 690-692 (1988).
    [CrossRef]
  8. J. Ye, “Absolute measurement of a long, arbitrary distance to less than an optical fringe,” Opt. Lett. 29, 1153-1155(2004).
    [CrossRef] [PubMed]
  9. 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]
  10. B. Edlén, “The refractive index of air,” Metrologia 2, 71-80(1966).
    [CrossRef]
  11. R. Muijlwijk, “Update of the Edlén formulae for the refractive index of air,” Metrologia 25, 189 (1988).
    [CrossRef]
  12. K. P. Birch and M. J. Downs, “An updated Edlén equation for the refractive index of air,” Metrologia 30, 155-162 (1993).
    [CrossRef]
  13. 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]
  14. K. P. Birch, “Precise determination of refractometric parameters for atmospheric gases,” J. Opt. Soc. Am. A 8, 647-651(1991).
    [CrossRef]
  15. P. E. Ciddor, “Refractive index of air: new equations for the visible and near infrared,” Appl. Opt. 35, 1566-1573(1996).
    [CrossRef] [PubMed]
  16. J. D. Wright, “Gas property equations for the NIST fluid flow group gas flow measurement calibration services” (National Institute of Standards and Technology, 2004), http://www.cstl.nist.gov/div836/836.01/PDFs/2004/Gas_Properties.pdf.
  17. C. E. Bennett, “Precise measurements of dispersion in nitrogen,” Phys. Rev. 45, 200-207 (1934).
    [CrossRef]
  18. C. E. Bennett, “Optical dispersion and molar refraction at zero frequency for compressed nitrogen, argon, and carbon dioxide measured as functions of density,” Phys. Rev. 58, 263-266(1940).
    [CrossRef]
  19. E. R. Peck and B. N. Khanna, “Dispersion of nitrogen,” J. Opt. Soc. Am. 56, 1059-1063 (1966).
    [CrossRef]
  20. C. C. Bradley and H. A. Gebbie, “Refractive index of nitrogen, water vapor, and their mixtures at submillimeter wavelengths,” Appl. Opt. 10, 755-785 (1971).
    [CrossRef] [PubMed]
  21. U. Griesmann and J. H. Burnett, “Refractivity of nitrogen gas in the vacuum ultraviolet,” Opt. Lett. 24, 1699-1701 (1999).
    [CrossRef]
  22. J. T. Howell, “Index of refraction of gases,” Phys. Rev. 6, 81-93(1915).
    [CrossRef]
  23. J. Hilsenrath, C. W. Beckett, W. S. Benedict, L. Fano, H. J. Hoge, J. F. Masi, R. L. Nuttall, Y. S. Touloukian, and H. W. Woolley, eds., Tables of Thermal Properties of Gases, Natl. Bur. Std. (U.S.) Circ. 564 (U.S. Government Printing Office, 1955).
  24. E. R. Peck and D. J. Fisher, “Dispersion of argon,” J. Opt. Soc. Am. 54, 1362-1364 (1964).
    [CrossRef]
  25. J. G. Old, K. L. Gentili, and E. R. Peck, “Dispersion of carbon dioxide,” J. Opt. Soc. Am. 61, 89-90 (1971).
    [CrossRef]
  26. C. Cuthbertson and M. Cuthbertson, “On the refraction and dispersion of carbon dioxide, carbon monoxide, and methane,” Proc. R. Soc. London A 97, 152-159 (1920).
    [CrossRef]
  27. A. Bideau-Mehu, Y. Guern, R. Abjean, and A. Johannin-Gilles, “Interferometric determination of the refractive index of carbon dioxide in the ultraviolet region,” Opt. Commun. 9, 432-434 (1973).
    [CrossRef]
  28. A. C. Simmons, “The refractive index and Lorentz-Lorenz functions of propane, nitrogen and carbon-dioxide in the spectral range 15 803-22 002 cm−1 and at 944 cm−1,” Opt. Commun. 25, 211-214 (1978).
    [CrossRef]

2007 (1)

2006 (3)

A. Couairon, J. Biegert, C. P. Hauri, W. Kornelis, F. W. Helbing, U. Keller, and A. Mysyrowicz, “Self-compression of ultra-short laser pulses down to one optical cycle by filamentation,” J. Mod. Opt. 53, 75-85 (2006).
[CrossRef]

W. C. Swann and N. R. Newbury, “Frequency-resolved coherent lidar using a femtosecond fiber laser,” Opt. Lett. 31, 826-828 (2006).
[CrossRef] [PubMed]

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)

1999 (1)

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 (1)

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]

1993 (2)

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

N. Bobroff, “Recent advances in displacement measuring interferometry,” Meas. Sci. Technol. 4, 907-926 (1993).
[CrossRef]

1991 (1)

1988 (2)

R. Muijlwijk, “Update of the Edlén formulae for the refractive index of air,” Metrologia 25, 189 (1988).
[CrossRef]

K. P. Birch, M. J. Downs, and D. H. Ferriss, “Optical path length changes induced in cell windows and solid etalons by evacuation,” J. Phys. E 21, 690-692 (1988).
[CrossRef]

1978 (1)

A. C. Simmons, “The refractive index and Lorentz-Lorenz functions of propane, nitrogen and carbon-dioxide in the spectral range 15 803-22 002 cm−1 and at 944 cm−1,” Opt. Commun. 25, 211-214 (1978).
[CrossRef]

1973 (1)

A. Bideau-Mehu, Y. Guern, R. Abjean, and A. Johannin-Gilles, “Interferometric determination of the refractive index of carbon dioxide in the ultraviolet region,” Opt. Commun. 9, 432-434 (1973).
[CrossRef]

1971 (2)

1966 (2)

1964 (1)

1940 (1)

C. E. Bennett, “Optical dispersion and molar refraction at zero frequency for compressed nitrogen, argon, and carbon dioxide measured as functions of density,” Phys. Rev. 58, 263-266(1940).
[CrossRef]

1934 (1)

C. E. Bennett, “Precise measurements of dispersion in nitrogen,” Phys. Rev. 45, 200-207 (1934).
[CrossRef]

1920 (1)

C. Cuthbertson and M. Cuthbertson, “On the refraction and dispersion of carbon dioxide, carbon monoxide, and methane,” Proc. R. Soc. London A 97, 152-159 (1920).
[CrossRef]

1915 (1)

J. T. Howell, “Index of refraction of gases,” Phys. Rev. 6, 81-93(1915).
[CrossRef]

Abjean, R.

A. Bideau-Mehu, Y. Guern, R. Abjean, and A. Johannin-Gilles, “Interferometric determination of the refractive index of carbon dioxide in the ultraviolet region,” Opt. Commun. 9, 432-434 (1973).
[CrossRef]

Bennett, C. E.

C. E. Bennett, “Optical dispersion and molar refraction at zero frequency for compressed nitrogen, argon, and carbon dioxide measured as functions of density,” Phys. Rev. 58, 263-266(1940).
[CrossRef]

C. E. Bennett, “Precise measurements of dispersion in nitrogen,” Phys. Rev. 45, 200-207 (1934).
[CrossRef]

Bideau-Mehu, A.

A. Bideau-Mehu, Y. Guern, R. Abjean, and A. Johannin-Gilles, “Interferometric determination of the refractive index of carbon dioxide in the ultraviolet region,” Opt. Commun. 9, 432-434 (1973).
[CrossRef]

Biegert, J.

A. Couairon, J. Biegert, C. P. Hauri, W. Kornelis, F. W. Helbing, U. Keller, and A. Mysyrowicz, “Self-compression of ultra-short laser pulses down to one optical cycle by filamentation,” J. Mod. Opt. 53, 75-85 (2006).
[CrossRef]

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]

K. P. Birch, M. J. Downs, and D. H. Ferriss, “Optical path length changes induced in cell windows and solid etalons by evacuation,” J. Phys. E 21, 690-692 (1988).
[CrossRef]

Bobroff, N.

N. Bobroff, “Recent advances in displacement measuring interferometry,” Meas. Sci. Technol. 4, 907-926 (1993).
[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]

Bradley, C. C.

Burnett, J. H.

Ciddor, P. E.

Couairon, A.

A. Couairon, J. Biegert, C. P. Hauri, W. Kornelis, F. W. Helbing, U. Keller, and A. Mysyrowicz, “Self-compression of ultra-short laser pulses down to one optical cycle by filamentation,” J. Mod. Opt. 53, 75-85 (2006).
[CrossRef]

Cuthbertson, C.

C. Cuthbertson and M. Cuthbertson, “On the refraction and dispersion of carbon dioxide, carbon monoxide, and methane,” Proc. R. Soc. London A 97, 152-159 (1920).
[CrossRef]

Cuthbertson, M.

C. Cuthbertson and M. Cuthbertson, “On the refraction and dispersion of carbon dioxide, carbon monoxide, and methane,” Proc. R. Soc. London A 97, 152-159 (1920).
[CrossRef]

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]

K. P. Birch, M. J. Downs, and D. H. Ferriss, “Optical path length changes induced in cell windows and solid etalons by evacuation,” J. Phys. E 21, 690-692 (1988).
[CrossRef]

Edlén, B.

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

Ferriss, D. H.

K. P. Birch, M. J. Downs, and D. H. Ferriss, “Optical path length changes induced in cell windows and solid etalons by evacuation,” J. Phys. E 21, 690-692 (1988).
[CrossRef]

Fisher, D. J.

Gebbie, H. A.

Gentili, K. L.

Griesmann, U.

Guern, Y.

A. Bideau-Mehu, Y. Guern, R. Abjean, and A. Johannin-Gilles, “Interferometric determination of the refractive index of carbon dioxide in the ultraviolet region,” Opt. Commun. 9, 432-434 (1973).
[CrossRef]

Hauri, C. P.

A. Couairon, J. Biegert, C. P. Hauri, W. Kornelis, F. W. Helbing, U. Keller, and A. Mysyrowicz, “Self-compression of ultra-short laser pulses down to one optical cycle by filamentation,” J. Mod. Opt. 53, 75-85 (2006).
[CrossRef]

Helbing, F. W.

A. Couairon, J. Biegert, C. P. Hauri, W. Kornelis, F. W. Helbing, U. Keller, and A. Mysyrowicz, “Self-compression of ultra-short laser pulses down to one optical cycle by filamentation,” J. Mod. Opt. 53, 75-85 (2006).
[CrossRef]

Howell, J. T.

J. T. Howell, “Index of refraction of gases,” Phys. Rev. 6, 81-93(1915).
[CrossRef]

Johannin-Gilles, A.

A. Bideau-Mehu, Y. Guern, R. Abjean, and A. Johannin-Gilles, “Interferometric determination of the refractive index of carbon dioxide in the ultraviolet region,” Opt. Commun. 9, 432-434 (1973).
[CrossRef]

Keller, U.

A. Couairon, J. Biegert, C. P. Hauri, W. Kornelis, F. W. Helbing, U. Keller, and A. Mysyrowicz, “Self-compression of ultra-short laser pulses down to one optical cycle by filamentation,” J. Mod. Opt. 53, 75-85 (2006).
[CrossRef]

Khanna, B. N.

Kornelis, W.

A. Couairon, J. Biegert, C. P. Hauri, W. Kornelis, F. W. Helbing, U. Keller, and A. Mysyrowicz, “Self-compression of ultra-short laser pulses down to one optical cycle by filamentation,” J. Mod. Opt. 53, 75-85 (2006).
[CrossRef]

Lu, Z. 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]

Muijlwijk, R.

R. Muijlwijk, “Update of the Edlén formulae for the refractive index of air,” Metrologia 25, 189 (1988).
[CrossRef]

Mysyrowicz, A.

A. Couairon, J. Biegert, C. P. Hauri, W. Kornelis, F. W. Helbing, U. Keller, and A. Mysyrowicz, “Self-compression of ultra-short laser pulses down to one optical cycle by filamentation,” J. Mod. Opt. 53, 75-85 (2006).
[CrossRef]

Newbury, N. R.

Old, J. G.

Peck, E. 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]

Simmons, A. C.

A. C. Simmons, “The refractive index and Lorentz-Lorenz functions of propane, nitrogen and carbon-dioxide in the spectral range 15 803-22 002 cm−1 and at 944 cm−1,” Opt. Commun. 25, 211-214 (1978).
[CrossRef]

Swann, W. C.

Wang, L. J.

Wright, J. D.

J. D. Wright, “Gas property equations for the NIST fluid flow group gas flow measurement calibration services” (National Institute of Standards and Technology, 2004), http://www.cstl.nist.gov/div836/836.01/PDFs/2004/Gas_Properties.pdf.

Ye, J.

Zhang, J.

Appl. Opt. (2)

J. Mod. Opt. (1)

A. Couairon, J. Biegert, C. P. Hauri, W. Kornelis, F. W. Helbing, U. Keller, and A. Mysyrowicz, “Self-compression of ultra-short laser pulses down to one optical cycle by filamentation,” J. Mod. Opt. 53, 75-85 (2006).
[CrossRef]

J. Opt. Soc. Am. (3)

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

J. Phys. E (1)

K. P. Birch, M. J. Downs, and D. H. Ferriss, “Optical path length changes induced in cell windows and solid etalons by evacuation,” J. Phys. E 21, 690-692 (1988).
[CrossRef]

Meas. Sci. Technol. (1)

N. Bobroff, “Recent advances in displacement measuring interferometry,” Meas. Sci. Technol. 4, 907-926 (1993).
[CrossRef]

Metrologia (5)

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]

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

R. Muijlwijk, “Update of the Edlén formulae for the refractive index of air,” Metrologia 25, 189 (1988).
[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. (2)

A. Bideau-Mehu, Y. Guern, R. Abjean, and A. Johannin-Gilles, “Interferometric determination of the refractive index of carbon dioxide in the ultraviolet region,” Opt. Commun. 9, 432-434 (1973).
[CrossRef]

A. C. Simmons, “The refractive index and Lorentz-Lorenz functions of propane, nitrogen and carbon-dioxide in the spectral range 15 803-22 002 cm−1 and at 944 cm−1,” Opt. Commun. 25, 211-214 (1978).
[CrossRef]

Opt. Lett. (5)

Phys. Rev. (3)

C. E. Bennett, “Precise measurements of dispersion in nitrogen,” Phys. Rev. 45, 200-207 (1934).
[CrossRef]

C. E. Bennett, “Optical dispersion and molar refraction at zero frequency for compressed nitrogen, argon, and carbon dioxide measured as functions of density,” Phys. Rev. 58, 263-266(1940).
[CrossRef]

J. T. Howell, “Index of refraction of gases,” Phys. Rev. 6, 81-93(1915).
[CrossRef]

Proc. R. Soc. London A (1)

C. Cuthbertson and M. Cuthbertson, “On the refraction and dispersion of carbon dioxide, carbon monoxide, and methane,” Proc. R. Soc. London A 97, 152-159 (1920).
[CrossRef]

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)

J. D. Wright, “Gas property equations for the NIST fluid flow group gas flow measurement calibration services” (National Institute of Standards and Technology, 2004), http://www.cstl.nist.gov/div836/836.01/PDFs/2004/Gas_Properties.pdf.

J. Hilsenrath, C. W. Beckett, W. S. Benedict, L. Fano, H. J. Hoge, J. F. Masi, R. L. Nuttall, Y. S. Touloukian, and H. W. Woolley, eds., Tables of Thermal Properties of Gases, Natl. Bur. Std. (U.S.) Circ. 564 (U.S. Government Printing Office, 1955).

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Figures (8)

Fig. 1
Fig. 1

Experimental setup. BS1, BS2, cube beam splitters; MPC, multipass cell; RR, retroreflector; L, lens; FC, fiber coupler; OSA, optical spectrum analyzer; PZT, piezoelectric transducer; PD1, PD2, photodiodes; PC, computer; HV Amp, high-voltage amplifier. The dashed line corresponds to the He–Ne laser optical path.

Fig. 2
Fig. 2

Interferograms in the time domain versus laser repetition rate when the multipass cell is filled with standard dry air or pumped out to a vacuum.

Fig. 3
Fig. 3

Interferograms in the frequency domain. The black solid curve shows spectral modulation, and the red dashed curve shows spectrum I 1 ˜ ( λ ) + I 2 ˜ ( λ ) .

Fig. 4
Fig. 4

Refractive index of dry air. Black dashed curve, Edlén’s result [4]; red solid curve, our experimental result. Each data point represents an average of 50 measurements. The error bar at 800 nm is 4.3 × 10 9 .

Fig. 5
Fig. 5

Refractive index of N 2 . Black dashed curve, Peck and Khanna’s result [19]; red solid curve, our experimental result. Each data point represents an average of 50 measurements. The error bar at 800 nm is 1.8 × 10 8 .

Fig. 6
Fig. 6

Refractive index of O 2 . The red dotted curve stands for our experimental result. The error bar at 800 nm is 1.0 × 10 8 . Birch’s result [14] is shown with a black circle, together with a corresponding error bar.

Fig. 7
Fig. 7

Refractive index of Ar. Black dashed curve, Peck and Fisher’s result [24]; red solid curve, our experimental result. The error bar at 800 nm is 6.1 × 10 9 .

Fig. 8
Fig. 8

Refractive index of CO 2 . Black dashed curve, result of Old et al. [25]; red solid curve, our experimental result. A typical error bar is 7.8 × 10 8 .

Tables (2)

Tables Icon

Table 1 Dispersion Formulas for Air, CO 2 , N 2 , O 2 , and Ar a

Tables Icon

Table 2 Refractivity Values of Air, CO 2 , N 2 , O 2 , and Ar for 800 and 632.99 nm a

Equations (33)

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

I ( τ ) | E 1 ( t τ ) | 2 + | E 2 ( t ) | 2 + E 1 ( t τ ) E 2 * ( t ) + E 1 * ( t τ ) E 2 ( t ) ,
τ = ( N / f 2 ) δ f ,
τ g = [ n g ( λ 0 ) 1 ] l cell c ,
I ˜ ( λ ) = I 1 ˜ ( λ ) + I 2 ˜ ( λ ) + 2 I 1 ˜ ( λ ) I 2 ˜ ( λ ) cos Φ ( λ ) ,
Φ air ( λ ) = 2 π [ n air ( λ ) l cell + n Δ l ] λ + ϕ ( λ ) .
Φ vac ( λ ) = 2 π ( l cell + n Δ l ) λ + ϕ ( λ ) ,
Δ Φ ( λ ) = Φ air ( λ ) Φ vac ( λ ) = 2 π [ n air ( λ ) 1 ] l cell λ .
d Δ Φ ( λ ) d λ = 2 π l cell [ n air ( λ ) λ d n air ( λ ) / d λ 1 ] λ 2 = 2 π l cell [ n g ( λ ) 1 ] λ 2 .
n gas ( λ ) = 1 + λ Δ Φ ( λ ) 2 π l cell .
Z air = 1 101 , 325 × ( 0.57409 0.0124784 t + 0.000066 t 2 ) × 10 - 8 ,
D air , tp = p 1 + p ( 0.621811 0.0126531 t + 0.000066 t 2 ) × 10 8 1 + 0.0036610 t ,
( n air 1 ) x = ( n air 1 ) s [ 1 + 0.5327 ( x 0.0004 ) ] .
( n air 1 ) s = 94,449.94 D air , tp 1 [ 1 + 0.5327 ( x 0.0004 ) ] ( n air 1 ) tp .
( n air 1 ) s × 10 8 = 8015.514 + 2,368,616 128.7459 1 / λ 2 + 19,085.73 50.01974 1 / λ 2 .
Z N 2 = 1 101 , 325 × ( 0.449805 0.01177 t + 0.00006 t 2 ) × 10 8 .
D N 2 , t p = p 1 + p ( 0.498526 0.0119484 t + 0.00006 t 2 ) × 10 - 8 1 + 0.0036610 t .
( n N 2 1 ) s = 94,439.27 D N 2 , tp ( n N 2 1 ) tp .
( n N 2 1 ) s × 10 8 = 8736.28 + 2,398,095.2 128.7 1 / λ 2 .
Z O 2 = 1 101 , 325 × ( 0.93809 0.01460 t + 0.00007 t 2 ) × 10 8 .
D O 2 , tp = p × 1 + p ( 0.982463 0.0147624 t + 0.00007 t 2 ) × 10 8 1 + 0.0036610 t ,
( n O 2 1 ) s = 94,480.56 D O 2 , t p ( n O 2 1 ) tp .
( n O 2 1 ) s × 10 8 = 15,532.45 + 456,402.97 50.0 1 / λ 2 .
Z Ar = 1 101 , 325 × ( 0.93057 0.01400 t + 0.00007 t 2 ) × 10 8 .
D Ar , tp = p 1 + p ( 0.976579 0.0141684 t + 0.00007 t 2 ) × 10 8 1 + 0.0036610 t ,
( n Ar 1 ) s = 94 , 481.14 D Ar , tp × ( n Ar 1 ) tp .
( n Ar 1 ) s × 10 8 = 12 , 236.13 + 1 , 232 , 158.1 90.7 1 / λ 2 .
Z C O 2 = 1 101 , 325 × ( 6.64793 0.0775199 t + 0.0004250 t 2 ) × 10 8 .
D C O 2 , tp = p 1 + p ( 6.72112 0.0777879 t + 0.0004250 t 2 ) × 10 8 1 + 0.0036610 t ,
( n C O 2 1 ) s = 94,922.54 D CO 2 , t p ( n C O 2 1 ) tp .
( n CO 2 1 ) s × 10 8 = 7137.238 + 341,712.4 57.75340 1 / λ 2 + 6,946,980 248.5560 1 / λ 2 .
( n air 1 ) x = ( n air 1 ) s [ 1 + 0.5294 ( x 0.0004 ) ] .
L gas = n gas 2 1 n gas 2 + 2 ,
L air = C N 2 L N 2 + C O 2 L O 2 .

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