Abstract

The precision of modern length interferometry and geodetic surveying far exceeds the accuracy, which is ultimately limited by the inadequacy of currently used equations for the refractive index of the atmosphere. I have critically reviewed recent research at the National Physical Laboratory, the International Bureau of Weights and Measures, and elsewhere that has led to revised formulas and data for the dispersion and density of the major components of the atmosphere. I have combined selected formulas from these sources to yield a set of equations that match recently reported measurements to within the experimental error, and that are expected to be reliable over very wide ranges of atmospheric parameters and wavelength.

© 1996 Optical Society of America

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  1. B. Edlen, “The refractive index of air,” Metrologia 2, 71–80 (1966).
  2. B. Edlen, “The dispersion of standard air,” J. Opt. Soc. Am. 43, 339–344 (1953).
  3. K. P. Birch, M. J. Downs, “An updated Edlen equation for the refractive index of air,” Metrologia 30, 155–162 (1993).
  4. K. P. Birch, M. J. Downs, “Correction to the updated Edlen equation for the refractive index of air,” Metrologia 31, 315–316 (1994).
  5. W. Hou, R. Thalmann, “Accurate measurement of the refractive index of air,” Measurement 13, 307–314 (1994).
  6. P. Schellekens, G. Wilkening, F. Reinboth, M. J. Downs, K. P. Birch, J. Spronck, “Measurements of the refractive index of air using interference refractometers,” Metrologia 22, 279–287 (1986).
  7. J. C. Owens, “Optical refractive index of air: dependence on pressure, temperature and composition,” Appl. Opt. 6, 51–59 (1967).
  8. E. R. Peck, K. Reeder, “Dispersion of air,” J. Opt. Soc. Am. 62, 958–962 (1972).
  9. K. E. Erickson, “Investigation of the invariance of atmospheric dispersion with a long-path interferometer,” J. Opt. Soc. Am. 52, 777–780 (1962).
  10. H. Barrell, J. E. Sears, “The refraction and dispersion of air for the visible spectrum,” Philos. Trans. R. Soc. London Ser. A 238, 1–64 (1939).
  11. K. P. Birch, M. J. Downs, “The precise determination of the refractive index of air,” Rep. MOM90 (National Physical Laboratory, Teddington, U.K., 1988), p. 35.
  12. J. Beers, T. Doiron, “Verification of revised water vapour correction to the refractive index of air,” Metrologia 29, 315–316 (1992).
  13. R. Mujlwijk, “Update of the Edlen formulae for the refractive index of air,” Metrologia 25, 189 (1988);C. Rischel, P. S. Ramanujam, “Refractive index of air—errata,” Metrologia 26, 263 (1989).
  14. F. E. Jones, “The refractivity of air,” J. Res. Natl. Bur. Stand. 86, 27–32 (1981).
  15. F. E. Jones, “Simplified equation for calculating the refractivity of air,” Appl. Opt. 19, 4129–4130 (1980).
  16. R. J. Hill, “Refractive index of atmospheric gases,” in The Upper Atmosphere, W. Diemenger, G. Hartmann, R. Leitinger, eds. (Springer-Verlag, Berlin, 1995).
  17. S. P. Velsko, D. Eimerl, “Precise measurements of optical dispersion using a new interferometric technique,” Appl. Opt. 25, 1344–1349 (1986).
  18. E. R. Peck, “Precise measurements of optical dispersion using a new interferometric technique: comment,” Appl. Opt. 25, 3597–3598 (1986).
  19. C. Cuthbertson, M. Cuthbertson, “On the refraction and dispersion of carbon dioxide, carbon monoxide, and methane,” Proc. R. Soc. London Ser.A 97, 152–159 (1920).
  20. J. G. Old, K. L. Gentili, E. R. Peck, “Dispersion of carbon dioxide,” J. Opt. Soc. Am. 61, 89–90 (1971).
  21. A. C. Simmons, “The refractive index and Lorentz-Lorenz functions of propane, nitrogen and carbon-dioxide in the spectral range 15803–22002cm−1 and at 944 cm−1,” Opt. Commun. 25, 211–214 (1978).
  22. P. Schiebener, J. Straub, J. M. H. Levelt Sengers, J. S. Gallagher, “Refractive index of water and steam as function of wavelength, temperature, and density,” J. Phys. Chem. Ref. Data 19, 677–715 (1990).
  23. P. Giacomo, “Equation for the determination of the density of moist air (1981),” Metrologia 18, 33–40 (1982).
  24. R. S. Davis, “Equation for the determination of the density of moist air (1981/1991),” Metrologia 29, 67–70 (1992).
  25. E. C. Morris, CSIRO Division of Applied Physics, Lindfield, N.S.W., Australia 2070 (personal communication, 1995).
  26. K. B. Earnshaw, J. C. Owens, “A dual wavelength optical distance measuring instrument which corrects for air density,” IEEE J. Quantum Electron. QE-3, 544–550 (1967).
  27. E. C. MorrisMATHCAD software package, Mathsoft Inc., Cambridge, Mass. 02139.
  28. J. M. Rueger, P. E. Ciddor, “Refractive index of air: new equations for the visible and near infrared,” presented at the Twenty-first General Assembly of the International Association of Geodesy and Geophysics, Boulder, Colo., 2–14 July 1995.
  29. J. Terrien, “An air refractometer for interference length metrology,” Metrologia 1, 80–83 (1965).
  30. K. P. Birch, F. Reinboth, R. E. Ward, G. Wilkening, “The effect of variations in the refractive index of industrial air upon the uncertainty of precision length measurement,” Metrologia 30, 7–14 (1993).
  31. “Report to BIPM on international intercomparison of line standard scales,” Cal. Rep. NML2941/2942 (National Measurement Laboratory Commonwealth Scientific and Industrial Research Organization, Lindfield, Australia, 1978).
  32. Y. Galkin, R. A. Tatevian, “Resonances influence on the phase and group refractive indices of the air,” presented at the Twenty-First General Assembly of the International Association of Geodesy and Geophysics, Boulder, Colo., 2–14 July 1995.
  33. Y. Galkin, R. A. Tatevian, “The problem of obtaining the formulas of the refractive indices of the air for high precision EDM,” presented at the Twenty-First General Assembly of the International Association of Geodesy and Geophysics, Boulder, Colo., 2–14 July 1995.
  34. R. W. Hyland, A. Wexler, “Formulations for the thermodynamic properties of the saturated phases of H2O from 173.15 K to 473.15 K,”ASHRAE Trans. 89, 500–511 (1983).
  35. G. Jancso, J. Pupezin, W. A. Van Hook, “The vapor pressure of ice between +102 and −10+2,” J. Phys. Chem. 74, 2984–2989 (1970).
  36. J. Marti, K. Mauersberger, “A survey and new measurements of ice vapor pressure at temperatures between 170 and 250 K,” Geophys. Res. Lett. 20, 363–366 (1993).

1994 (2)

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

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

1993 (3)

K. P. Birch, F. Reinboth, R. E. Ward, G. Wilkening, “The effect of variations in the refractive index of industrial air upon the uncertainty of precision length measurement,” Metrologia 30, 7–14 (1993).

J. Marti, K. Mauersberger, “A survey and new measurements of ice vapor pressure at temperatures between 170 and 250 K,” Geophys. Res. Lett. 20, 363–366 (1993).

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

1992 (2)

R. S. Davis, “Equation for the determination of the density of moist air (1981/1991),” Metrologia 29, 67–70 (1992).

J. Beers, T. Doiron, “Verification of revised water vapour correction to the refractive index of air,” Metrologia 29, 315–316 (1992).

1990 (1)

P. Schiebener, J. Straub, J. M. H. Levelt Sengers, J. S. Gallagher, “Refractive index of water and steam as function of wavelength, temperature, and density,” J. Phys. Chem. Ref. Data 19, 677–715 (1990).

1988 (1)

R. Mujlwijk, “Update of the Edlen formulae for the refractive index of air,” Metrologia 25, 189 (1988);C. Rischel, P. S. Ramanujam, “Refractive index of air—errata,” Metrologia 26, 263 (1989).

1986 (3)

P. Schellekens, G. Wilkening, F. Reinboth, M. J. Downs, K. P. Birch, J. Spronck, “Measurements of the refractive index of air using interference refractometers,” Metrologia 22, 279–287 (1986).

S. P. Velsko, D. Eimerl, “Precise measurements of optical dispersion using a new interferometric technique,” Appl. Opt. 25, 1344–1349 (1986).

E. R. Peck, “Precise measurements of optical dispersion using a new interferometric technique: comment,” Appl. Opt. 25, 3597–3598 (1986).

1983 (1)

R. W. Hyland, A. Wexler, “Formulations for the thermodynamic properties of the saturated phases of H2O from 173.15 K to 473.15 K,”ASHRAE Trans. 89, 500–511 (1983).

1982 (1)

P. Giacomo, “Equation for the determination of the density of moist air (1981),” Metrologia 18, 33–40 (1982).

1981 (1)

F. E. Jones, “The refractivity of air,” J. Res. Natl. Bur. Stand. 86, 27–32 (1981).

1980 (1)

1978 (1)

A. C. Simmons, “The refractive index and Lorentz-Lorenz functions of propane, nitrogen and carbon-dioxide in the spectral range 15803–22002cm−1 and at 944 cm−1,” Opt. Commun. 25, 211–214 (1978).

1972 (1)

1971 (1)

1970 (1)

G. Jancso, J. Pupezin, W. A. Van Hook, “The vapor pressure of ice between +102 and −10+2,” J. Phys. Chem. 74, 2984–2989 (1970).

1967 (2)

K. B. Earnshaw, J. C. Owens, “A dual wavelength optical distance measuring instrument which corrects for air density,” IEEE J. Quantum Electron. QE-3, 544–550 (1967).

J. C. Owens, “Optical refractive index of air: dependence on pressure, temperature and composition,” Appl. Opt. 6, 51–59 (1967).

1966 (1)

B. Edlen, “The refractive index of air,” Metrologia 2, 71–80 (1966).

1965 (1)

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

1962 (1)

1953 (1)

1939 (1)

H. Barrell, J. E. Sears, “The refraction and dispersion of air for the visible spectrum,” Philos. Trans. R. Soc. London Ser. A 238, 1–64 (1939).

1920 (1)

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

Barrell, H.

H. Barrell, J. E. Sears, “The refraction and dispersion of air for the visible spectrum,” Philos. Trans. R. Soc. London Ser. A 238, 1–64 (1939).

Beers, J.

J. Beers, T. Doiron, “Verification of revised water vapour correction to the refractive index of air,” Metrologia 29, 315–316 (1992).

Birch, K. P.

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

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

K. P. Birch, F. Reinboth, R. E. Ward, G. Wilkening, “The effect of variations in the refractive index of industrial air upon the uncertainty of precision length measurement,” Metrologia 30, 7–14 (1993).

P. Schellekens, G. Wilkening, F. Reinboth, M. J. Downs, K. P. Birch, J. Spronck, “Measurements of the refractive index of air using interference refractometers,” Metrologia 22, 279–287 (1986).

K. P. Birch, M. J. Downs, “The precise determination of the refractive index of air,” Rep. MOM90 (National Physical Laboratory, Teddington, U.K., 1988), p. 35.

Ciddor, P. E.

J. M. Rueger, P. E. Ciddor, “Refractive index of air: new equations for the visible and near infrared,” presented at the Twenty-first General Assembly of the International Association of Geodesy and Geophysics, Boulder, Colo., 2–14 July 1995.

Cuthbertson, C.

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

Cuthbertson, M.

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

Davis, R. S.

R. S. Davis, “Equation for the determination of the density of moist air (1981/1991),” Metrologia 29, 67–70 (1992).

Doiron, T.

J. Beers, T. Doiron, “Verification of revised water vapour correction to the refractive index of air,” Metrologia 29, 315–316 (1992).

Downs, M. J.

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

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

P. Schellekens, G. Wilkening, F. Reinboth, M. J. Downs, K. P. Birch, J. Spronck, “Measurements of the refractive index of air using interference refractometers,” Metrologia 22, 279–287 (1986).

K. P. Birch, M. J. Downs, “The precise determination of the refractive index of air,” Rep. MOM90 (National Physical Laboratory, Teddington, U.K., 1988), p. 35.

Earnshaw, K. B.

K. B. Earnshaw, J. C. Owens, “A dual wavelength optical distance measuring instrument which corrects for air density,” IEEE J. Quantum Electron. QE-3, 544–550 (1967).

Edlen, B.

B. Edlen, “The refractive index of air,” Metrologia 2, 71–80 (1966).

B. Edlen, “The dispersion of standard air,” J. Opt. Soc. Am. 43, 339–344 (1953).

Eimerl, D.

Erickson, K. E.

Galkin, Y.

Y. Galkin, R. A. Tatevian, “Resonances influence on the phase and group refractive indices of the air,” presented at the Twenty-First General Assembly of the International Association of Geodesy and Geophysics, Boulder, Colo., 2–14 July 1995.

Y. Galkin, R. A. Tatevian, “The problem of obtaining the formulas of the refractive indices of the air for high precision EDM,” presented at the Twenty-First General Assembly of the International Association of Geodesy and Geophysics, Boulder, Colo., 2–14 July 1995.

Gallagher, J. S.

P. Schiebener, J. Straub, J. M. H. Levelt Sengers, J. S. Gallagher, “Refractive index of water and steam as function of wavelength, temperature, and density,” J. Phys. Chem. Ref. Data 19, 677–715 (1990).

Gentili, K. L.

Giacomo, P.

P. Giacomo, “Equation for the determination of the density of moist air (1981),” Metrologia 18, 33–40 (1982).

Hill, R. J.

R. J. Hill, “Refractive index of atmospheric gases,” in The Upper Atmosphere, W. Diemenger, G. Hartmann, R. Leitinger, eds. (Springer-Verlag, Berlin, 1995).

Hou, W.

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

Hyland, R. W.

R. W. Hyland, A. Wexler, “Formulations for the thermodynamic properties of the saturated phases of H2O from 173.15 K to 473.15 K,”ASHRAE Trans. 89, 500–511 (1983).

Jancso, G.

G. Jancso, J. Pupezin, W. A. Van Hook, “The vapor pressure of ice between +102 and −10+2,” J. Phys. Chem. 74, 2984–2989 (1970).

Jones, F. E.

F. E. Jones, “The refractivity of air,” J. Res. Natl. Bur. Stand. 86, 27–32 (1981).

F. E. Jones, “Simplified equation for calculating the refractivity of air,” Appl. Opt. 19, 4129–4130 (1980).

Levelt Sengers, J. M. H.

P. Schiebener, J. Straub, J. M. H. Levelt Sengers, J. S. Gallagher, “Refractive index of water and steam as function of wavelength, temperature, and density,” J. Phys. Chem. Ref. Data 19, 677–715 (1990).

Marti, J.

J. Marti, K. Mauersberger, “A survey and new measurements of ice vapor pressure at temperatures between 170 and 250 K,” Geophys. Res. Lett. 20, 363–366 (1993).

Mauersberger, K.

J. Marti, K. Mauersberger, “A survey and new measurements of ice vapor pressure at temperatures between 170 and 250 K,” Geophys. Res. Lett. 20, 363–366 (1993).

Morris, E. C.

E. C. MorrisMATHCAD software package, Mathsoft Inc., Cambridge, Mass. 02139.

E. C. Morris, CSIRO Division of Applied Physics, Lindfield, N.S.W., Australia 2070 (personal communication, 1995).

Mujlwijk, R.

R. Mujlwijk, “Update of the Edlen formulae for the refractive index of air,” Metrologia 25, 189 (1988);C. Rischel, P. S. Ramanujam, “Refractive index of air—errata,” Metrologia 26, 263 (1989).

Old, J. G.

Owens, J. C.

J. C. Owens, “Optical refractive index of air: dependence on pressure, temperature and composition,” Appl. Opt. 6, 51–59 (1967).

K. B. Earnshaw, J. C. Owens, “A dual wavelength optical distance measuring instrument which corrects for air density,” IEEE J. Quantum Electron. QE-3, 544–550 (1967).

Peck, E. R.

Pupezin, J.

G. Jancso, J. Pupezin, W. A. Van Hook, “The vapor pressure of ice between +102 and −10+2,” J. Phys. Chem. 74, 2984–2989 (1970).

Reeder, K.

Reinboth, F.

K. P. Birch, F. Reinboth, R. E. Ward, G. Wilkening, “The effect of variations in the refractive index of industrial air upon the uncertainty of precision length measurement,” Metrologia 30, 7–14 (1993).

P. Schellekens, G. Wilkening, F. Reinboth, M. J. Downs, K. P. Birch, J. Spronck, “Measurements of the refractive index of air using interference refractometers,” Metrologia 22, 279–287 (1986).

Rueger, J. M.

J. M. Rueger, P. E. Ciddor, “Refractive index of air: new equations for the visible and near infrared,” presented at the Twenty-first General Assembly of the International Association of Geodesy and Geophysics, Boulder, Colo., 2–14 July 1995.

Schellekens, P.

P. Schellekens, G. Wilkening, F. Reinboth, M. J. Downs, K. P. Birch, J. Spronck, “Measurements of the refractive index of air using interference refractometers,” Metrologia 22, 279–287 (1986).

Schiebener, P.

P. Schiebener, J. Straub, J. M. H. Levelt Sengers, J. S. Gallagher, “Refractive index of water and steam as function of wavelength, temperature, and density,” J. Phys. Chem. Ref. Data 19, 677–715 (1990).

Sears, J. E.

H. Barrell, J. E. Sears, “The refraction and dispersion of air for the visible spectrum,” Philos. Trans. R. Soc. London Ser. A 238, 1–64 (1939).

Simmons, A. C.

A. C. Simmons, “The refractive index and Lorentz-Lorenz functions of propane, nitrogen and carbon-dioxide in the spectral range 15803–22002cm−1 and at 944 cm−1,” Opt. Commun. 25, 211–214 (1978).

Spronck, J.

P. Schellekens, G. Wilkening, F. Reinboth, M. J. Downs, K. P. Birch, J. Spronck, “Measurements of the refractive index of air using interference refractometers,” Metrologia 22, 279–287 (1986).

Straub, J.

P. Schiebener, J. Straub, J. M. H. Levelt Sengers, J. S. Gallagher, “Refractive index of water and steam as function of wavelength, temperature, and density,” J. Phys. Chem. Ref. Data 19, 677–715 (1990).

Tatevian, R. A.

Y. Galkin, R. A. Tatevian, “The problem of obtaining the formulas of the refractive indices of the air for high precision EDM,” presented at the Twenty-First General Assembly of the International Association of Geodesy and Geophysics, Boulder, Colo., 2–14 July 1995.

Y. Galkin, R. A. Tatevian, “Resonances influence on the phase and group refractive indices of the air,” presented at the Twenty-First General Assembly of the International Association of Geodesy and Geophysics, Boulder, Colo., 2–14 July 1995.

Terrien, J.

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

Thalmann, R.

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

Van Hook, W. A.

G. Jancso, J. Pupezin, W. A. Van Hook, “The vapor pressure of ice between +102 and −10+2,” J. Phys. Chem. 74, 2984–2989 (1970).

Velsko, S. P.

Ward, R. E.

K. P. Birch, F. Reinboth, R. E. Ward, G. Wilkening, “The effect of variations in the refractive index of industrial air upon the uncertainty of precision length measurement,” Metrologia 30, 7–14 (1993).

Wexler, A.

R. W. Hyland, A. Wexler, “Formulations for the thermodynamic properties of the saturated phases of H2O from 173.15 K to 473.15 K,”ASHRAE Trans. 89, 500–511 (1983).

Wilkening, G.

K. P. Birch, F. Reinboth, R. E. Ward, G. Wilkening, “The effect of variations in the refractive index of industrial air upon the uncertainty of precision length measurement,” Metrologia 30, 7–14 (1993).

P. Schellekens, G. Wilkening, F. Reinboth, M. J. Downs, K. P. Birch, J. Spronck, “Measurements of the refractive index of air using interference refractometers,” Metrologia 22, 279–287 (1986).

Appl. Opt. (4)

ASHRAE Trans. (1)

R. W. Hyland, A. Wexler, “Formulations for the thermodynamic properties of the saturated phases of H2O from 173.15 K to 473.15 K,”ASHRAE Trans. 89, 500–511 (1983).

Geophys. Res. Lett. (1)

J. Marti, K. Mauersberger, “A survey and new measurements of ice vapor pressure at temperatures between 170 and 250 K,” Geophys. Res. Lett. 20, 363–366 (1993).

IEEE J. Quantum Electron. (1)

K. B. Earnshaw, J. C. Owens, “A dual wavelength optical distance measuring instrument which corrects for air density,” IEEE J. Quantum Electron. QE-3, 544–550 (1967).

J. Opt. Soc. Am. (4)

J. Phys. Chem. (1)

G. Jancso, J. Pupezin, W. A. Van Hook, “The vapor pressure of ice between +102 and −10+2,” J. Phys. Chem. 74, 2984–2989 (1970).

J. Phys. Chem. Ref. Data (1)

P. Schiebener, J. Straub, J. M. H. Levelt Sengers, J. S. Gallagher, “Refractive index of water and steam as function of wavelength, temperature, and density,” J. Phys. Chem. Ref. Data 19, 677–715 (1990).

J. Res. Natl. Bur. Stand. (1)

F. E. Jones, “The refractivity of air,” J. Res. Natl. Bur. Stand. 86, 27–32 (1981).

Measurement (1)

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

Metrologia (10)

P. Schellekens, G. Wilkening, F. Reinboth, M. J. Downs, K. P. Birch, J. Spronck, “Measurements of the refractive index of air using interference refractometers,” Metrologia 22, 279–287 (1986).

P. Giacomo, “Equation for the determination of the density of moist air (1981),” Metrologia 18, 33–40 (1982).

R. S. Davis, “Equation for the determination of the density of moist air (1981/1991),” Metrologia 29, 67–70 (1992).

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

K. P. Birch, F. Reinboth, R. E. Ward, G. Wilkening, “The effect of variations in the refractive index of industrial air upon the uncertainty of precision length measurement,” Metrologia 30, 7–14 (1993).

B. Edlen, “The refractive index of air,” Metrologia 2, 71–80 (1966).

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

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

J. Beers, T. Doiron, “Verification of revised water vapour correction to the refractive index of air,” Metrologia 29, 315–316 (1992).

R. Mujlwijk, “Update of the Edlen formulae for the refractive index of air,” Metrologia 25, 189 (1988);C. Rischel, P. S. Ramanujam, “Refractive index of air—errata,” Metrologia 26, 263 (1989).

Opt. Commun. (1)

A. C. Simmons, “The refractive index and Lorentz-Lorenz functions of propane, nitrogen and carbon-dioxide in the spectral range 15803–22002cm−1 and at 944 cm−1,” Opt. Commun. 25, 211–214 (1978).

Philos. Trans. R. Soc. London Ser. A (1)

H. Barrell, J. E. Sears, “The refraction and dispersion of air for the visible spectrum,” Philos. Trans. R. Soc. London Ser. A 238, 1–64 (1939).

Proc. R. Soc. London Ser.A (1)

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

Other (8)

R. J. Hill, “Refractive index of atmospheric gases,” in The Upper Atmosphere, W. Diemenger, G. Hartmann, R. Leitinger, eds. (Springer-Verlag, Berlin, 1995).

K. P. Birch, M. J. Downs, “The precise determination of the refractive index of air,” Rep. MOM90 (National Physical Laboratory, Teddington, U.K., 1988), p. 35.

E. C. MorrisMATHCAD software package, Mathsoft Inc., Cambridge, Mass. 02139.

J. M. Rueger, P. E. Ciddor, “Refractive index of air: new equations for the visible and near infrared,” presented at the Twenty-first General Assembly of the International Association of Geodesy and Geophysics, Boulder, Colo., 2–14 July 1995.

“Report to BIPM on international intercomparison of line standard scales,” Cal. Rep. NML2941/2942 (National Measurement Laboratory Commonwealth Scientific and Industrial Research Organization, Lindfield, Australia, 1978).

Y. Galkin, R. A. Tatevian, “Resonances influence on the phase and group refractive indices of the air,” presented at the Twenty-First General Assembly of the International Association of Geodesy and Geophysics, Boulder, Colo., 2–14 July 1995.

Y. Galkin, R. A. Tatevian, “The problem of obtaining the formulas of the refractive indices of the air for high precision EDM,” presented at the Twenty-First General Assembly of the International Association of Geodesy and Geophysics, Boulder, Colo., 2–14 July 1995.

E. C. Morris, CSIRO Division of Applied Physics, Lindfield, N.S.W., Australia 2070 (personal communication, 1995).

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Tables (3)

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Table 1 Phase Refractivity of Dry Air with 450 ppm CO2 (λ = 633 nm)

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Table 2 Phase Refractivity of Moist Air(λ = 633 nm)

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Table 3 Comparison of Birch and Downs Equation for Phase Refractivity at Extreme Atmospheric Conditions; CO2 Content = 450 ppm, λ = 633 nm

Equations (19)

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

10 8 ( n a s 1 ) = k 1 / ( k 0 σ 2 ) + k 3 / ( k 2 σ 2 ) ,
( n a x s 1 ) = ( n a s 1 ) [ 1 + 0.534 × 10 6 ( x c 450 ) ] ,
10 8 ( n w s 1 ) = cf ( w 0 + w 1 σ 2 + w 2 σ 4 + w 3 σ 6 ) ,
ρ = ( p M a /ZRT ) [ 1 x w ( 1 M w / M a ) ] ,
n prop 1 = ( ρ a / ρ a x s ) ( n a x s 1 ) + ( ρ w / ρ w s ) ( n w s 1 ) .
L i = ( n i 2 1 ) / ( n i 2 + 2 ) ,  with  i = a ( air ) , w ( water ) ,
L = ( ρ a / ρ a x s ) L a + ( ρ w / ρ w s ) L w ,
n LL = [ ( 1 + 2 L ) / ( 1 L ) ] 1 / 2 .
n g = n + σ ( d n /dσ ) ,
10 8 ( n g a s x 1 ) = [ k 1 ( k 0 + σ 2 ) ( k 0 σ 2 ) 2 + k 3 ( k 2 + σ 2 ) ( k 2 σ 2 ) 2 ]        × [ 1 + 0.534 × 10 6 ( x c 450 ) ] ,
10 8 ( n g w s 1 ) = cf ( w 0 + 3 w 1 σ 2 + 5 w 2 σ 4 + 7 w 3 σ 6 ) .
d n g /d n = ( d n g /dσ ) / ( d n /dσ ) ,
k 0 = 238.0185    μ m 2 ;     k 1 = 5792105    μ m 2 , k 2 = 57.362    μ m 2 ,     k 3 = 167917    μ m 2 .
w 0 = 295.235    μ m 2 ;     w 1 = 2.6422    μ m 2 , w 2 = 0.032380    μ m 4 ,     w 3 = 0.004028    μ m 6 .
A = 1.2378847 × 10 5   K 2 , B = 1.9121316 × 10 2   K 1 , C = 33.93711047 ,    D = 6.3431645 × 10 3   K .
α = 1.00062 ,  β = 3.14 × 10 8 Pa 1 , γ = 5.6 × 10 7 ° C 2 .
Z = 1 ( p / T ) [ a 0 + a 1 t + a 2 t 2 + ( b 0 + b 1 t ) x w + ( c 0 + c 1 t ) x w 2 ] + ( p / T ) 2 ( d + e x w 2 ) ,
a 0 = 1.58123 × 10 6   K  Pa 1 ,    a 1 = 2.9331 × 10 8   Pa 1 , a 2 = 1.1043 × 10 10   K 1   Pa 1 , b 0 = 5.707 × 10 6   K  Pa 1 ,    b 1 = 2.051 × 10 8   Pa 1 , c 0 = 1.9898 × 10 4   K   Pa 1 , c 1 = 2.376 × 10 6   Pa 1 , d = 1.83 × 10 11   K 2   Pa 2 , e = 0.765 × 10 8   K 2   Pa 2 .
log 10 ( svp ) = 2663.5 / T + 12.537.

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