Abstract

Models for the index of refraction of water are reviewed and reduced to wavelength-dependent formulas. A simple three-term nonlinear model derived from Quan and Fry [Appl. Opt. 34, 3477–3480 (1995)], originally developed for the visible region, fits the available data well over an extended range covering the UV to the near-IR (200–1100 nm).

© 1997 Optical Society of America

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References

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  1. P. Schiebener, J. Straub, J. M. H. Levelt Sengers, J. S. Gallagher, “Refractive index of water and steam as a function of wavelength, temperature and density,” J. Phys. Chem. Ref. Data 19, 677–717 (1990).
    [CrossRef]
  2. W. M. Irvine, J. B. Pollack, “Infrared optical properties of water and ice spheres,” Icarus 8, 324–360 (1968).
    [CrossRef]
  3. R. W. Austin, G. Halikas, “The index of refraction of seawater,” (Scripps Institution of Oceanography, La Jolla, Calif., 1976).
  4. X. Quan, E. S. Fry, “Empirical equation for the index of refraction of seawater,” Appl. Opt. 34, 3477–3480 (1995).
    [CrossRef] [PubMed]
  5. W. Matthaus, “Empirische Gleichungen für den Brechungsindex des Meerwassers,” Beitr. Meereskd. 33, 73–78 (1974).
  6. G. T. McNeil, “Metrical fundamentals of underwater lens system,” Opt. Eng. 16, 128–139 (1977).
    [CrossRef]
  7. I. Thormählen, J. Straub, U. Grigull, “Refractive index of water and its dependence on wavelength, temperature, and density,” J. Phys. Chem. Ref. Data 14, 933–945 (1985).
    [CrossRef]
  8. G. M. Hale, M. R. Querry, “Optical constants of water in the 200-nm to 200-µm wavelength region,” Appl. Opt. 12, 555–563 (1973).
    [CrossRef] [PubMed]
  9. G. D. Kerr, R. N. Hamm, M. W. Williams, R. D. Birkhoff, L. R. Painter, “Optical and dielectric properties of water in the vacuum ultraviolet,” Phys. Rev. A 5, 2523 (1972).
    [CrossRef]

1995 (1)

1990 (1)

P. Schiebener, J. Straub, J. M. H. Levelt Sengers, J. S. Gallagher, “Refractive index of water and steam as a function of wavelength, temperature and density,” J. Phys. Chem. Ref. Data 19, 677–717 (1990).
[CrossRef]

1985 (1)

I. Thormählen, J. Straub, U. Grigull, “Refractive index of water and its dependence on wavelength, temperature, and density,” J. Phys. Chem. Ref. Data 14, 933–945 (1985).
[CrossRef]

1977 (1)

G. T. McNeil, “Metrical fundamentals of underwater lens system,” Opt. Eng. 16, 128–139 (1977).
[CrossRef]

1974 (1)

W. Matthaus, “Empirische Gleichungen für den Brechungsindex des Meerwassers,” Beitr. Meereskd. 33, 73–78 (1974).

1973 (1)

1972 (1)

G. D. Kerr, R. N. Hamm, M. W. Williams, R. D. Birkhoff, L. R. Painter, “Optical and dielectric properties of water in the vacuum ultraviolet,” Phys. Rev. A 5, 2523 (1972).
[CrossRef]

1968 (1)

W. M. Irvine, J. B. Pollack, “Infrared optical properties of water and ice spheres,” Icarus 8, 324–360 (1968).
[CrossRef]

Austin, R. W.

R. W. Austin, G. Halikas, “The index of refraction of seawater,” (Scripps Institution of Oceanography, La Jolla, Calif., 1976).

Birkhoff, R. D.

G. D. Kerr, R. N. Hamm, M. W. Williams, R. D. Birkhoff, L. R. Painter, “Optical and dielectric properties of water in the vacuum ultraviolet,” Phys. Rev. A 5, 2523 (1972).
[CrossRef]

Fry, E. S.

Gallagher, J. S.

P. Schiebener, J. Straub, J. M. H. Levelt Sengers, J. S. Gallagher, “Refractive index of water and steam as a function of wavelength, temperature and density,” J. Phys. Chem. Ref. Data 19, 677–717 (1990).
[CrossRef]

Grigull, U.

I. Thormählen, J. Straub, U. Grigull, “Refractive index of water and its dependence on wavelength, temperature, and density,” J. Phys. Chem. Ref. Data 14, 933–945 (1985).
[CrossRef]

Hale, G. M.

Halikas, G.

R. W. Austin, G. Halikas, “The index of refraction of seawater,” (Scripps Institution of Oceanography, La Jolla, Calif., 1976).

Hamm, R. N.

G. D. Kerr, R. N. Hamm, M. W. Williams, R. D. Birkhoff, L. R. Painter, “Optical and dielectric properties of water in the vacuum ultraviolet,” Phys. Rev. A 5, 2523 (1972).
[CrossRef]

Irvine, W. M.

W. M. Irvine, J. B. Pollack, “Infrared optical properties of water and ice spheres,” Icarus 8, 324–360 (1968).
[CrossRef]

Kerr, G. D.

G. D. Kerr, R. N. Hamm, M. W. Williams, R. D. Birkhoff, L. R. Painter, “Optical and dielectric properties of water in the vacuum ultraviolet,” Phys. Rev. A 5, 2523 (1972).
[CrossRef]

Levelt Sengers, J. M. H.

P. Schiebener, J. Straub, J. M. H. Levelt Sengers, J. S. Gallagher, “Refractive index of water and steam as a function of wavelength, temperature and density,” J. Phys. Chem. Ref. Data 19, 677–717 (1990).
[CrossRef]

Matthaus, W.

W. Matthaus, “Empirische Gleichungen für den Brechungsindex des Meerwassers,” Beitr. Meereskd. 33, 73–78 (1974).

McNeil, G. T.

G. T. McNeil, “Metrical fundamentals of underwater lens system,” Opt. Eng. 16, 128–139 (1977).
[CrossRef]

Painter, L. R.

G. D. Kerr, R. N. Hamm, M. W. Williams, R. D. Birkhoff, L. R. Painter, “Optical and dielectric properties of water in the vacuum ultraviolet,” Phys. Rev. A 5, 2523 (1972).
[CrossRef]

Pollack, J. B.

W. M. Irvine, J. B. Pollack, “Infrared optical properties of water and ice spheres,” Icarus 8, 324–360 (1968).
[CrossRef]

Quan, X.

Querry, M. R.

Schiebener, P.

P. Schiebener, J. Straub, J. M. H. Levelt Sengers, J. S. Gallagher, “Refractive index of water and steam as a function of wavelength, temperature and density,” J. Phys. Chem. Ref. Data 19, 677–717 (1990).
[CrossRef]

Straub, J.

P. Schiebener, J. Straub, J. M. H. Levelt Sengers, J. S. Gallagher, “Refractive index of water and steam as a function of wavelength, temperature and density,” J. Phys. Chem. Ref. Data 19, 677–717 (1990).
[CrossRef]

I. Thormählen, J. Straub, U. Grigull, “Refractive index of water and its dependence on wavelength, temperature, and density,” J. Phys. Chem. Ref. Data 14, 933–945 (1985).
[CrossRef]

Thormählen, I.

I. Thormählen, J. Straub, U. Grigull, “Refractive index of water and its dependence on wavelength, temperature, and density,” J. Phys. Chem. Ref. Data 14, 933–945 (1985).
[CrossRef]

Williams, M. W.

G. D. Kerr, R. N. Hamm, M. W. Williams, R. D. Birkhoff, L. R. Painter, “Optical and dielectric properties of water in the vacuum ultraviolet,” Phys. Rev. A 5, 2523 (1972).
[CrossRef]

Appl. Opt. (2)

Beitr. Meereskd. (1)

W. Matthaus, “Empirische Gleichungen für den Brechungsindex des Meerwassers,” Beitr. Meereskd. 33, 73–78 (1974).

Icarus (1)

W. M. Irvine, J. B. Pollack, “Infrared optical properties of water and ice spheres,” Icarus 8, 324–360 (1968).
[CrossRef]

J. Phys. Chem. Ref. Data (2)

I. Thormählen, J. Straub, U. Grigull, “Refractive index of water and its dependence on wavelength, temperature, and density,” J. Phys. Chem. Ref. Data 14, 933–945 (1985).
[CrossRef]

P. Schiebener, J. Straub, J. M. H. Levelt Sengers, J. S. Gallagher, “Refractive index of water and steam as a function of wavelength, temperature and density,” J. Phys. Chem. Ref. Data 19, 677–717 (1990).
[CrossRef]

Opt. Eng. (1)

G. T. McNeil, “Metrical fundamentals of underwater lens system,” Opt. Eng. 16, 128–139 (1977).
[CrossRef]

Phys. Rev. A (1)

G. D. Kerr, R. N. Hamm, M. W. Williams, R. D. Birkhoff, L. R. Painter, “Optical and dielectric properties of water in the vacuum ultraviolet,” Phys. Rev. A 5, 2523 (1972).
[CrossRef]

Other (1)

R. W. Austin, G. Halikas, “The index of refraction of seawater,” (Scripps Institution of Oceanography, La Jolla, Calif., 1976).

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Figures (2)

Fig. 1
Fig. 1

Comparison of several models with data for the wavelength dependence of the index of refraction of water.

Fig. 2
Fig. 2

Differences between the calculated index of refraction of water and the experimental data for the two best models.

Tables (2)

Tables Icon

Table 1 Data for the Index of Refraction versus Wavelength

Tables Icon

Table 2 Average Error (Σ|nmodel - nmeasured|/ N) of Different Models for the Wavelength Dependence of the Index of Refraction of Water across the Specified Wavelength Rangesa

Equations (5)

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nλ=1.446316-4.89040×10-4λ+7.28364×10-7λ2-3.83745×1010λ3,
nλ=1.3231+3300λ-2-3.2×107λ-4,
nλ=1.31279+15.762λ-1-4382λ-2+1.1455×106λ-3.
LL=n2-1n2+21ρ*,
LL=0.233225+8.35872×10-10λ2+552.261λ2+852.502λ2-18225.0+311354λ2-1.02400×107,

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