Abstract

The use of density derivative of the refractive index from the classic Lorentz-Lorenz equation or its variations performed poorly in estimating the scattering by water, leading to the alternative use of pressure derivative instead, which however has been scarcely measured due to its extremely low sensitivity. Recently, density derivative has been deduced directly from theoretical models. Three characterizations of density derivative of the refractive index were evaluated and scattering of water thus calculated converge with each other within 3.5% and agree with the measurement by Morel (Cahiers Oceanographiques, 20, 157, 1968) within 2% (with depolarization ratio = 0.039), all improving over the earlier estimates based on either density or pressure derivatives. Taking into account of uncertainty associated with the depolarization ratio, the prediction based on the model by Proutiere et al. (J. Phy. Chem., 96, 3485, 1992) still agrees with the measurement within the experimental errors (2%).

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References

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  1. A. Morel, "Optical properties of pure water and pure sea water," in Optical Aspects of Oceanography, N. G. Jerlov, and E. S. Nielsen, eds., (Academic Press, New York, 1974), pp. 1-24.
  2. K. S. Shifrin, Physical Optics of Ocean Water (American Institute of Physics, New York, 1988).
  3. I. L. Fabelinskii, Molecular Scattering of Light (Plenum Press, New York, 1968).
  4. A. Morel, "Etude Experimentale de la diffusion de la lumiere par l'eau, les solutions de chlorure de sodium et l'eau de mer optiquement pures," Journal de Chimie Physique 10, 1359-1366 (1966).
  5. A. Morel, "Note au sujet des constantes de diffusion de la lumiere pour l'eau et l'eau de mer optiquement pures," Cahiers Oceanographiques 20, 157-162 (1968).
  6. M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic Press, New York, 1969).
  7. H. Buiteveld, J. H. M. Hakvoort, and M. Donze, "The optical properties of pure water," Proc. SPIE 2258, 174-183 (1994).
    [CrossRef]
  8. M. S. Twardowski, H. Claustre, S. A. Freeman, D. Stramski, and Y. Huot, "Optical backscattering properties of the "clearest" natural waters," Biogeosciences 4, 1041-1058 (2007).
    [CrossRef]
  9. A. Morel, B. Gentili, H. Claustre, M. Babin, A. Bricaud, J. Ras, and F. Tieche, "Optical properties of the "clearest" natural waters," Limnol. Oceanogr. 52, 217-229 (2007).
    [CrossRef]
  10. E. W. Washburn, International Critical Tables of Numerical Data, Physics, Chemistry and Technology (McGraw Book Co., New York, 1930).
  11. A. M. Evtyushenkov,and Y. F. Kiyachenko, "Determination of the dependence of liquid refractive index on pressure and temperature," Opt. Spectrosc. 52, 95-98 (1982).
  12. R. M. Waxler, C. E. Weir, and H. W. Schamp, "Effect of pressure and temperature upon the optical dispersion of Benzene, carbon tetrachloride and water," J. Res. Natl. Bur. Stand. 5, 489-498 (1964).
  13. R. W. Austin and G. Halikas, "The index of refraction of seawater," (Scripps Institute of Oceanography, La Jolla, 1974), p. 121.
  14. Z. Niedrich, "Dispersion interactions and the refractive index of liquids," Physica 128B, 69-75 (1985).
  15. H. Eisenberg, "Equation for the Refractive Index of Water," J. Chem. Phys. 43, 3887-3892 (1965).
    [CrossRef]
  16. A. Proutiere, E. Megnassan, and H. Hucteau, "Refractive index and density variations in pure liquids: A new theoretical relation," J. Phys. Chem. 96, 3485-3489 (1992).
    [CrossRef]
  17. A. Bot, "Comment on "Refractive index variations in pure liquids. A new theorectical relation," J. Phys. Chem. 97, 2804 (1993).
    [CrossRef]
  18. L. W. Tilton and J. K. Taylor, "Refractive index and dispersion of distilled water for visible radiation at temperature 0 to 60 C," J. Res. Natl. Bur. Stand. 20, 419 (1938).
  19. M. Jonasz and G. R. Fournier, Light Scattering by Particles in Water: Theoretical and Experimental Foundations (Academic Press, New York, 2007).
  20. R. S. Farinato and R. L. Rowell, "New values of the light scattering depolarization and anisotropy of water," J. Chem. Phys. 65, 593-595 (1976).
    [CrossRef]
  21. G. S. Kell, "Isothermal compressibility of liquid water at 1 atm," J. Chem. Eng. Data 15, 119-122 (1970).
    [CrossRef]
  22. X. Quan and E. S. Fry, "Empirical equation for the index of refraction of seawater," Appl. Opt. 34, 3477-3480 (1995).
    [CrossRef] [PubMed]
  23. P. D. T. Huibers, "Models for the wavelength dependence of the index of refraction of water," Appl. Opt. 36, 3785-3787 (1997).
    [CrossRef] [PubMed]
  24. P. E. Ciddor, "Refractive index of air: new equation for the visible and near infrared," Appl. Opt. 35, 1566-1573 (1996).
    [CrossRef] [PubMed]
  25. G. Cohen and H. Eisenberg, "Light scattering of water, deuterium oxide, and other pure liquids," J. Chem. Phys. 43, 3881-3887 (1965).
    [CrossRef]

2007

M. S. Twardowski, H. Claustre, S. A. Freeman, D. Stramski, and Y. Huot, "Optical backscattering properties of the "clearest" natural waters," Biogeosciences 4, 1041-1058 (2007).
[CrossRef]

A. Morel, B. Gentili, H. Claustre, M. Babin, A. Bricaud, J. Ras, and F. Tieche, "Optical properties of the "clearest" natural waters," Limnol. Oceanogr. 52, 217-229 (2007).
[CrossRef]

1997

1996

1995

1994

H. Buiteveld, J. H. M. Hakvoort, and M. Donze, "The optical properties of pure water," Proc. SPIE 2258, 174-183 (1994).
[CrossRef]

1993

A. Bot, "Comment on "Refractive index variations in pure liquids. A new theorectical relation," J. Phys. Chem. 97, 2804 (1993).
[CrossRef]

1992

A. Proutiere, E. Megnassan, and H. Hucteau, "Refractive index and density variations in pure liquids: A new theoretical relation," J. Phys. Chem. 96, 3485-3489 (1992).
[CrossRef]

1985

Z. Niedrich, "Dispersion interactions and the refractive index of liquids," Physica 128B, 69-75 (1985).

1982

A. M. Evtyushenkov,and Y. F. Kiyachenko, "Determination of the dependence of liquid refractive index on pressure and temperature," Opt. Spectrosc. 52, 95-98 (1982).

1976

R. S. Farinato and R. L. Rowell, "New values of the light scattering depolarization and anisotropy of water," J. Chem. Phys. 65, 593-595 (1976).
[CrossRef]

1970

G. S. Kell, "Isothermal compressibility of liquid water at 1 atm," J. Chem. Eng. Data 15, 119-122 (1970).
[CrossRef]

1968

A. Morel, "Note au sujet des constantes de diffusion de la lumiere pour l'eau et l'eau de mer optiquement pures," Cahiers Oceanographiques 20, 157-162 (1968).

1966

A. Morel, "Etude Experimentale de la diffusion de la lumiere par l'eau, les solutions de chlorure de sodium et l'eau de mer optiquement pures," Journal de Chimie Physique 10, 1359-1366 (1966).

1965

H. Eisenberg, "Equation for the Refractive Index of Water," J. Chem. Phys. 43, 3887-3892 (1965).
[CrossRef]

G. Cohen and H. Eisenberg, "Light scattering of water, deuterium oxide, and other pure liquids," J. Chem. Phys. 43, 3881-3887 (1965).
[CrossRef]

1964

R. M. Waxler, C. E. Weir, and H. W. Schamp, "Effect of pressure and temperature upon the optical dispersion of Benzene, carbon tetrachloride and water," J. Res. Natl. Bur. Stand. 5, 489-498 (1964).

1938

L. W. Tilton and J. K. Taylor, "Refractive index and dispersion of distilled water for visible radiation at temperature 0 to 60 C," J. Res. Natl. Bur. Stand. 20, 419 (1938).

Babin, M.

A. Morel, B. Gentili, H. Claustre, M. Babin, A. Bricaud, J. Ras, and F. Tieche, "Optical properties of the "clearest" natural waters," Limnol. Oceanogr. 52, 217-229 (2007).
[CrossRef]

Bot, A.

A. Bot, "Comment on "Refractive index variations in pure liquids. A new theorectical relation," J. Phys. Chem. 97, 2804 (1993).
[CrossRef]

Bricaud, A.

A. Morel, B. Gentili, H. Claustre, M. Babin, A. Bricaud, J. Ras, and F. Tieche, "Optical properties of the "clearest" natural waters," Limnol. Oceanogr. 52, 217-229 (2007).
[CrossRef]

Buiteveld, H.

H. Buiteveld, J. H. M. Hakvoort, and M. Donze, "The optical properties of pure water," Proc. SPIE 2258, 174-183 (1994).
[CrossRef]

Ciddor, P. E.

Claustre, H.

A. Morel, B. Gentili, H. Claustre, M. Babin, A. Bricaud, J. Ras, and F. Tieche, "Optical properties of the "clearest" natural waters," Limnol. Oceanogr. 52, 217-229 (2007).
[CrossRef]

M. S. Twardowski, H. Claustre, S. A. Freeman, D. Stramski, and Y. Huot, "Optical backscattering properties of the "clearest" natural waters," Biogeosciences 4, 1041-1058 (2007).
[CrossRef]

Cohen, G.

G. Cohen and H. Eisenberg, "Light scattering of water, deuterium oxide, and other pure liquids," J. Chem. Phys. 43, 3881-3887 (1965).
[CrossRef]

Donze, M.

H. Buiteveld, J. H. M. Hakvoort, and M. Donze, "The optical properties of pure water," Proc. SPIE 2258, 174-183 (1994).
[CrossRef]

Eisenberg, H.

G. Cohen and H. Eisenberg, "Light scattering of water, deuterium oxide, and other pure liquids," J. Chem. Phys. 43, 3881-3887 (1965).
[CrossRef]

H. Eisenberg, "Equation for the Refractive Index of Water," J. Chem. Phys. 43, 3887-3892 (1965).
[CrossRef]

Evtyushenkov, A. M.

A. M. Evtyushenkov,and Y. F. Kiyachenko, "Determination of the dependence of liquid refractive index on pressure and temperature," Opt. Spectrosc. 52, 95-98 (1982).

Farinato, R. S.

R. S. Farinato and R. L. Rowell, "New values of the light scattering depolarization and anisotropy of water," J. Chem. Phys. 65, 593-595 (1976).
[CrossRef]

Freeman, S. A.

M. S. Twardowski, H. Claustre, S. A. Freeman, D. Stramski, and Y. Huot, "Optical backscattering properties of the "clearest" natural waters," Biogeosciences 4, 1041-1058 (2007).
[CrossRef]

Fry, E. S.

Gentili, B.

A. Morel, B. Gentili, H. Claustre, M. Babin, A. Bricaud, J. Ras, and F. Tieche, "Optical properties of the "clearest" natural waters," Limnol. Oceanogr. 52, 217-229 (2007).
[CrossRef]

Hakvoort, J. H. M.

H. Buiteveld, J. H. M. Hakvoort, and M. Donze, "The optical properties of pure water," Proc. SPIE 2258, 174-183 (1994).
[CrossRef]

Hucteau, H.

A. Proutiere, E. Megnassan, and H. Hucteau, "Refractive index and density variations in pure liquids: A new theoretical relation," J. Phys. Chem. 96, 3485-3489 (1992).
[CrossRef]

Huibers, P. D. T.

Huot, Y.

M. S. Twardowski, H. Claustre, S. A. Freeman, D. Stramski, and Y. Huot, "Optical backscattering properties of the "clearest" natural waters," Biogeosciences 4, 1041-1058 (2007).
[CrossRef]

Kell, G. S.

G. S. Kell, "Isothermal compressibility of liquid water at 1 atm," J. Chem. Eng. Data 15, 119-122 (1970).
[CrossRef]

Kiyachenko, Y. F.

A. M. Evtyushenkov,and Y. F. Kiyachenko, "Determination of the dependence of liquid refractive index on pressure and temperature," Opt. Spectrosc. 52, 95-98 (1982).

Megnassan, E.

A. Proutiere, E. Megnassan, and H. Hucteau, "Refractive index and density variations in pure liquids: A new theoretical relation," J. Phys. Chem. 96, 3485-3489 (1992).
[CrossRef]

Morel, A.

A. Morel, B. Gentili, H. Claustre, M. Babin, A. Bricaud, J. Ras, and F. Tieche, "Optical properties of the "clearest" natural waters," Limnol. Oceanogr. 52, 217-229 (2007).
[CrossRef]

A. Morel, "Note au sujet des constantes de diffusion de la lumiere pour l'eau et l'eau de mer optiquement pures," Cahiers Oceanographiques 20, 157-162 (1968).

A. Morel, "Etude Experimentale de la diffusion de la lumiere par l'eau, les solutions de chlorure de sodium et l'eau de mer optiquement pures," Journal de Chimie Physique 10, 1359-1366 (1966).

Niedrich, Z.

Z. Niedrich, "Dispersion interactions and the refractive index of liquids," Physica 128B, 69-75 (1985).

Proutiere, A.

A. Proutiere, E. Megnassan, and H. Hucteau, "Refractive index and density variations in pure liquids: A new theoretical relation," J. Phys. Chem. 96, 3485-3489 (1992).
[CrossRef]

Quan, X.

Ras, J.

A. Morel, B. Gentili, H. Claustre, M. Babin, A. Bricaud, J. Ras, and F. Tieche, "Optical properties of the "clearest" natural waters," Limnol. Oceanogr. 52, 217-229 (2007).
[CrossRef]

Rowell, R. L.

R. S. Farinato and R. L. Rowell, "New values of the light scattering depolarization and anisotropy of water," J. Chem. Phys. 65, 593-595 (1976).
[CrossRef]

Schamp, H. W.

R. M. Waxler, C. E. Weir, and H. W. Schamp, "Effect of pressure and temperature upon the optical dispersion of Benzene, carbon tetrachloride and water," J. Res. Natl. Bur. Stand. 5, 489-498 (1964).

Stramski, D.

M. S. Twardowski, H. Claustre, S. A. Freeman, D. Stramski, and Y. Huot, "Optical backscattering properties of the "clearest" natural waters," Biogeosciences 4, 1041-1058 (2007).
[CrossRef]

Taylor, J. K.

L. W. Tilton and J. K. Taylor, "Refractive index and dispersion of distilled water for visible radiation at temperature 0 to 60 C," J. Res. Natl. Bur. Stand. 20, 419 (1938).

Tieche, F.

A. Morel, B. Gentili, H. Claustre, M. Babin, A. Bricaud, J. Ras, and F. Tieche, "Optical properties of the "clearest" natural waters," Limnol. Oceanogr. 52, 217-229 (2007).
[CrossRef]

Tilton, L. W.

L. W. Tilton and J. K. Taylor, "Refractive index and dispersion of distilled water for visible radiation at temperature 0 to 60 C," J. Res. Natl. Bur. Stand. 20, 419 (1938).

Twardowski, M. S.

M. S. Twardowski, H. Claustre, S. A. Freeman, D. Stramski, and Y. Huot, "Optical backscattering properties of the "clearest" natural waters," Biogeosciences 4, 1041-1058 (2007).
[CrossRef]

Waxler, R. M.

R. M. Waxler, C. E. Weir, and H. W. Schamp, "Effect of pressure and temperature upon the optical dispersion of Benzene, carbon tetrachloride and water," J. Res. Natl. Bur. Stand. 5, 489-498 (1964).

Weir, C. E.

R. M. Waxler, C. E. Weir, and H. W. Schamp, "Effect of pressure and temperature upon the optical dispersion of Benzene, carbon tetrachloride and water," J. Res. Natl. Bur. Stand. 5, 489-498 (1964).

Appl. Opt.

Biogeosciences

M. S. Twardowski, H. Claustre, S. A. Freeman, D. Stramski, and Y. Huot, "Optical backscattering properties of the "clearest" natural waters," Biogeosciences 4, 1041-1058 (2007).
[CrossRef]

Cahiers Oceanographiques

A. Morel, "Note au sujet des constantes de diffusion de la lumiere pour l'eau et l'eau de mer optiquement pures," Cahiers Oceanographiques 20, 157-162 (1968).

J. Chem. Eng. Data

G. S. Kell, "Isothermal compressibility of liquid water at 1 atm," J. Chem. Eng. Data 15, 119-122 (1970).
[CrossRef]

J. Chem. Phys.

G. Cohen and H. Eisenberg, "Light scattering of water, deuterium oxide, and other pure liquids," J. Chem. Phys. 43, 3881-3887 (1965).
[CrossRef]

R. S. Farinato and R. L. Rowell, "New values of the light scattering depolarization and anisotropy of water," J. Chem. Phys. 65, 593-595 (1976).
[CrossRef]

H. Eisenberg, "Equation for the Refractive Index of Water," J. Chem. Phys. 43, 3887-3892 (1965).
[CrossRef]

J. Phys. Chem.

A. Proutiere, E. Megnassan, and H. Hucteau, "Refractive index and density variations in pure liquids: A new theoretical relation," J. Phys. Chem. 96, 3485-3489 (1992).
[CrossRef]

A. Bot, "Comment on "Refractive index variations in pure liquids. A new theorectical relation," J. Phys. Chem. 97, 2804 (1993).
[CrossRef]

J. Res. Natl. Bur. Stand.

L. W. Tilton and J. K. Taylor, "Refractive index and dispersion of distilled water for visible radiation at temperature 0 to 60 C," J. Res. Natl. Bur. Stand. 20, 419 (1938).

R. M. Waxler, C. E. Weir, and H. W. Schamp, "Effect of pressure and temperature upon the optical dispersion of Benzene, carbon tetrachloride and water," J. Res. Natl. Bur. Stand. 5, 489-498 (1964).

Journal de Chimie Physique

A. Morel, "Etude Experimentale de la diffusion de la lumiere par l'eau, les solutions de chlorure de sodium et l'eau de mer optiquement pures," Journal de Chimie Physique 10, 1359-1366 (1966).

Limnol. Oceanogr.

A. Morel, B. Gentili, H. Claustre, M. Babin, A. Bricaud, J. Ras, and F. Tieche, "Optical properties of the "clearest" natural waters," Limnol. Oceanogr. 52, 217-229 (2007).
[CrossRef]

Opt. Spectrosc.

A. M. Evtyushenkov,and Y. F. Kiyachenko, "Determination of the dependence of liquid refractive index on pressure and temperature," Opt. Spectrosc. 52, 95-98 (1982).

Physica

Z. Niedrich, "Dispersion interactions and the refractive index of liquids," Physica 128B, 69-75 (1985).

Proc. SPIE

H. Buiteveld, J. H. M. Hakvoort, and M. Donze, "The optical properties of pure water," Proc. SPIE 2258, 174-183 (1994).
[CrossRef]

Other

E. W. Washburn, International Critical Tables of Numerical Data, Physics, Chemistry and Technology (McGraw Book Co., New York, 1930).

M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic Press, New York, 1969).

A. Morel, "Optical properties of pure water and pure sea water," in Optical Aspects of Oceanography, N. G. Jerlov, and E. S. Nielsen, eds., (Academic Press, New York, 1974), pp. 1-24.

K. S. Shifrin, Physical Optics of Ocean Water (American Institute of Physics, New York, 1988).

I. L. Fabelinskii, Molecular Scattering of Light (Plenum Press, New York, 1968).

R. W. Austin and G. Halikas, "The index of refraction of seawater," (Scripps Institute of Oceanography, La Jolla, 1974), p. 121.

M. Jonasz and G. R. Fournier, Light Scattering by Particles in Water: Theoretical and Experimental Foundations (Academic Press, New York, 2007).

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Figures (1)

Fig 1.
Fig 1.

Comparison of pure water scattering β(90) from the theories and the experiment. The percentage difference relative to the values of calculation using Eq. 3 and PMH model (Eq. 7) are plotted. The value used for the depolarization ratio δ was 0.039 in (a) and 0.051 in (b). Values for Eisenberg and Niedrich are calculated using Eq. 3, and the Eisenberg (Eq. 10) and Niedrich (Eq. 8) models, respectively. Other values are from Buiteveld et al. [7], Morel [4, 5] for experiment, and Morel [table 4 of 1] for his theoretical calculation. Note Morel and Buiteveld et al. used δ = 0.09 and 0.051 in their respective calculations, here we scaled their values correspondingly.

Tables (1)

Tables Icon

Table 1. β(90) measured by Morel (row 1) and its comparison with various theoretical calculations with δ = 0.039 at 20U°C. In the last column, the numbers in the parenthesis are the results if δ = 0.051 or 0.09 were used in the calculations.

Equations (13)

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

β ( 90 ) = π 2 2 λ 4 Δ V Δ ε 2 ¯ f ( δ )
Δ ε 2 ¯ = ( n 2 ρ ) T 2 Δ ρ 2 ¯ + ( n 2 T ) ρ 2 Δ T 2 ¯
β ( 90 ) = π 2 2 λ 4 ( ρ n 2 ρ ) T 2 kT β T f ( δ )
β ( 90 ) = 2 π 2 n 2 λ 4 β T ( n P ) T 2 kTf ( δ ) .
n 2 1 = N ε 0 3 n ¯ 2 ( n ¯ 2 + 2 ) α ¯ ( 2 n ¯ 2 + 1 ) ( n ¯ 2 + 2 ) 2 ( n ¯ 2 1 ) 2 / N ¯ v ¯
1 ρ n 2 1 n 2 + 2 = N A α 3 M ε 0
ρ ( n 2 ρ ) T = ρ ( n 2 ρ ) P = ( n 2 1 ) [ 1 + 2 3 ( n 2 + 2 ) ( n 2 1 3 n ) 2 ]
ρ ( n 2 ρ ) T = ( n 2 1 ) 2 n 2 + 1 2 n 2 + 1 / n 2
n 2 1 n 2 + 2 = A ρ B exp ( CT )
ρ n 2 ρ = B ( n 2 1 ) ( n 2 + 2 ) 3
β T × 10 6 = a 0 + a 1 T c + a 2 T c 2 + a 3 T c 3 + a 4 T c 4 + a 5 T c 5 b 0 + b 1 T c
n ( T c , λ ) = n 0 + n 4 T c 2 + n 5 + n 7 T c λ + n 8 λ 2 + n 9 λ 3 .
( n air 1 ) × 10 8 = k 1 k 0 v ¯ 2 + k 3 k 2 v ¯ 2 ,

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