Abstract

We have determined an empirical equation for the index of refraction of water as a function of temperature, salinity, and wavelength at atmospheric pressure. The experimental data selected by Austin and Halikas [“The index of refraction of seawater,” SIO Ref. 76-1 (Scripps Institution of Oceanography, La Jolla, Calif., 1976)] were fitted to power series in the variables. A ten-parameter empirical equation that reproduces the original data to within its experimental errors was obtained.

© 1995 Optical Society of America

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References

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  1. G. Seaver, “The index of refraction to specific volume relation for seawater—a linearized equation of state,” J. Phys. Oceanogr. 15, 1339–1343 (1985).
    [CrossRef]
  2. G. T. McNeil, “Metrical fundamentals of underwater lens system,” Opt. Eng. 16, 128–139 (1977).
  3. G. Sager, “Zur Refraktion von Licht im Meerwasser,” Beitr. Meereskd. 33, 63–72 (1974).
  4. W. Matthaus, “Empirische Gleichungen fur den Brechungsindex des Meerwassers,” Beitr. Meereskd. 33, 73–78 (1974).
  5. N. G. Jerlov, Marine Optics, Vol. 14 of Elsevier Oceanography Series (Elsevier, Amsterdam, 1976).
    [CrossRef]
  6. R. W. Austin, G. Halikas, “The index of refraction of seawater,” SIO Ref. 76-1 (Scripps Institution of Oceanography, La Jolla, Calif., 1976).
  7. A. Mehu, A. Johannin-Gilles, “Variation de l’indice de refraction de l’eau de mer étalon de Copenhague et des ses dilutions en fonction de la longeur d’onde, de la temperature et de la chlorinité,” Cah. Oceanogr. 20, 803–812 (1968).
  8. K. S. Shifrin, Physical Optics of Ocean Water (American Institute of Physics, New York, 1988).
  9. G. Seaver, “The optical determination of temperature, pressure, salinity and density in physical oceanography,” Mar. Technol. Soc. J. 21, 69–79 (1987).

1987 (1)

G. Seaver, “The optical determination of temperature, pressure, salinity and density in physical oceanography,” Mar. Technol. Soc. J. 21, 69–79 (1987).

1985 (1)

G. Seaver, “The index of refraction to specific volume relation for seawater—a linearized equation of state,” J. Phys. Oceanogr. 15, 1339–1343 (1985).
[CrossRef]

1977 (1)

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

1974 (2)

G. Sager, “Zur Refraktion von Licht im Meerwasser,” Beitr. Meereskd. 33, 63–72 (1974).

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

1968 (1)

A. Mehu, A. Johannin-Gilles, “Variation de l’indice de refraction de l’eau de mer étalon de Copenhague et des ses dilutions en fonction de la longeur d’onde, de la temperature et de la chlorinité,” Cah. Oceanogr. 20, 803–812 (1968).

Austin, R. W.

R. W. Austin, G. Halikas, “The index of refraction of seawater,” SIO Ref. 76-1 (Scripps Institution of Oceanography, La Jolla, Calif., 1976).

Halikas, G.

R. W. Austin, G. Halikas, “The index of refraction of seawater,” SIO Ref. 76-1 (Scripps Institution of Oceanography, La Jolla, Calif., 1976).

Jerlov, N. G.

N. G. Jerlov, Marine Optics, Vol. 14 of Elsevier Oceanography Series (Elsevier, Amsterdam, 1976).
[CrossRef]

Johannin-Gilles, A.

A. Mehu, A. Johannin-Gilles, “Variation de l’indice de refraction de l’eau de mer étalon de Copenhague et des ses dilutions en fonction de la longeur d’onde, de la temperature et de la chlorinité,” Cah. Oceanogr. 20, 803–812 (1968).

Matthaus, W.

W. Matthaus, “Empirische Gleichungen fur 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).

Mehu, A.

A. Mehu, A. Johannin-Gilles, “Variation de l’indice de refraction de l’eau de mer étalon de Copenhague et des ses dilutions en fonction de la longeur d’onde, de la temperature et de la chlorinité,” Cah. Oceanogr. 20, 803–812 (1968).

Sager, G.

G. Sager, “Zur Refraktion von Licht im Meerwasser,” Beitr. Meereskd. 33, 63–72 (1974).

Seaver, G.

G. Seaver, “The optical determination of temperature, pressure, salinity and density in physical oceanography,” Mar. Technol. Soc. J. 21, 69–79 (1987).

G. Seaver, “The index of refraction to specific volume relation for seawater—a linearized equation of state,” J. Phys. Oceanogr. 15, 1339–1343 (1985).
[CrossRef]

Shifrin, K. S.

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

Beitr. Meereskd. (2)

G. Sager, “Zur Refraktion von Licht im Meerwasser,” Beitr. Meereskd. 33, 63–72 (1974).

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

Cah. Oceanogr. (1)

A. Mehu, A. Johannin-Gilles, “Variation de l’indice de refraction de l’eau de mer étalon de Copenhague et des ses dilutions en fonction de la longeur d’onde, de la temperature et de la chlorinité,” Cah. Oceanogr. 20, 803–812 (1968).

J. Phys. Oceanogr. (1)

G. Seaver, “The index of refraction to specific volume relation for seawater—a linearized equation of state,” J. Phys. Oceanogr. 15, 1339–1343 (1985).
[CrossRef]

Mar. Technol. Soc. J. (1)

G. Seaver, “The optical determination of temperature, pressure, salinity and density in physical oceanography,” Mar. Technol. Soc. J. 21, 69–79 (1987).

Opt. Eng. (1)

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

Other (3)

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

N. G. Jerlov, Marine Optics, Vol. 14 of Elsevier Oceanography Series (Elsevier, Amsterdam, 1976).
[CrossRef]

R. W. Austin, G. Halikas, “The index of refraction of seawater,” SIO Ref. 76-1 (Scripps Institution of Oceanography, La Jolla, Calif., 1976).

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Figures (4)

Fig. 1
Fig. 1

Differences between the A&H data and results calculated from Eq. (1), which was obtained by McNeil. The sets of data points at each wavelength are separated by vertical dashed lines; the wavelength of each of these sets is given in units of nanometers at the top of the plot. There are 11 sets corresponding to each of the 11 wavelengths in Table 1. At a given wavelength, the δn values for S = 0‰ are the filled circles, and those for S = 35‰ are open circles. Within a wavelength range, the points from left to right are for temperatures of 1, 5, 10, 15, 20, 25, and 30 °C. The horizontal dashed lines correspond to the quoted errors in the experimental data.

Fig. 2
Fig. 2

Differences between the A&H data and the results calculated from Eq. (2), which was obtained by Matthaus. The terminology is the same as in Fig. 1. Deviations at 700 nm are so large they are plotted separately with an expanded scale.

Fig. 3
Fig. 3

Differences between the A&H data and results calculated from our new equation, Eq. (3). The terminology is the same as in Fig. 1. Most of the data points lie between the horizontal lines that correspond to the quoted errors in the experimental data.

Fig. 4
Fig. 4

Differences between Sager’s data at a wavelength of 589.3 nm and results calculated from our Eq. (3) are shown as crosses. The sets of data points at each salinity are separated by vertical dashed lines and are labeled in units of ‰ at the top of the plot. Within each salinity section the data points from left to right are from 0 to 30 °C in steps of 5 °C. For reference, the δn″ data at 589.3 nm from Fig. 3 are reproduced here and shown as open circles.

Tables (1)

Tables Icon

Table 1 Data for Index of Refraction as a Function of Wavelength, Salinity, and Temperature at Atmospheric Pressure as Given in Ref. 6

Equations (4)

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n ( S , T , λ ) = 1.3247 - 2.5 × 10 - 6 T 2 + S ( 2 × 10 - 4 - 8 × 10 - 7 T ) + 3300 λ 2 - 3.2 × 10 7 λ 4 ,
n ( S , T , λ ) = 1.447824 + 3.0110 × 10 - 4 S - 1.8029 × 10 - 5 T - 1.6916 × 10 - 6 T 2 - 4.89040 × 10 - 1 λ + 7.28364 × 10 - 1 λ 2 - 3.83745 × 10 - 1 λ 3 - S ( 7.9362 × 10 - 7 T - 8.0597 × 10 - 9 T 2 + 4.249 × 10 - 4 λ - 5.847 × 10 - 4 λ 2 + 2.812 × 10 - 4 λ 3 ) ,
n ( S , T , λ ) = n 0 + ( n 1 + n 2 T + n 3 T 2 ) S + n 4 T 2 + n 5 + n 6 S + n 7 T λ + n 8 λ 2 + n 9 λ 3 ,
n 0 = 1.31405 , n 1 = 1.779 × 10 - 4 , n 2 = - 1.05 × 10 - 6 , n 3 = 1.6 × 10 - 8 , n 4 = - 2.02 × 10 - 6 , n 5 = 15.868 , n 6 = 0.01155 , n 7 = - 0.00423 , n 8 = - 4382 , n 9 = 1.1455 × 10 6 .

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