Abstract

I describe here a new simple method for measuring the absolute refractive index of liquid water as a function of temperature at a wavelength of 1.064 μm with a Michelson interferometer. The mirror of the measuring arm is located in a water cell and displaced by a well-known distance. Compensation for a change in the optical path length in the reference arm of the interferometer is not necessary.

© 1996 Optical Society of America

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References

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  1. L. Pontier, C. Dechambenoy, “Détermination des constantes optiques de l’eau liquide entre 1 et 40 μm. Application au calcul de son pouvoir réflecteur et de son émissivité,” Ann. Geophys. 22, 633–641 (1966).
  2. U. M. Centeno, “The refractive index of water in the near infra-red spectrum,” J. Opt. Soc. Am. 31, 244–247 (1941).
    [CrossRef]
  3. H. Rubens, “Über Dispersion ultrarother Strahlen,” Ann. Phys. Wied. 45, 238–253 (1892).
    [CrossRef]
  4. H. Rubens, E. Ladenburg, “Über die Dispersion des Wassers im ultraroten Spektrum,” Ber. Dtsch. Phys. Ges. 11, 16–27 (1909).
  5. L. R. Ingersoll, “Magnetic rotation in various liquids in the short infrared spectrum,” J. Opt. Soc. Am. 6, 663–681 (1922).
    [CrossRef]
  6. J. Vincent-Geisse, G. Vagner, F. Gans, “Mesures d’indices de réfraction dans l’infrarouge par des méthodes réfrac-tométriques,” Rev. Opt. 43, 15–21 (1964).
  7. 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, 677–717 (1990).
    [CrossRef]
  8. P. Schiebener, J. Straub, J. M. H. Levelt Sengers, J. S. Gallagher, “Erratum: refractive index of water and steam as function of wavelength, temperature, and density,” J. Phys. Chem. Ref. Data 19, 1617 (1990).
    [CrossRef]
  9. E. Moreels, C. de Greef, R. Finsy, “Laser light refractometer,” Appl. Opt. 23, 3010–3013 (1984).
    [CrossRef] [PubMed]
  10. K. Kuhler, E. L. Dereniak, M. Buchanan, “Measurement of the index of refraction of the plastic phenoxy PKFE,” Appl. Opt. 30, 1711–1714 (1991).
    [CrossRef] [PubMed]
  11. S. Nemoto, “Measurement of the refractive index of liquid using laser beam displacement,” Appl. Opt. 31, 6690–6694 (1992).
    [CrossRef] [PubMed]
  12. Y. Makdisi, A. A. Zaidi, K. S. Bhatia, “Laser refractometry of liquids with a diffraction grating,” Opt. Commun. 72, 148–152 (1989).
    [CrossRef]
  13. G. Abbate, A. Attanasio, U. Bernini, E. Ragozzino, F. Somma, “The direct determination of the temperature dependence of the refractive index of liquids and solids,” J. Phys. D 9, 1945–1951 (1976).
    [CrossRef]
  14. W. Lea, W. M. Work, “Two-wavelength interferometric technique for measuring the refractive index of salt-water solutions,” Appl. Opt. 32, 3992–4002 (1993).
  15. H. M. Dobbins, E. R. Peck, “Change of refractive index of water as a function of temperature,” J. Opt. Soc. Am.. 63, 318–320 (1973).
    [CrossRef]
  16. J. M. St-Arnaud, J. Ge, J. Orbriot, T. K. Bose, Ph. Marteau, “An accurate method for refractive-index measurements of liquids using two Michelson laser interferometers,” Rev. Sci. Instrum. 62, 1411–1414 (1991).
    [CrossRef]

1993 (1)

1992 (1)

1991 (2)

J. M. St-Arnaud, J. Ge, J. Orbriot, T. K. Bose, Ph. Marteau, “An accurate method for refractive-index measurements of liquids using two Michelson laser interferometers,” Rev. Sci. Instrum. 62, 1411–1414 (1991).
[CrossRef]

K. Kuhler, E. L. Dereniak, M. Buchanan, “Measurement of the index of refraction of the plastic phenoxy PKFE,” Appl. Opt. 30, 1711–1714 (1991).
[CrossRef] [PubMed]

1990 (2)

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, 677–717 (1990).
[CrossRef]

P. Schiebener, J. Straub, J. M. H. Levelt Sengers, J. S. Gallagher, “Erratum: refractive index of water and steam as function of wavelength, temperature, and density,” J. Phys. Chem. Ref. Data 19, 1617 (1990).
[CrossRef]

1989 (1)

Y. Makdisi, A. A. Zaidi, K. S. Bhatia, “Laser refractometry of liquids with a diffraction grating,” Opt. Commun. 72, 148–152 (1989).
[CrossRef]

1984 (1)

1976 (1)

G. Abbate, A. Attanasio, U. Bernini, E. Ragozzino, F. Somma, “The direct determination of the temperature dependence of the refractive index of liquids and solids,” J. Phys. D 9, 1945–1951 (1976).
[CrossRef]

1973 (1)

1966 (1)

L. Pontier, C. Dechambenoy, “Détermination des constantes optiques de l’eau liquide entre 1 et 40 μm. Application au calcul de son pouvoir réflecteur et de son émissivité,” Ann. Geophys. 22, 633–641 (1966).

1964 (1)

J. Vincent-Geisse, G. Vagner, F. Gans, “Mesures d’indices de réfraction dans l’infrarouge par des méthodes réfrac-tométriques,” Rev. Opt. 43, 15–21 (1964).

1941 (1)

1922 (1)

1909 (1)

H. Rubens, E. Ladenburg, “Über die Dispersion des Wassers im ultraroten Spektrum,” Ber. Dtsch. Phys. Ges. 11, 16–27 (1909).

1892 (1)

H. Rubens, “Über Dispersion ultrarother Strahlen,” Ann. Phys. Wied. 45, 238–253 (1892).
[CrossRef]

Abbate, G.

G. Abbate, A. Attanasio, U. Bernini, E. Ragozzino, F. Somma, “The direct determination of the temperature dependence of the refractive index of liquids and solids,” J. Phys. D 9, 1945–1951 (1976).
[CrossRef]

Attanasio, A.

G. Abbate, A. Attanasio, U. Bernini, E. Ragozzino, F. Somma, “The direct determination of the temperature dependence of the refractive index of liquids and solids,” J. Phys. D 9, 1945–1951 (1976).
[CrossRef]

Bernini, U.

G. Abbate, A. Attanasio, U. Bernini, E. Ragozzino, F. Somma, “The direct determination of the temperature dependence of the refractive index of liquids and solids,” J. Phys. D 9, 1945–1951 (1976).
[CrossRef]

Bhatia, K. S.

Y. Makdisi, A. A. Zaidi, K. S. Bhatia, “Laser refractometry of liquids with a diffraction grating,” Opt. Commun. 72, 148–152 (1989).
[CrossRef]

Bose, T. K.

J. M. St-Arnaud, J. Ge, J. Orbriot, T. K. Bose, Ph. Marteau, “An accurate method for refractive-index measurements of liquids using two Michelson laser interferometers,” Rev. Sci. Instrum. 62, 1411–1414 (1991).
[CrossRef]

Buchanan, M.

Centeno, U. M.

de Greef, C.

Dechambenoy, C.

L. Pontier, C. Dechambenoy, “Détermination des constantes optiques de l’eau liquide entre 1 et 40 μm. Application au calcul de son pouvoir réflecteur et de son émissivité,” Ann. Geophys. 22, 633–641 (1966).

Dereniak, E. L.

Dobbins, H. M.

Finsy, R.

Gallagher, J. S.

P. Schiebener, J. Straub, J. M. H. Levelt Sengers, J. S. Gallagher, “Erratum: refractive index of water and steam as function of wavelength, temperature, and density,” J. Phys. Chem. Ref. Data 19, 1617 (1990).
[CrossRef]

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, 677–717 (1990).
[CrossRef]

Gans, F.

J. Vincent-Geisse, G. Vagner, F. Gans, “Mesures d’indices de réfraction dans l’infrarouge par des méthodes réfrac-tométriques,” Rev. Opt. 43, 15–21 (1964).

Ge, J.

J. M. St-Arnaud, J. Ge, J. Orbriot, T. K. Bose, Ph. Marteau, “An accurate method for refractive-index measurements of liquids using two Michelson laser interferometers,” Rev. Sci. Instrum. 62, 1411–1414 (1991).
[CrossRef]

Ingersoll, L. R.

Kuhler, K.

Ladenburg, E.

H. Rubens, E. Ladenburg, “Über die Dispersion des Wassers im ultraroten Spektrum,” Ber. Dtsch. Phys. Ges. 11, 16–27 (1909).

Lea, W.

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, 677–717 (1990).
[CrossRef]

P. Schiebener, J. Straub, J. M. H. Levelt Sengers, J. S. Gallagher, “Erratum: refractive index of water and steam as function of wavelength, temperature, and density,” J. Phys. Chem. Ref. Data 19, 1617 (1990).
[CrossRef]

Makdisi, Y.

Y. Makdisi, A. A. Zaidi, K. S. Bhatia, “Laser refractometry of liquids with a diffraction grating,” Opt. Commun. 72, 148–152 (1989).
[CrossRef]

Marteau, Ph.

J. M. St-Arnaud, J. Ge, J. Orbriot, T. K. Bose, Ph. Marteau, “An accurate method for refractive-index measurements of liquids using two Michelson laser interferometers,” Rev. Sci. Instrum. 62, 1411–1414 (1991).
[CrossRef]

Moreels, E.

Nemoto, S.

Orbriot, J.

J. M. St-Arnaud, J. Ge, J. Orbriot, T. K. Bose, Ph. Marteau, “An accurate method for refractive-index measurements of liquids using two Michelson laser interferometers,” Rev. Sci. Instrum. 62, 1411–1414 (1991).
[CrossRef]

Peck, E. R.

Pontier, L.

L. Pontier, C. Dechambenoy, “Détermination des constantes optiques de l’eau liquide entre 1 et 40 μm. Application au calcul de son pouvoir réflecteur et de son émissivité,” Ann. Geophys. 22, 633–641 (1966).

Ragozzino, E.

G. Abbate, A. Attanasio, U. Bernini, E. Ragozzino, F. Somma, “The direct determination of the temperature dependence of the refractive index of liquids and solids,” J. Phys. D 9, 1945–1951 (1976).
[CrossRef]

Rubens, H.

H. Rubens, E. Ladenburg, “Über die Dispersion des Wassers im ultraroten Spektrum,” Ber. Dtsch. Phys. Ges. 11, 16–27 (1909).

H. Rubens, “Über Dispersion ultrarother Strahlen,” Ann. Phys. Wied. 45, 238–253 (1892).
[CrossRef]

Schiebener, P.

P. Schiebener, J. Straub, J. M. H. Levelt Sengers, J. S. Gallagher, “Erratum: refractive index of water and steam as function of wavelength, temperature, and density,” J. Phys. Chem. Ref. Data 19, 1617 (1990).
[CrossRef]

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, 677–717 (1990).
[CrossRef]

Somma, F.

G. Abbate, A. Attanasio, U. Bernini, E. Ragozzino, F. Somma, “The direct determination of the temperature dependence of the refractive index of liquids and solids,” J. Phys. D 9, 1945–1951 (1976).
[CrossRef]

St-Arnaud, J. M.

J. M. St-Arnaud, J. Ge, J. Orbriot, T. K. Bose, Ph. Marteau, “An accurate method for refractive-index measurements of liquids using two Michelson laser interferometers,” Rev. Sci. Instrum. 62, 1411–1414 (1991).
[CrossRef]

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, 677–717 (1990).
[CrossRef]

P. Schiebener, J. Straub, J. M. H. Levelt Sengers, J. S. Gallagher, “Erratum: refractive index of water and steam as function of wavelength, temperature, and density,” J. Phys. Chem. Ref. Data 19, 1617 (1990).
[CrossRef]

Vagner, G.

J. Vincent-Geisse, G. Vagner, F. Gans, “Mesures d’indices de réfraction dans l’infrarouge par des méthodes réfrac-tométriques,” Rev. Opt. 43, 15–21 (1964).

Vincent-Geisse, J.

J. Vincent-Geisse, G. Vagner, F. Gans, “Mesures d’indices de réfraction dans l’infrarouge par des méthodes réfrac-tométriques,” Rev. Opt. 43, 15–21 (1964).

Work, W. M.

Zaidi, A. A.

Y. Makdisi, A. A. Zaidi, K. S. Bhatia, “Laser refractometry of liquids with a diffraction grating,” Opt. Commun. 72, 148–152 (1989).
[CrossRef]

Ann. Geophys. (1)

L. Pontier, C. Dechambenoy, “Détermination des constantes optiques de l’eau liquide entre 1 et 40 μm. Application au calcul de son pouvoir réflecteur et de son émissivité,” Ann. Geophys. 22, 633–641 (1966).

Ann. Phys. Wied. (1)

H. Rubens, “Über Dispersion ultrarother Strahlen,” Ann. Phys. Wied. 45, 238–253 (1892).
[CrossRef]

Appl. Opt. (4)

Ber. Dtsch. Phys. Ges. (1)

H. Rubens, E. Ladenburg, “Über die Dispersion des Wassers im ultraroten Spektrum,” Ber. Dtsch. Phys. Ges. 11, 16–27 (1909).

J. Opt. Soc. Am. (3)

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

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, 677–717 (1990).
[CrossRef]

P. Schiebener, J. Straub, J. M. H. Levelt Sengers, J. S. Gallagher, “Erratum: refractive index of water and steam as function of wavelength, temperature, and density,” J. Phys. Chem. Ref. Data 19, 1617 (1990).
[CrossRef]

J. Phys. D (1)

G. Abbate, A. Attanasio, U. Bernini, E. Ragozzino, F. Somma, “The direct determination of the temperature dependence of the refractive index of liquids and solids,” J. Phys. D 9, 1945–1951 (1976).
[CrossRef]

Opt. Commun. (1)

Y. Makdisi, A. A. Zaidi, K. S. Bhatia, “Laser refractometry of liquids with a diffraction grating,” Opt. Commun. 72, 148–152 (1989).
[CrossRef]

Rev. Opt. (1)

J. Vincent-Geisse, G. Vagner, F. Gans, “Mesures d’indices de réfraction dans l’infrarouge par des méthodes réfrac-tométriques,” Rev. Opt. 43, 15–21 (1964).

Rev. Sci. Instrum. (1)

J. M. St-Arnaud, J. Ge, J. Orbriot, T. K. Bose, Ph. Marteau, “An accurate method for refractive-index measurements of liquids using two Michelson laser interferometers,” Rev. Sci. Instrum. 62, 1411–1414 (1991).
[CrossRef]

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Figures (4)

Fig. 1.
Fig. 1.

Measurement principle: A Michelson interferometer with one of the mirrors placed directly in water is used.

Fig. 2.
Fig. 2.

Experimental setup: 1, Nd:YAG laser; 2, objective, 25×; 3, monochromator, HR 250, Jobin Yvon; 4, objective, 20×; 5, cylindrical lens, f = 60 mm; 6, mirror HR1064; 7, diaphragm, 2 mm; 8, beam splitter, 50/50; 9, thermally isolated water cell; 10, thermostatic water circuit; 11, mirror HR1064, metallic coating; 12, thermoelement; 13, mirror HR1064; 14, diaphragm, 1 mm; 15, photodiode.

Fig. 3.
Fig. 3.

Index of refraction of water measured between 20 and 60 °C. The curve is a fit with a fourth-order polynome.

Fig. 4.
Fig. 4.

Index of refraction of water versus temperature obtained with our fit (solid curve), the Schiebener et al.7 equation (dashed curve), and three previous measurements.3 6

Equations (5)

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n = N λ 2 z ,
n = n 0 + a 1 T + a 2 T 2 + a 3 T 3 + a 4 T 4
n 0 = 1.32439 , a 1 = 1.80493 × 10 6 , a 2 = 3.51125 × 10 7 , a 3 = 3.43087 × 10 8 , a 4 = 1.92607 × 10 10 .
Δ N N = 0.5 6350 , Δλ λ = 0.1   nm 1064   nm , Δ z z = 0.1   μm 2550   μm ,
Δ N N = 0.01 6350 , Δλ λ 10 6 , Δ z z = 5   nm 2550   μm ,

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