Abstract

An iterative interferometric technique for accurately determining the refractive index (RI) of liquid samples is presented. The liquid is measured in an extremely stable stepped cell that is inserted into one arm of a Michelson-type interferometer. The uncertainty of the RI measurement is repeatedly improved by taking successive measurements of the interferometric fringe shifts on adjacent steps in the cell. It is shown that in practice the temperature nonuniformity in the liquid limits the ultimate uncertainty of the RI measurement. The RI resolution of the apparatus described is designed to be 4.3 × 10E-6, and the final RI uncertainty is 1.2 × 10E-5 (2σ) for a liquid with a RI temperature coefficient of 4 × 10E-4.

© 1993 Optical Society of America

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References

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  1. See, for example, N. Bauer, K. Fajans, Z. Lewin, Refractometry Techniques of Organic Chemistry, Vol. 1 of Physical Methods of Organic Chemistry, Part II, A. Weissberger, ed. (Interscience, New York, 1960). p. 1139.
  2. M. D. Hopler, J. R. Rogers, “Interferometric measurement of group and phase refractive index,” Appl. Opt. 30, 735–744 (1991).
    [Crossref] [PubMed]
  3. J. Locke, M. Underhill, “Automatic refractive index measurement of glass particles,” Forensic Sci. Int. 27, 247–260 (1985).
    [Crossref]
  4. T. Li, Y. Fang, X. Tan, M. Wang, Z. Fang, “Standard apparatus for the measurement of geometric parameters and refractive index profiles of optical fiber at NIM,” presented at IMEKO'XII, Beijing, 1991.
  5. X. Tan, “Refractive index profile measurement of optical fiber and its calibration,” M.S. Thesis (Beijing Institute of Technology, Beijing, 1990).
  6. T. H. Barnes, K. Matsumoto, T. Eiju, K. Matsuda, N. Ooyama, “Grating interferometer with extremely high stability, suitable for measuring small refractive index changes,” Appl. Opt. 30, 745–751 (1991).
    [Crossref] [PubMed]
  7. L. J. Edwards, B. D. Hopkins, D. D. Rice, “Apparatus for measuring changes in the optical refractive index of fluids,” U.S. patent3,680,963 (1August1972).
  8. C. Sainz, J. Calatroni, G. Tribillon, “Refractometry of liquid samples with spectrally resolved white light interferometry,” Meas. Sci. Technol. 1, 356–361 (1990).
    [Crossref]
  9. See, for example, W. H. Steel, Interferometry (Cambridge U. Press, Cambridge, 1967).
  10. J. E. Chamberlain, J. E. Gibbs, H. A. Gebbie, “Refractometry in the far infra-red using a two-beam interferometer,” Nature (London) 198, 874–875 (1963).
    [Crossref]

1991 (2)

1990 (1)

C. Sainz, J. Calatroni, G. Tribillon, “Refractometry of liquid samples with spectrally resolved white light interferometry,” Meas. Sci. Technol. 1, 356–361 (1990).
[Crossref]

1985 (1)

J. Locke, M. Underhill, “Automatic refractive index measurement of glass particles,” Forensic Sci. Int. 27, 247–260 (1985).
[Crossref]

1963 (1)

J. E. Chamberlain, J. E. Gibbs, H. A. Gebbie, “Refractometry in the far infra-red using a two-beam interferometer,” Nature (London) 198, 874–875 (1963).
[Crossref]

Barnes, T. H.

Bauer, N.

See, for example, N. Bauer, K. Fajans, Z. Lewin, Refractometry Techniques of Organic Chemistry, Vol. 1 of Physical Methods of Organic Chemistry, Part II, A. Weissberger, ed. (Interscience, New York, 1960). p. 1139.

Calatroni, J.

C. Sainz, J. Calatroni, G. Tribillon, “Refractometry of liquid samples with spectrally resolved white light interferometry,” Meas. Sci. Technol. 1, 356–361 (1990).
[Crossref]

Chamberlain, J. E.

J. E. Chamberlain, J. E. Gibbs, H. A. Gebbie, “Refractometry in the far infra-red using a two-beam interferometer,” Nature (London) 198, 874–875 (1963).
[Crossref]

Edwards, L. J.

L. J. Edwards, B. D. Hopkins, D. D. Rice, “Apparatus for measuring changes in the optical refractive index of fluids,” U.S. patent3,680,963 (1August1972).

Eiju, T.

Fajans, K.

See, for example, N. Bauer, K. Fajans, Z. Lewin, Refractometry Techniques of Organic Chemistry, Vol. 1 of Physical Methods of Organic Chemistry, Part II, A. Weissberger, ed. (Interscience, New York, 1960). p. 1139.

Fang, Y.

T. Li, Y. Fang, X. Tan, M. Wang, Z. Fang, “Standard apparatus for the measurement of geometric parameters and refractive index profiles of optical fiber at NIM,” presented at IMEKO'XII, Beijing, 1991.

Fang, Z.

T. Li, Y. Fang, X. Tan, M. Wang, Z. Fang, “Standard apparatus for the measurement of geometric parameters and refractive index profiles of optical fiber at NIM,” presented at IMEKO'XII, Beijing, 1991.

Gebbie, H. A.

J. E. Chamberlain, J. E. Gibbs, H. A. Gebbie, “Refractometry in the far infra-red using a two-beam interferometer,” Nature (London) 198, 874–875 (1963).
[Crossref]

Gibbs, J. E.

J. E. Chamberlain, J. E. Gibbs, H. A. Gebbie, “Refractometry in the far infra-red using a two-beam interferometer,” Nature (London) 198, 874–875 (1963).
[Crossref]

Hopkins, B. D.

L. J. Edwards, B. D. Hopkins, D. D. Rice, “Apparatus for measuring changes in the optical refractive index of fluids,” U.S. patent3,680,963 (1August1972).

Hopler, M. D.

Lewin, Z.

See, for example, N. Bauer, K. Fajans, Z. Lewin, Refractometry Techniques of Organic Chemistry, Vol. 1 of Physical Methods of Organic Chemistry, Part II, A. Weissberger, ed. (Interscience, New York, 1960). p. 1139.

Li, T.

T. Li, Y. Fang, X. Tan, M. Wang, Z. Fang, “Standard apparatus for the measurement of geometric parameters and refractive index profiles of optical fiber at NIM,” presented at IMEKO'XII, Beijing, 1991.

Locke, J.

J. Locke, M. Underhill, “Automatic refractive index measurement of glass particles,” Forensic Sci. Int. 27, 247–260 (1985).
[Crossref]

Matsuda, K.

Matsumoto, K.

Ooyama, N.

Rice, D. D.

L. J. Edwards, B. D. Hopkins, D. D. Rice, “Apparatus for measuring changes in the optical refractive index of fluids,” U.S. patent3,680,963 (1August1972).

Rogers, J. R.

Sainz, C.

C. Sainz, J. Calatroni, G. Tribillon, “Refractometry of liquid samples with spectrally resolved white light interferometry,” Meas. Sci. Technol. 1, 356–361 (1990).
[Crossref]

Steel, W. H.

See, for example, W. H. Steel, Interferometry (Cambridge U. Press, Cambridge, 1967).

Tan, X.

X. Tan, “Refractive index profile measurement of optical fiber and its calibration,” M.S. Thesis (Beijing Institute of Technology, Beijing, 1990).

T. Li, Y. Fang, X. Tan, M. Wang, Z. Fang, “Standard apparatus for the measurement of geometric parameters and refractive index profiles of optical fiber at NIM,” presented at IMEKO'XII, Beijing, 1991.

Tribillon, G.

C. Sainz, J. Calatroni, G. Tribillon, “Refractometry of liquid samples with spectrally resolved white light interferometry,” Meas. Sci. Technol. 1, 356–361 (1990).
[Crossref]

Underhill, M.

J. Locke, M. Underhill, “Automatic refractive index measurement of glass particles,” Forensic Sci. Int. 27, 247–260 (1985).
[Crossref]

Wang, M.

T. Li, Y. Fang, X. Tan, M. Wang, Z. Fang, “Standard apparatus for the measurement of geometric parameters and refractive index profiles of optical fiber at NIM,” presented at IMEKO'XII, Beijing, 1991.

Appl. Opt. (2)

Forensic Sci. Int. (1)

J. Locke, M. Underhill, “Automatic refractive index measurement of glass particles,” Forensic Sci. Int. 27, 247–260 (1985).
[Crossref]

Meas. Sci. Technol. (1)

C. Sainz, J. Calatroni, G. Tribillon, “Refractometry of liquid samples with spectrally resolved white light interferometry,” Meas. Sci. Technol. 1, 356–361 (1990).
[Crossref]

Nature (London) (1)

J. E. Chamberlain, J. E. Gibbs, H. A. Gebbie, “Refractometry in the far infra-red using a two-beam interferometer,” Nature (London) 198, 874–875 (1963).
[Crossref]

Other (5)

See, for example, N. Bauer, K. Fajans, Z. Lewin, Refractometry Techniques of Organic Chemistry, Vol. 1 of Physical Methods of Organic Chemistry, Part II, A. Weissberger, ed. (Interscience, New York, 1960). p. 1139.

See, for example, W. H. Steel, Interferometry (Cambridge U. Press, Cambridge, 1967).

L. J. Edwards, B. D. Hopkins, D. D. Rice, “Apparatus for measuring changes in the optical refractive index of fluids,” U.S. patent3,680,963 (1August1972).

T. Li, Y. Fang, X. Tan, M. Wang, Z. Fang, “Standard apparatus for the measurement of geometric parameters and refractive index profiles of optical fiber at NIM,” presented at IMEKO'XII, Beijing, 1991.

X. Tan, “Refractive index profile measurement of optical fiber and its calibration,” M.S. Thesis (Beijing Institute of Technology, Beijing, 1990).

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Figures (3)

Fig. 1
Fig. 1

(a) Stepped cell fitted on a Michelson-type interferometer. After reflecting from the surfaces (hatched area) of the steps and the step platen in the cell, the measuring beam then recombines with the reference beam on the surface of the beam splitter: LE, lens; BS, beam splitter; SC, stepped cell assembly; LI, liquid under measurement. (b) Interference fringes on three steps and the platen.

Fig. 2
Fig. 2

Stepped cell assembly: CU, Invar cup; CG, cover glass; SB, stepped block. The hatched faces were silvered to ensure sufficient reflectivity when they were covered with liquid.

Fig. 3
Fig. 3

Refractive indices of an immersion liquid (Cargille Laboratory) versus temperatures, measured by using this stepwise interferometric technique with a RI measurement uncertainty of 1.2 × 10E-5 (2σ). RI, refractive index of the liquid; T, temperature. The solid line is a least-squares fit to the measured data.

Equations (10)

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L = n L = ( E + e ) λ 0 / 2 ,
d ( E + e ) i = ( 2 L i / λ 0 ) d n i 1 ,
L 1 < ( λ 0 / 2 ) ( d E / d n 0 ) .
E 1 = 2 int ( n 0 L 1 / λ 0 ) .
( d n i ) F = ( λ 0 / 2 L i ) d e i ,
( d n i ) λ 0 / n i = ( d λ 0 ) / λ 0 .
( d n i ) G = n ( d L / L i ) = 1.5 ( 0.014 / L i ) ,
L 1 < ( λ 0 / 2 ) ( d E / d n 0 ) = 0.264 mm .
wavelength , ( d n ) W = 8 × 10 E - 8 ; temperature , ( d n ) T = 1 × 10 E - 5 ; step geometric , ( d n 1 ) G = 9 × 10 E - 5 ; fringe fraction reading , ( d n 1 ) F = 9 × 10 E - 5 ; total RI uncertainty for this step , d n 1 = 1.3 × 10 E - 4.
L 1 = 0.24 mm , ( d n 1 ) F = 0.9 × 10 E - 4 , d n 1 = 1.3 × 10 E - 4 , L 2 = 1.1 mm , ( d n 2 ) F = 1.9 × 10 E - 5 , d n 2 = 2.9 × 10 E - 5 , L 3 = 4.9 mm , ( d n 3 ) F = 4.3 × 10 E - 6 , d n 3 = 1.2 × 10 E - 5 ,

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