Abstract

This study presents a laser diffractometric refractometer for measuring the refractive index of liquids. The refractive index is determined by rotating a reflection grating that is immersed in the fluid under test, and measuring the first-order Littrow diffraction angle. The Littrow angle is easily detected form the interferogram formed by the diffracted beam from the grating and the reflected beam from the liquid surface. No special cell for liquids is required. The alignment and measuring processes are simpler than those of other refractometers. The results of a feasibility experiment reveal that the accuracy of the proposed approach is about 0.003 for a refractive index of around 1.3.

© 2007 Optical Society of America

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References

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  1. J. H. Burnett and S.G. Kaplan, "Measurement of the refractive index and thermo-optic coefficient of water near 193 nm," J. Microlithogr. Microfabr. Microsyst. 3, 68-72 (2004).
    [CrossRef]
  2. S. G. Kaplan and J. H. Burnett, "Optical properties of fluids for 248 and 193 nm immersion photo-lithography," Appl. Opt. 45, 1721-1724 (2006).
    [CrossRef] [PubMed]
  3. E. Moreels, C. de Greef, and R. Finsy, "Laser light refractometer," Appl. Opt. 23, 3010-3013 (1984).
    [CrossRef] [PubMed]
  4. S. Nemoto, "Measurement of the refractive index of liquid using laser beam displacement," Appl. Opt. 31, 690-694 (1992).
    [CrossRef]
  5. T. Li and X. Tan, "Stepwise interferometric method of measuring the refractive index of liquid samples," Appl. Opt. 32, 2274-2277 (1993).
    [CrossRef] [PubMed]
  6. M. Musso, R. Aschauer, A. Asenbaum, C. Vasi, and E. Wilhelm, "Interferometric determination of the refractive index of liquid sulphur dioxide," Meas. Sci. and Technol. 11, 1714-1720 (2000).
    [CrossRef]
  7. M. de Angelis, S. De Nicola, P. Ferraro, A. Finizio, and G. Pierattini, "Liquid refractometer based on interferometric fringe projection," Opt. Commun. 175, 315-321 (2000).
    [CrossRef]
  8. A. F. Leung and J. J. Vandiver, "Automatic refractometer," Opt. Eng. 42, 1128-1131 (2003).
    [CrossRef]
  9. S. H. Lu, L. C. Tseng, C. F. Kao, S. P. Pan, and L. C. Chang, "Immersion diffractometry for determining nanoscale grating pitch," Opt. Express 14, 9564-9569 (2006).
    [CrossRef] [PubMed]
  10. A. A. Zaidi, "Simple laser refractometer for liquids," Rev. Sci. Instrum. 59, 1153-1155 (1988).
    [CrossRef]
  11. S. Singh, "Diffraction method measures refractive indices of liquids," Phys. Educ. 39, 235 (2004).
    [CrossRef]

2006 (2)

2004 (2)

S. Singh, "Diffraction method measures refractive indices of liquids," Phys. Educ. 39, 235 (2004).
[CrossRef]

J. H. Burnett and S.G. Kaplan, "Measurement of the refractive index and thermo-optic coefficient of water near 193 nm," J. Microlithogr. Microfabr. Microsyst. 3, 68-72 (2004).
[CrossRef]

2003 (1)

A. F. Leung and J. J. Vandiver, "Automatic refractometer," Opt. Eng. 42, 1128-1131 (2003).
[CrossRef]

2000 (2)

M. Musso, R. Aschauer, A. Asenbaum, C. Vasi, and E. Wilhelm, "Interferometric determination of the refractive index of liquid sulphur dioxide," Meas. Sci. and Technol. 11, 1714-1720 (2000).
[CrossRef]

M. de Angelis, S. De Nicola, P. Ferraro, A. Finizio, and G. Pierattini, "Liquid refractometer based on interferometric fringe projection," Opt. Commun. 175, 315-321 (2000).
[CrossRef]

1993 (1)

1992 (1)

1988 (1)

A. A. Zaidi, "Simple laser refractometer for liquids," Rev. Sci. Instrum. 59, 1153-1155 (1988).
[CrossRef]

1984 (1)

Aschauer, R.

M. Musso, R. Aschauer, A. Asenbaum, C. Vasi, and E. Wilhelm, "Interferometric determination of the refractive index of liquid sulphur dioxide," Meas. Sci. and Technol. 11, 1714-1720 (2000).
[CrossRef]

Asenbaum, A.

M. Musso, R. Aschauer, A. Asenbaum, C. Vasi, and E. Wilhelm, "Interferometric determination of the refractive index of liquid sulphur dioxide," Meas. Sci. and Technol. 11, 1714-1720 (2000).
[CrossRef]

Burnett, J. H.

S. G. Kaplan and J. H. Burnett, "Optical properties of fluids for 248 and 193 nm immersion photo-lithography," Appl. Opt. 45, 1721-1724 (2006).
[CrossRef] [PubMed]

J. H. Burnett and S.G. Kaplan, "Measurement of the refractive index and thermo-optic coefficient of water near 193 nm," J. Microlithogr. Microfabr. Microsyst. 3, 68-72 (2004).
[CrossRef]

Chang, L. C.

de Angelis, M.

M. de Angelis, S. De Nicola, P. Ferraro, A. Finizio, and G. Pierattini, "Liquid refractometer based on interferometric fringe projection," Opt. Commun. 175, 315-321 (2000).
[CrossRef]

de Greef, C.

De Nicola, S.

M. de Angelis, S. De Nicola, P. Ferraro, A. Finizio, and G. Pierattini, "Liquid refractometer based on interferometric fringe projection," Opt. Commun. 175, 315-321 (2000).
[CrossRef]

Ferraro, P.

M. de Angelis, S. De Nicola, P. Ferraro, A. Finizio, and G. Pierattini, "Liquid refractometer based on interferometric fringe projection," Opt. Commun. 175, 315-321 (2000).
[CrossRef]

Finizio, A.

M. de Angelis, S. De Nicola, P. Ferraro, A. Finizio, and G. Pierattini, "Liquid refractometer based on interferometric fringe projection," Opt. Commun. 175, 315-321 (2000).
[CrossRef]

Finsy, R.

Kao, C. F.

Kaplan, S. G.

Kaplan, S.G.

J. H. Burnett and S.G. Kaplan, "Measurement of the refractive index and thermo-optic coefficient of water near 193 nm," J. Microlithogr. Microfabr. Microsyst. 3, 68-72 (2004).
[CrossRef]

Leung, A. F.

A. F. Leung and J. J. Vandiver, "Automatic refractometer," Opt. Eng. 42, 1128-1131 (2003).
[CrossRef]

Li, T.

Lu, S. H.

Moreels, E.

Musso, M.

M. Musso, R. Aschauer, A. Asenbaum, C. Vasi, and E. Wilhelm, "Interferometric determination of the refractive index of liquid sulphur dioxide," Meas. Sci. and Technol. 11, 1714-1720 (2000).
[CrossRef]

Nemoto, S.

Pan, S. P.

Pierattini, G.

M. de Angelis, S. De Nicola, P. Ferraro, A. Finizio, and G. Pierattini, "Liquid refractometer based on interferometric fringe projection," Opt. Commun. 175, 315-321 (2000).
[CrossRef]

Singh, S.

S. Singh, "Diffraction method measures refractive indices of liquids," Phys. Educ. 39, 235 (2004).
[CrossRef]

Tan, X.

Tseng, L. C.

Vandiver, J. J.

A. F. Leung and J. J. Vandiver, "Automatic refractometer," Opt. Eng. 42, 1128-1131 (2003).
[CrossRef]

Vasi, C.

M. Musso, R. Aschauer, A. Asenbaum, C. Vasi, and E. Wilhelm, "Interferometric determination of the refractive index of liquid sulphur dioxide," Meas. Sci. and Technol. 11, 1714-1720 (2000).
[CrossRef]

Wilhelm, E.

M. Musso, R. Aschauer, A. Asenbaum, C. Vasi, and E. Wilhelm, "Interferometric determination of the refractive index of liquid sulphur dioxide," Meas. Sci. and Technol. 11, 1714-1720 (2000).
[CrossRef]

Zaidi, A. A.

A. A. Zaidi, "Simple laser refractometer for liquids," Rev. Sci. Instrum. 59, 1153-1155 (1988).
[CrossRef]

Appl. Opt. (4)

J. Microlithogr. Microfabr. Microsyst. (1)

J. H. Burnett and S.G. Kaplan, "Measurement of the refractive index and thermo-optic coefficient of water near 193 nm," J. Microlithogr. Microfabr. Microsyst. 3, 68-72 (2004).
[CrossRef]

Meas. Sci. and Technol. (1)

M. Musso, R. Aschauer, A. Asenbaum, C. Vasi, and E. Wilhelm, "Interferometric determination of the refractive index of liquid sulphur dioxide," Meas. Sci. and Technol. 11, 1714-1720 (2000).
[CrossRef]

Opt. Commun. (1)

M. de Angelis, S. De Nicola, P. Ferraro, A. Finizio, and G. Pierattini, "Liquid refractometer based on interferometric fringe projection," Opt. Commun. 175, 315-321 (2000).
[CrossRef]

Opt. Eng. (1)

A. F. Leung and J. J. Vandiver, "Automatic refractometer," Opt. Eng. 42, 1128-1131 (2003).
[CrossRef]

Opt. Express (1)

Phys. Educ. (1)

S. Singh, "Diffraction method measures refractive indices of liquids," Phys. Educ. 39, 235 (2004).
[CrossRef]

Rev. Sci. Instrum. (1)

A. A. Zaidi, "Simple laser refractometer for liquids," Rev. Sci. Instrum. 59, 1153-1155 (1988).
[CrossRef]

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Figures (4)

Fig. 1.
Fig. 1.

Diffractometric liquid refractometer

Fig. 2.
Fig. 2.

Relationships between the refractive index of a liquid ns and the diffraction angle θ corresponding to different wavelength-to-period ratios λv/p.

Fig. 3.
Fig. 3.

Experimental configuration used to measure the refractive index of a liquid. (a) Side view (b) Front view (c) Grating in Littrow configuration.

Fig. 4.
Fig. 4.

Graphs of (a) δp/p versus δθ and (b) δns/ns versus δθ.

Tables (2)

Tables Icon

Table 1. Measured refractive indices of four different liquids

Tables Icon

Table 2. Sources of error in the measurement of refractive index by the proposed method

Equations (6)

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

n s = λ v 2 p sin θ
δ n s = n s · δ λ v λ v
δ n s = n s · δ p p
p = λ v 2 n a sin θ
δp p = [ ( 2 n a p λ v ) 2 1 ] 1 2 · δ θ
δ n s = n s · [ ( 2 n s p λ v ) 2 1 ] 1 2 · δ θ

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