Abstract

A total internal reflection-based differencial refractometer, capable of measuring the real and imaginary parts of the complex refractive index in real time, is presented. The device takes advantage of the phase difference acquired by s- and p-polarized light to generate an easily detectable minimum at the reflected profile. The method allows to sensitively measuring transparent and turbid liquid samples.

© 2012 OSA

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References

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  1. G. H. Meeten and A. N. North, “Refractive index measurement of absorbing and turbid fluids by reflection near the critical angle,” Meas. Sci. Technol. 6(2), 214–221 (1995).
    [CrossRef]
  2. A. J. Jääskeläinen, K. E. Peiponen, and J. A. Räty, “On reflectometric measurement of a refractive index of milk,” J. Dairy Sci. 84(1), 38–43 (2001).
    [CrossRef] [PubMed]
  3. W. R. Calhoun, H. Maeta, A. Combs, L. M. Bali, and S. Bali, “Measurement of the refractive index of highly turbid media,” Opt. Lett. 35(8), 1224–1226 (2010).
    [CrossRef] [PubMed]
  4. W. R. Calhoun, H. Maeta, S. Roy, L. M. Bali, and S. Bali, “Sensitive real-time measurement of the refractive index and attenuation coefficient of milk and milk-cream mixtures,” J. Dairy Sci. 93(8), 3497–3504 (2010).
    [CrossRef] [PubMed]
  5. M. McClimans, C. LaPlante, D. Bonner, and S. Bali, “Real-time differential refractometry without interferometry at a sensitivity level of 10(-6),” Appl. Opt. 45(25), 6477–6486 (2006).
    [CrossRef] [PubMed]
  6. G. R. Fowles, Introduction to Modern Optics, Holt, Rinehart and Winston, Inc., New York, 1968.
  7. M. H. Chiu, J. Y. Lee, and D. C. Su, “Complex refractive-index measurement based on Fresnel’s equations and the uses of heterodyne interferometry,” Appl. Opt. 38(19), 4047–4052 (1999).
    [CrossRef] [PubMed]
  8. S. T. Flock, B. C. Wilson, and M. S. Patterson, “Total attenuation coefficients and scattering phase functions of tissues and phantom materials at 633 nm,” Med. Phys. 14(5), 835–841 (1987).
    [CrossRef] [PubMed]
  9. http://refractiveindex.inf
  10. S. C. Zilio, “Refratômetro diferencial para medir o índice de refração e coeficiente de atenuação de um líquido em tempo real”, Patent pending.

2010 (2)

W. R. Calhoun, H. Maeta, S. Roy, L. M. Bali, and S. Bali, “Sensitive real-time measurement of the refractive index and attenuation coefficient of milk and milk-cream mixtures,” J. Dairy Sci. 93(8), 3497–3504 (2010).
[CrossRef] [PubMed]

W. R. Calhoun, H. Maeta, A. Combs, L. M. Bali, and S. Bali, “Measurement of the refractive index of highly turbid media,” Opt. Lett. 35(8), 1224–1226 (2010).
[CrossRef] [PubMed]

2006 (1)

2001 (1)

A. J. Jääskeläinen, K. E. Peiponen, and J. A. Räty, “On reflectometric measurement of a refractive index of milk,” J. Dairy Sci. 84(1), 38–43 (2001).
[CrossRef] [PubMed]

1999 (1)

1995 (1)

G. H. Meeten and A. N. North, “Refractive index measurement of absorbing and turbid fluids by reflection near the critical angle,” Meas. Sci. Technol. 6(2), 214–221 (1995).
[CrossRef]

1987 (1)

S. T. Flock, B. C. Wilson, and M. S. Patterson, “Total attenuation coefficients and scattering phase functions of tissues and phantom materials at 633 nm,” Med. Phys. 14(5), 835–841 (1987).
[CrossRef] [PubMed]

Bali, L. M.

W. R. Calhoun, H. Maeta, A. Combs, L. M. Bali, and S. Bali, “Measurement of the refractive index of highly turbid media,” Opt. Lett. 35(8), 1224–1226 (2010).
[CrossRef] [PubMed]

W. R. Calhoun, H. Maeta, S. Roy, L. M. Bali, and S. Bali, “Sensitive real-time measurement of the refractive index and attenuation coefficient of milk and milk-cream mixtures,” J. Dairy Sci. 93(8), 3497–3504 (2010).
[CrossRef] [PubMed]

Bali, S.

Bonner, D.

Calhoun, W. R.

W. R. Calhoun, H. Maeta, S. Roy, L. M. Bali, and S. Bali, “Sensitive real-time measurement of the refractive index and attenuation coefficient of milk and milk-cream mixtures,” J. Dairy Sci. 93(8), 3497–3504 (2010).
[CrossRef] [PubMed]

W. R. Calhoun, H. Maeta, A. Combs, L. M. Bali, and S. Bali, “Measurement of the refractive index of highly turbid media,” Opt. Lett. 35(8), 1224–1226 (2010).
[CrossRef] [PubMed]

Chiu, M. H.

Combs, A.

Flock, S. T.

S. T. Flock, B. C. Wilson, and M. S. Patterson, “Total attenuation coefficients and scattering phase functions of tissues and phantom materials at 633 nm,” Med. Phys. 14(5), 835–841 (1987).
[CrossRef] [PubMed]

Jääskeläinen, A. J.

A. J. Jääskeläinen, K. E. Peiponen, and J. A. Räty, “On reflectometric measurement of a refractive index of milk,” J. Dairy Sci. 84(1), 38–43 (2001).
[CrossRef] [PubMed]

LaPlante, C.

Lee, J. Y.

Maeta, H.

W. R. Calhoun, H. Maeta, A. Combs, L. M. Bali, and S. Bali, “Measurement of the refractive index of highly turbid media,” Opt. Lett. 35(8), 1224–1226 (2010).
[CrossRef] [PubMed]

W. R. Calhoun, H. Maeta, S. Roy, L. M. Bali, and S. Bali, “Sensitive real-time measurement of the refractive index and attenuation coefficient of milk and milk-cream mixtures,” J. Dairy Sci. 93(8), 3497–3504 (2010).
[CrossRef] [PubMed]

McClimans, M.

Meeten, G. H.

G. H. Meeten and A. N. North, “Refractive index measurement of absorbing and turbid fluids by reflection near the critical angle,” Meas. Sci. Technol. 6(2), 214–221 (1995).
[CrossRef]

North, A. N.

G. H. Meeten and A. N. North, “Refractive index measurement of absorbing and turbid fluids by reflection near the critical angle,” Meas. Sci. Technol. 6(2), 214–221 (1995).
[CrossRef]

Patterson, M. S.

S. T. Flock, B. C. Wilson, and M. S. Patterson, “Total attenuation coefficients and scattering phase functions of tissues and phantom materials at 633 nm,” Med. Phys. 14(5), 835–841 (1987).
[CrossRef] [PubMed]

Peiponen, K. E.

A. J. Jääskeläinen, K. E. Peiponen, and J. A. Räty, “On reflectometric measurement of a refractive index of milk,” J. Dairy Sci. 84(1), 38–43 (2001).
[CrossRef] [PubMed]

Räty, J. A.

A. J. Jääskeläinen, K. E. Peiponen, and J. A. Räty, “On reflectometric measurement of a refractive index of milk,” J. Dairy Sci. 84(1), 38–43 (2001).
[CrossRef] [PubMed]

Roy, S.

W. R. Calhoun, H. Maeta, S. Roy, L. M. Bali, and S. Bali, “Sensitive real-time measurement of the refractive index and attenuation coefficient of milk and milk-cream mixtures,” J. Dairy Sci. 93(8), 3497–3504 (2010).
[CrossRef] [PubMed]

Su, D. C.

Wilson, B. C.

S. T. Flock, B. C. Wilson, and M. S. Patterson, “Total attenuation coefficients and scattering phase functions of tissues and phantom materials at 633 nm,” Med. Phys. 14(5), 835–841 (1987).
[CrossRef] [PubMed]

Appl. Opt. (2)

J. Dairy Sci. (2)

A. J. Jääskeläinen, K. E. Peiponen, and J. A. Räty, “On reflectometric measurement of a refractive index of milk,” J. Dairy Sci. 84(1), 38–43 (2001).
[CrossRef] [PubMed]

W. R. Calhoun, H. Maeta, S. Roy, L. M. Bali, and S. Bali, “Sensitive real-time measurement of the refractive index and attenuation coefficient of milk and milk-cream mixtures,” J. Dairy Sci. 93(8), 3497–3504 (2010).
[CrossRef] [PubMed]

Meas. Sci. Technol. (1)

G. H. Meeten and A. N. North, “Refractive index measurement of absorbing and turbid fluids by reflection near the critical angle,” Meas. Sci. Technol. 6(2), 214–221 (1995).
[CrossRef]

Med. Phys. (1)

S. T. Flock, B. C. Wilson, and M. S. Patterson, “Total attenuation coefficients and scattering phase functions of tissues and phantom materials at 633 nm,” Med. Phys. 14(5), 835–841 (1987).
[CrossRef] [PubMed]

Opt. Lett. (1)

Other (3)

http://refractiveindex.inf

S. C. Zilio, “Refratômetro diferencial para medir o índice de refração e coeficiente de atenuação de um líquido em tempo real”, Patent pending.

G. R. Fowles, Introduction to Modern Optics, Holt, Rinehart and Winston, Inc., New York, 1968.

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Figures (5)

Fig. 1
Fig. 1

Schematic view of the refractometer.

Fig. 2
Fig. 2

Light transmitted through the analyzer as a function of incidence angle for (a) α = 0 cm−1, (b) α = 1000 cm−1 and (c) α = 2000 cm−1. We used n = 0.775 and α = (4π/λ)knglass.

Fig. 3
Fig. 3

(a) Image captured by the CCD webcam. (b) Intensity along the horizontal line at the center of the profile, for the saturated condition. In these figures, the sample in contact with the semi-cylindrical lens is water.

Fig. 4
Fig. 4

Refractive index obtained with a Pulfrich refractometer (open circles) and position of the dark line measured with the present refractometer (red squares). The solid line is just a guide for the eye.

Fig. 5
Fig. 5

Dark line pattern observed for fat concentrations of (a) 0%, (b) 1% and (c) 3%. (d) Dependence of the refractive index (solid squares) and attenuation coefficient (open circles) on the fat concentration. The refractive index was calibrated with the Pulfrich refractometer using water/ethanol solutions and the attenuation coefficient was calibrated through the transmission of a collimated beam through the samples. The solid (open) stars correspond to the refractive index (attenuation) obtained in [4]. The solid lines are just guides for the eye.

Equations (9)

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r s = cosθ n 2 se n 2 θ cosθ+ n 2 se n 2 θ ,
r p = n 2 cosθ+ n 2 se n 2 θ n 2 cosθ+ n 2 se n 2 θ ,
δ= θ σ θ π =π2{ tan 1 ( se n 2 θ n 2 /cosθ ) tan 1 ( se n 2 θ n 2 / n 2 cosθ ) },
r s = cosθ n ˜ 2 se n 2 θ cosθ+ n ˜ 2 se n 2 θ = cosθ(u+iv) cosθ+(u+iv) =| r s |exp(i δ s ),
r p = n ˜ 2 cosθ+ n ˜ 2 se n 2 θ n ˜ 2 cosθ+ n ˜ 2 se n 2 θ = n ˜ 2 cosθ+(u+iv) n ˜ 2 cosθ+(u+iv) =| r p |exp(i δ p ),
u 2 = 1 2 { ( n 2 k 2 sin 2 θ )+ ( n 2 k 2 sin 2 θ ) 2 +4 n 2 k 2 },
v 2 = 1 2 { ( n 2 k 2 sin 2 θ )+ ( n 2 k 2 sin 2 θ ) 2 +4 n 2 k 2 }.
θ min sin 1 n,
V min αk.

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