Abstract

We demonstrate a first simultaneous measurement of the real and imaginary parts of the refractive index of a highly turbid medium by observing the real-time reflectance profile of a divergent laser beam made incident on the surface of the turbid medium. We find that the reflectance data are well described by Fresnel theory that correctly includes the effect on total internal reflection of angle-dependent penetration into the turbid medium.

© 2010 Optical Society of America

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References

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  1. J. Lai, Z. Li, C. Wang, and A. He, Appl. Opt. 44, 1845 (2005).
    [CrossRef] [PubMed]
  2. S. Taylor, J. Czarnecki, and J. Masliyah, Fuel 80, 2013 (2001).
    [CrossRef]
  3. K. Alexander, A. Killey, G. H. Meeten, and M. Senior, J. Chem. Soc. Faraday Trans. 77, 361 (1981).
  4. G. Meeten and A. North, Meas. Sci. Technol. 6, 214 (1995).
    [CrossRef]
  5. A. Reyes-Coronado, A. Garcia-Valenzuela, C. Sanchez-Perez, R. G. Barrera, New J. Phys. 7, 891 (2005).
    [CrossRef]
  6. I. Niskanen, J. Räty, and K.-E. Peiponen, Opt. Lett. 32, 862 (2007).
    [CrossRef] [PubMed]
  7. M. A. Heald and J. B. Marion, Classical Electromagnetic Radiation, 3rd ed. (Brooks Cole, 1994)
  8. M. McClimans, C. LaPlante, D. Bonner, and S. Bali, Appl. Opt. 45, 6477 (2006).
    [CrossRef] [PubMed]
  9. A. W. Snyder and J. D. Love, Appl. Opt. 15, 236 (1976).
    [CrossRef] [PubMed]
  10. Z. Wu, R. L. Nelson, J. W. Haus, and Q. Zhan, Opt. Lett. 33, 551 (2008).
    [CrossRef] [PubMed]

2008 (1)

2007 (1)

2006 (1)

2005 (2)

J. Lai, Z. Li, C. Wang, and A. He, Appl. Opt. 44, 1845 (2005).
[CrossRef] [PubMed]

A. Reyes-Coronado, A. Garcia-Valenzuela, C. Sanchez-Perez, R. G. Barrera, New J. Phys. 7, 891 (2005).
[CrossRef]

2001 (1)

S. Taylor, J. Czarnecki, and J. Masliyah, Fuel 80, 2013 (2001).
[CrossRef]

1995 (1)

G. Meeten and A. North, Meas. Sci. Technol. 6, 214 (1995).
[CrossRef]

1994 (1)

M. A. Heald and J. B. Marion, Classical Electromagnetic Radiation, 3rd ed. (Brooks Cole, 1994)

1981 (1)

K. Alexander, A. Killey, G. H. Meeten, and M. Senior, J. Chem. Soc. Faraday Trans. 77, 361 (1981).

1976 (1)

Alexander, K.

K. Alexander, A. Killey, G. H. Meeten, and M. Senior, J. Chem. Soc. Faraday Trans. 77, 361 (1981).

Bali, S.

Barrera, R. G.

A. Reyes-Coronado, A. Garcia-Valenzuela, C. Sanchez-Perez, R. G. Barrera, New J. Phys. 7, 891 (2005).
[CrossRef]

Bonner, D.

Czarnecki, J.

S. Taylor, J. Czarnecki, and J. Masliyah, Fuel 80, 2013 (2001).
[CrossRef]

Garcia-Valenzuela, A.

A. Reyes-Coronado, A. Garcia-Valenzuela, C. Sanchez-Perez, R. G. Barrera, New J. Phys. 7, 891 (2005).
[CrossRef]

Haus, J. W.

He, A.

Heald, M. A.

M. A. Heald and J. B. Marion, Classical Electromagnetic Radiation, 3rd ed. (Brooks Cole, 1994)

Killey, A.

K. Alexander, A. Killey, G. H. Meeten, and M. Senior, J. Chem. Soc. Faraday Trans. 77, 361 (1981).

Lai, J.

LaPlante, C.

Li, Z.

Love, J. D.

Marion, J. B.

M. A. Heald and J. B. Marion, Classical Electromagnetic Radiation, 3rd ed. (Brooks Cole, 1994)

Masliyah, J.

S. Taylor, J. Czarnecki, and J. Masliyah, Fuel 80, 2013 (2001).
[CrossRef]

McClimans, M.

Meeten, G.

G. Meeten and A. North, Meas. Sci. Technol. 6, 214 (1995).
[CrossRef]

Meeten, G. H.

K. Alexander, A. Killey, G. H. Meeten, and M. Senior, J. Chem. Soc. Faraday Trans. 77, 361 (1981).

Nelson, R. L.

Niskanen, I.

North, A.

G. Meeten and A. North, Meas. Sci. Technol. 6, 214 (1995).
[CrossRef]

Peiponen, K.-E.

Räty, J.

Reyes-Coronado, A.

A. Reyes-Coronado, A. Garcia-Valenzuela, C. Sanchez-Perez, R. G. Barrera, New J. Phys. 7, 891 (2005).
[CrossRef]

Sanchez-Perez, C.

A. Reyes-Coronado, A. Garcia-Valenzuela, C. Sanchez-Perez, R. G. Barrera, New J. Phys. 7, 891 (2005).
[CrossRef]

Senior, M.

K. Alexander, A. Killey, G. H. Meeten, and M. Senior, J. Chem. Soc. Faraday Trans. 77, 361 (1981).

Snyder, A. W.

Taylor, S.

S. Taylor, J. Czarnecki, and J. Masliyah, Fuel 80, 2013 (2001).
[CrossRef]

Wang, C.

Wu, Z.

Zhan, Q.

Appl. Opt. (3)

Fuel (1)

S. Taylor, J. Czarnecki, and J. Masliyah, Fuel 80, 2013 (2001).
[CrossRef]

J. Chem. Soc. Faraday Trans. (1)

K. Alexander, A. Killey, G. H. Meeten, and M. Senior, J. Chem. Soc. Faraday Trans. 77, 361 (1981).

Meas. Sci. Technol. (1)

G. Meeten and A. North, Meas. Sci. Technol. 6, 214 (1995).
[CrossRef]

New J. Phys. (1)

A. Reyes-Coronado, A. Garcia-Valenzuela, C. Sanchez-Perez, R. G. Barrera, New J. Phys. 7, 891 (2005).
[CrossRef]

Opt. Lett. (2)

Other (1)

M. A. Heald and J. B. Marion, Classical Electromagnetic Radiation, 3rd ed. (Brooks Cole, 1994)

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Figures (2)

Fig. 1
Fig. 1

(a) Prism–sample interface. (b) Plots of I r I i ( θ i ) from Eq. (1) for a transparent medium ( α = 0 ) and two highly turbid media, all with the same n r .

Fig. 2
Fig. 2

I r I i ( θ i ) measured at 660 nm for milk–cream mixtures with (i) 10% fat and (iii) 33% fat. The dark curves (i) and (iii) are least- χ 2 fits using Eqs. (1, 2), and incorporate angle-dependent penetration into the medium. The lighter gray curves (ii) and (iv) erroneously do not (see text). We obtain (i) n r = 1.35692 , n i = 0.00277 ( α = 527.60 cm 1 ) , and (iii) n r = 1.36541 , n i = 0.00618 ( α = 1177.0 cm 1 ) .

Equations (2)

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I r I i = M + P 2 cos 2 θ i 2 cos θ i ( M + sin 2 θ i ) M + L M + P 2 cos 2 θ i + 2 cos θ i ( M + sin 2 θ i ) M + L ,
n i ( θ ) = n i ( 4 π n prism ( M L ) 2 ) 1 .

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