Abstract

We derive a simple model for the angular-intensity profiles of diffuse light transmitted from a turbid colloid into a transparent medium of higher refractive index (RI) near the critical angle. Adjusting this model to experimental profiles obtained with an Abbe-type refractometer offers a sensitive and robust way of measuring the complex effective RI of highly scattering media.

© 2013 Optical Society of America

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References

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  1. D. Malacara, Geometrical and Instrumental Optics(Academic, 1988).
  2. G. H. Meeten and A. N. North, Meas. Sci. Technol. 2, 441 (1991).
    [CrossRef]
  3. W. R. Calhoun, H. Maeta, A. Combs, L. M. Bali, and S. Bali, Opt. Lett. 35, 1224 (2010).
    [CrossRef]
  4. A. Reyes-Coronado, A. García-Valenzuela, C. Sánchez-Pérez, and R. G. Barrera, New J. Phys. 7, 89 (2005).
    [CrossRef]
  5. S. C. Zilio, Opt. Express 20, 1862 (2012).
    [CrossRef]
  6. H. Contreras-Tello and A. García-Valenzuela, J. Phys.: Conf. Ser. 274, 012129 (2011).
    [CrossRef]
  7. E. Gutiérrez-Reyes, A. García-Valenzuela, and R. G. Barrera, Phys. Status Solidi B 249, 1140 (2012).
    [CrossRef]

2012

E. Gutiérrez-Reyes, A. García-Valenzuela, and R. G. Barrera, Phys. Status Solidi B 249, 1140 (2012).
[CrossRef]

S. C. Zilio, Opt. Express 20, 1862 (2012).
[CrossRef]

2011

H. Contreras-Tello and A. García-Valenzuela, J. Phys.: Conf. Ser. 274, 012129 (2011).
[CrossRef]

2010

2005

A. Reyes-Coronado, A. García-Valenzuela, C. Sánchez-Pérez, and R. G. Barrera, New J. Phys. 7, 89 (2005).
[CrossRef]

1991

G. H. Meeten and A. N. North, Meas. Sci. Technol. 2, 441 (1991).
[CrossRef]

Bali, L. M.

Bali, S.

Barrera, R. G.

E. Gutiérrez-Reyes, A. García-Valenzuela, and R. G. Barrera, Phys. Status Solidi B 249, 1140 (2012).
[CrossRef]

A. Reyes-Coronado, A. García-Valenzuela, C. Sánchez-Pérez, and R. G. Barrera, New J. Phys. 7, 89 (2005).
[CrossRef]

Calhoun, W. R.

Combs, A.

Contreras-Tello, H.

H. Contreras-Tello and A. García-Valenzuela, J. Phys.: Conf. Ser. 274, 012129 (2011).
[CrossRef]

García-Valenzuela, A.

E. Gutiérrez-Reyes, A. García-Valenzuela, and R. G. Barrera, Phys. Status Solidi B 249, 1140 (2012).
[CrossRef]

H. Contreras-Tello and A. García-Valenzuela, J. Phys.: Conf. Ser. 274, 012129 (2011).
[CrossRef]

A. Reyes-Coronado, A. García-Valenzuela, C. Sánchez-Pérez, and R. G. Barrera, New J. Phys. 7, 89 (2005).
[CrossRef]

Gutiérrez-Reyes, E.

E. Gutiérrez-Reyes, A. García-Valenzuela, and R. G. Barrera, Phys. Status Solidi B 249, 1140 (2012).
[CrossRef]

Maeta, H.

Malacara, D.

D. Malacara, Geometrical and Instrumental Optics(Academic, 1988).

Meeten, G. H.

G. H. Meeten and A. N. North, Meas. Sci. Technol. 2, 441 (1991).
[CrossRef]

North, A. N.

G. H. Meeten and A. N. North, Meas. Sci. Technol. 2, 441 (1991).
[CrossRef]

Reyes-Coronado, A.

A. Reyes-Coronado, A. García-Valenzuela, C. Sánchez-Pérez, and R. G. Barrera, New J. Phys. 7, 89 (2005).
[CrossRef]

Sánchez-Pérez, C.

A. Reyes-Coronado, A. García-Valenzuela, C. Sánchez-Pérez, and R. G. Barrera, New J. Phys. 7, 89 (2005).
[CrossRef]

Zilio, S. C.

J. Phys.: Conf. Ser.

H. Contreras-Tello and A. García-Valenzuela, J. Phys.: Conf. Ser. 274, 012129 (2011).
[CrossRef]

Meas. Sci. Technol.

G. H. Meeten and A. N. North, Meas. Sci. Technol. 2, 441 (1991).
[CrossRef]

New J. Phys.

A. Reyes-Coronado, A. García-Valenzuela, C. Sánchez-Pérez, and R. G. Barrera, New J. Phys. 7, 89 (2005).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Status Solidi B

E. Gutiérrez-Reyes, A. García-Valenzuela, and R. G. Barrera, Phys. Status Solidi B 249, 1140 (2012).
[CrossRef]

Other

D. Malacara, Geometrical and Instrumental Optics(Academic, 1988).

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Figures (2)

Fig. 1.
Fig. 1.

Transmission of light scattered by a particle in a turbid colloid to a medium of higher RI. The critical angle and the viewing direction are indicated.

Fig. 2.
Fig. 2.

Fits (smooth curves) of the model in Eq. (4) to experimental angular profiles obtained with latex colloidal suspensions at different particle volume fractions. The intensity images at the CCD for 2% and 12% latex volume concentration are shown in the insert.

Equations (5)

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

Ens(r)=ωμ08π2d2kexp[ik+·(rrn)]sn(k),
sn(k)=(Ik^+k^+)kz·Vnd3rexp(ik+·r)Jnind(r);
Ens(r)=E0cosθexp(ikpr)rexp(ikeff·rn)qn(k1,k2),
I(r)=ρAcos2θr2Ad2r0dznexp[2Im(kzeff)zn]q2,
I(θ)=Ccos2θμz+2Im(kzeff),

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