Abstract

We demonstrate a new approach for determining particle-size distribution in concentrated suspensions from spectral measurement of isotropic scattering coefficients by use of steady-state, continuous-wave photon-migration techniques. Successful recovery of particle-size distribution for TiO2 suspensions in the form of log-normal functions is achieved through a regularized inverse algorithm, into which a synthesized scheme of Marquardt and Tikhonov regularizations has been incorporated. Our results for dense TiO2 suspensions with three different particle concentrations are in excellent agreement with the size distribution as measured with x-ray sedimentation.

© 1998 Optical Society of America

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References

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  1. T. Allen, Particle Size Measurement (Chapman & Hall, New York, 1990).
    [CrossRef]
  2. J. Wang and F. R. Hallet, Appl. Opt. 35, 193 (1996).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  4. L.-H. Wang and S. L. Jacques, Appl. Opt. 34, 2362 (1995).
    [CrossRef] [PubMed]
  5. S.-P. Lin, L.-H. Wang, S. L. Jacques, and F. K. Tittel, Appl. Opt. 36, 136 (1997).
    [CrossRef] [PubMed]
  6. G. Marquez, L.-H. Wang, S.-P. Lin, J. A. Schwartz, and S. L. Thomsen, Appl. Opt. 37, 798 (1998).
    [CrossRef]
  7. H. Van de Hulst, Light Scattering by Small Particles (Dover, New York, 1983).
  8. G. Bohren and D. Hoffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).
  9. E. L. Crow and K. Shimizu, Lognormal Distributions (Marcell Dekker, New York, 1988).
  10. M. Lee, “New gel phantoms simulating optical properties of biological tissue,” M. S. thesis (Texas A&N University, College Station, Tex., 1997).

1998 (1)

1997 (2)

1996 (1)

1995 (1)

Allen, T.

T. Allen, Particle Size Measurement (Chapman & Hall, New York, 1990).
[CrossRef]

Bohren, G.

G. Bohren and D. Hoffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

Crow, E. L.

E. L. Crow and K. Shimizu, Lognormal Distributions (Marcell Dekker, New York, 1988).

Hallet, F. R.

Hoffman, D.

G. Bohren and D. Hoffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

Jacques, S. L.

Jiang, H.

Kao, J.

Lee, M.

M. Lee, “New gel phantoms simulating optical properties of biological tissue,” M. S. thesis (Texas A&N University, College Station, Tex., 1997).

Lin, S.-P.

Marquez, G.

Schwartz, J. A.

Sevick-Muraca, E.

Shimizu, K.

E. L. Crow and K. Shimizu, Lognormal Distributions (Marcell Dekker, New York, 1988).

Thomsen, S. L.

Tittel, F. K.

Van de Hulst, H.

H. Van de Hulst, Light Scattering by Small Particles (Dover, New York, 1983).

Wang, J.

Wang, L.-H.

Appl. Opt. (5)

Other (5)

H. Van de Hulst, Light Scattering by Small Particles (Dover, New York, 1983).

G. Bohren and D. Hoffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

E. L. Crow and K. Shimizu, Lognormal Distributions (Marcell Dekker, New York, 1988).

M. Lee, “New gel phantoms simulating optical properties of biological tissue,” M. S. thesis (Texas A&N University, College Station, Tex., 1997).

T. Allen, Particle Size Measurement (Chapman & Hall, New York, 1990).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Schematic of the experimental apparatus. White light was coupled to the oblique-incidence optical fiber probe. A source fiber delivered light to the gel phantoms at an angle of 45°, and the diffuse reflectance was collected by nine collection fibers. PC, personal computer.

Fig. 2
Fig. 2

Isotropic scattering spectra determined by the method of oblique-incidence reflectometry.

Fig. 3
Fig. 3

Particle-size distribution as a function of diameter for the TiO2 samples as inverted from the diffuse reflectance measurements and as measured from the sedimentation.

Equations (2)

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1-gμsλ=μsλ=03Qscatx, n, λ1-gx, n, λ2x×ϕfxdx,
TTT+αIΔζ=TTμso-μsc,

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