Abstract

We present a simple experimental method that permits an empirical determination of the effective boundary condition and the extrapolated end point for the diffuse photon density in a homogeneous turbid medium.

© 2000 Optical Society of America

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References

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  1. “Diffuse photons in turbid media,” B. Tromberg, A. Yodh, E. Sevick, D. Pines, eds. (feature issue), Appl. Opt.36, 9–231 (1997); “Diffuse photons in turbid media,” B. Tromberg, A. Yodh, E. Sevick, D. Pines, eds., J. Opt. Soc. Am. A14, 136–342 (1997).
    [CrossRef]
  2. A. Yodh, B. Chance, “Spectroscopy and imaging with diffusing light,” Phys. Today 48, 34–40 (1995).
    [CrossRef]
  3. K. M. Case, P. F. Zweiffel, Linear Transport Theory (Addison-Wesley, London, 1967).
  4. A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, London, 1978), Vol. 1, pp. 175–180.
  5. R. Aronson, “Boundary conditions for diffusion of light,” J. Opt. Soc. Am. A 12, 2532–2539 (1995), and references therein.
    [CrossRef]
  6. R. C. Haskell, L. O. Svaasand, T.-T. Tsay, T.-C. Feng, M. S. McAdams, B. J. Tromberg, “Boundary conditions for the diffusion equation in radiative transfer,” J. Opt. Soc. Am. A 11, 2727–2741 (1994).
    [CrossRef]
  7. C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).
  8. H. J. van Staveren, C. J. M. Moes, J. van Marle, S. A. Prahl, J. C. van Gemert, “Light scattering in Intralipid-10% in the wavelength range of 400–1100 nm,” Appl. Opt. 30, 4507–4514 (1991).
    [CrossRef] [PubMed]
  9. L. G. Henyey, J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70–83 (1941).
    [CrossRef]

1995

A. Yodh, B. Chance, “Spectroscopy and imaging with diffusing light,” Phys. Today 48, 34–40 (1995).
[CrossRef]

R. Aronson, “Boundary conditions for diffusion of light,” J. Opt. Soc. Am. A 12, 2532–2539 (1995), and references therein.
[CrossRef]

1994

1991

1941

L. G. Henyey, J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70–83 (1941).
[CrossRef]

Aronson, R.

Bohren, C. F.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

Case, K. M.

K. M. Case, P. F. Zweiffel, Linear Transport Theory (Addison-Wesley, London, 1967).

Chance, B.

A. Yodh, B. Chance, “Spectroscopy and imaging with diffusing light,” Phys. Today 48, 34–40 (1995).
[CrossRef]

Feng, T.-C.

Greenstein, J. L.

L. G. Henyey, J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70–83 (1941).
[CrossRef]

Haskell, R. C.

Henyey, L. G.

L. G. Henyey, J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70–83 (1941).
[CrossRef]

Huffman, D. R.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

Ishimaru, A.

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, London, 1978), Vol. 1, pp. 175–180.

McAdams, M. S.

Moes, C. J. M.

Prahl, S. A.

Svaasand, L. O.

Tromberg, B. J.

Tsay, T.-T.

van Gemert, J. C.

van Marle, J.

van Staveren, H. J.

Yodh, A.

A. Yodh, B. Chance, “Spectroscopy and imaging with diffusing light,” Phys. Today 48, 34–40 (1995).
[CrossRef]

Zweiffel, P. F.

K. M. Case, P. F. Zweiffel, Linear Transport Theory (Addison-Wesley, London, 1967).

Appl. Opt.

Astrophys. J.

L. G. Henyey, J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70–83 (1941).
[CrossRef]

J. Opt. Soc. Am. A

Phys. Today

A. Yodh, B. Chance, “Spectroscopy and imaging with diffusing light,” Phys. Today 48, 34–40 (1995).
[CrossRef]

Other

K. M. Case, P. F. Zweiffel, Linear Transport Theory (Addison-Wesley, London, 1967).

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, London, 1978), Vol. 1, pp. 175–180.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

“Diffuse photons in turbid media,” B. Tromberg, A. Yodh, E. Sevick, D. Pines, eds. (feature issue), Appl. Opt.36, 9–231 (1997); “Diffuse photons in turbid media,” B. Tromberg, A. Yodh, E. Sevick, D. Pines, eds., J. Opt. Soc. Am. A14, 136–342 (1997).
[CrossRef]

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Figures (2)

Fig. 1
Fig. 1

Top view of the experimental arrangement. A tall rectangular fused silica cell with width W=9.45 mm, length L=10.0 mm, and height H=50 mm is filled with a turbid medium. Two cell walls are black. One surface of the medium at y=-L/2 is illuminated uniformly. The diffuse photon flux j(x, z) (solid circles) emerging from the opposite surface at y=L/2 is detected with an imaging optics and a CCD detector (not shown). j(x, z) from x=-0.4W to x=0.4W or Δx=0.8W is fitted to theory to yield the extrapolated end point .

Fig. 2
Fig. 2

Measured extrapolated end point versus the scattering mean free path ls for aqueous solution of latex spheres with a diameter of 2.01 μm (solid circles), aqueous solution of latex spheres with a diameter of 2.88 μm (open circles), aqueous solution of latex spheres with a diameter of 0.37 μm (solid triangles), TiO2 particles in glycerol (open squares), and Intralipid emulsion (solid squares).

Tables (1)

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Table 1 Anisotropy Factors g for Various Turbid Media

Equations (5)

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Φ(x, y, z)=n=0,1,2 χn(y, z)cos(2n+1)πxW+2.
Φ(x, y, z)χ0(y, z)cos[πχ/(W+2)]+χ1(y, z)cos[3πx/(W+2)],
j(x, z)|y=L/2=a0(z)cos[πx/(W+2)]+a1(z)cos[3πx/(W+2)].
=γlsc+δ.
=0.71ls/(1-g)+δ.

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