Abstract

Measurements of optical properties (scattering coefficient μs, absorption coefficient μa, reduced scattering coefficient μs′, and asymmetry factor g) have been carried out up to a volume particle concentration of ρ = 0.227. The results for μs and μs′ show significant deviations from the linear dependence on ρ as expected when the independent scattering assumption is fulfilled. The asymmetry factor also changed significantly. In contrast, the dependence of μa remained linear even at the largest concentration investigated. The simple linear dependence of absorption on the chromophore concentration expected from the independent scattering assumption is thus applicable also to spectroscopic measurements of dense media. A comparison with an approximate theoretical model based on the Foldy-Twersky equation is also reported. The model provides a good description of the dependence of μs on particle concentration.

© 2003 Optical Society of America

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References

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2000 (2)

V. Sankaran, J. T. Walsh, D. J. Maitland, “Polarized light propagation through tissue phantoms containing densely packed scatterers,” Opt. Lett. 25, 239–241 (2000).
[CrossRef]

F. Martelli, M. Bassani, L. Alianelli, L. Zangheri, G. Zaccanti, “Accuracy of the diffusion equation to describe photon migration through an infinite medium: numerical and experimental investigation,” Phys. Med. Biol. 45, 1359–1373 (2000).
[CrossRef] [PubMed]

1999 (1)

1998 (1)

1997 (1)

1995 (1)

G. Göbel, J. Kuhn, J. Fricke, “Dependent scattering effects in latex sphere suspensions and scattering powders,” Waves Random Media 5, 413–426 (1995).
[CrossRef]

1994 (1)

1991 (1)

1988 (1)

G. Zaccanti, P. Bruscaglioni, “Deviation from the Lambert-Beer law in the transmittance of a light beam through diffusing media: experimental results,” J. Mod. Opt. 35, 229–242 (1988).
[CrossRef]

1986 (1)

B. C. Wilson, M. S. Patterson, D. M. Burns, “Effect of photosensitizer concentration in tissue on the penetration depth of photoactivating light,” Lasers Med. Sci. 1, 235–244 (1986).
[CrossRef]

1985 (1)

1982 (1)

1979 (1)

1973 (1)

1952 (1)

M. Lax, “Multiple scattering of waves. II. The effective field in dense systems,” Phys. Rev. 85, 621–629 (1952).
[CrossRef]

Alianelli, L.

F. Martelli, M. Bassani, L. Alianelli, L. Zangheri, G. Zaccanti, “Accuracy of the diffusion equation to describe photon migration through an infinite medium: numerical and experimental investigation,” Phys. Med. Biol. 45, 1359–1373 (2000).
[CrossRef] [PubMed]

Bassani, M.

F. Martelli, M. Bassani, L. Alianelli, L. Zangheri, G. Zaccanti, “Accuracy of the diffusion equation to describe photon migration through an infinite medium: numerical and experimental investigation,” Phys. Med. Biol. 45, 1359–1373 (2000).
[CrossRef] [PubMed]

M. Bassani, F. Martelli, G. Zaccanti, D. Contini, “Independence of the diffusion coefficient from absorption: experimental and numerical evidence,” Opt. Lett. 22, 853–855 (1997).
[CrossRef] [PubMed]

Borghese, F.

A. Giusto, R. Saija, M. A. Iati, P. Denti, F. Borghese, O. I. Sindoni, “Optical properties of high-density dispersions of particles: application to Intralipid solutions,” Appl. Opt. (to be published).

Bruscaglioni, P.

G. Zaccanti, P. Bruscaglioni, “Deviation from the Lambert-Beer law in the transmittance of a light beam through diffusing media: experimental results,” J. Mod. Opt. 35, 229–242 (1988).
[CrossRef]

Burns, D. M.

B. C. Wilson, M. S. Patterson, D. M. Burns, “Effect of photosensitizer concentration in tissue on the penetration depth of photoactivating light,” Lasers Med. Sci. 1, 235–244 (1986).
[CrossRef]

Contini, D.

Denti, P.

A. Giusto, R. Saija, M. A. Iati, P. Denti, F. Borghese, O. I. Sindoni, “Optical properties of high-density dispersions of particles: application to Intralipid solutions,” Appl. Opt. (to be published).

Dick, V. P.

Freeman, C. G.

Fricke, J.

G. Göbel, J. Kuhn, J. Fricke, “Dependent scattering effects in latex sphere suspensions and scattering powders,” Waves Random Media 5, 413–426 (1995).
[CrossRef]

Fung, A. K.

Gibbs, D.

Giusto, A.

A. Giusto, R. Saija, M. A. Iati, P. Denti, F. Borghese, O. I. Sindoni, “Optical properties of high-density dispersions of particles: application to Intralipid solutions,” Appl. Opt. (to be published).

Göbel, G.

G. Göbel, J. Kuhn, J. Fricke, “Dependent scattering effects in latex sphere suspensions and scattering powders,” Waves Random Media 5, 413–426 (1995).
[CrossRef]

Hale, G. H.

Iati, M. A.

A. Giusto, R. Saija, M. A. Iati, P. Denti, F. Borghese, O. I. Sindoni, “Optical properties of high-density dispersions of particles: application to Intralipid solutions,” Appl. Opt. (to be published).

Ishimaru, A.

Kuga, Y.

Kuhn, J.

G. Göbel, J. Kuhn, J. Fricke, “Dependent scattering effects in latex sphere suspensions and scattering powders,” Waves Random Media 5, 413–426 (1995).
[CrossRef]

Lax, M.

M. Lax, “Multiple scattering of waves. II. The effective field in dense systems,” Phys. Rev. 85, 621–629 (1952).
[CrossRef]

Litjens, R. A. J.

Maitland, D. J.

Martelli, F.

F. Martelli, M. Bassani, L. Alianelli, L. Zangheri, G. Zaccanti, “Accuracy of the diffusion equation to describe photon migration through an infinite medium: numerical and experimental investigation,” Phys. Med. Biol. 45, 1359–1373 (2000).
[CrossRef] [PubMed]

M. Bassani, F. Martelli, G. Zaccanti, D. Contini, “Independence of the diffusion coefficient from absorption: experimental and numerical evidence,” Opt. Lett. 22, 853–855 (1997).
[CrossRef] [PubMed]

Moes, C. J. M.

Patterson, M. S.

B. C. Wilson, M. S. Patterson, D. M. Burns, “Effect of photosensitizer concentration in tissue on the penetration depth of photoactivating light,” Lasers Med. Sci. 1, 235–244 (1986).
[CrossRef]

Prahl, S. A.

Querry, M. R.

Quickenden, T. I.

Saija, R.

A. Giusto, R. Saija, M. A. Iati, P. Denti, F. Borghese, O. I. Sindoni, “Optical properties of high-density dispersions of particles: application to Intralipid solutions,” Appl. Opt. (to be published).

Sankaran, V.

Sindoni, O. I.

A. Giusto, R. Saija, M. A. Iati, P. Denti, F. Borghese, O. I. Sindoni, “Optical properties of high-density dispersions of particles: application to Intralipid solutions,” Appl. Opt. (to be published).

Tsang, L.

Twersky, V.

van Gemert, M. J. C.

van Marle, J.

van Staveren, H. J.

Walsh, J. T.

West, R.

Wilson, B. C.

B. C. Wilson, M. S. Patterson, D. M. Burns, “Effect of photosensitizer concentration in tissue on the penetration depth of photoactivating light,” Lasers Med. Sci. 1, 235–244 (1986).
[CrossRef]

Zaccanti, G.

F. Martelli, M. Bassani, L. Alianelli, L. Zangheri, G. Zaccanti, “Accuracy of the diffusion equation to describe photon migration through an infinite medium: numerical and experimental investigation,” Phys. Med. Biol. 45, 1359–1373 (2000).
[CrossRef] [PubMed]

M. Bassani, F. Martelli, G. Zaccanti, D. Contini, “Independence of the diffusion coefficient from absorption: experimental and numerical evidence,” Opt. Lett. 22, 853–855 (1997).
[CrossRef] [PubMed]

G. Zaccanti, P. Bruscaglioni, “Deviation from the Lambert-Beer law in the transmittance of a light beam through diffusing media: experimental results,” J. Mod. Opt. 35, 229–242 (1988).
[CrossRef]

Zangheri, L.

F. Martelli, M. Bassani, L. Alianelli, L. Zangheri, G. Zaccanti, “Accuracy of the diffusion equation to describe photon migration through an infinite medium: numerical and experimental investigation,” Phys. Med. Biol. 45, 1359–1373 (2000).
[CrossRef] [PubMed]

Appl. Opt. (4)

J. Mod. Opt. (1)

G. Zaccanti, P. Bruscaglioni, “Deviation from the Lambert-Beer law in the transmittance of a light beam through diffusing media: experimental results,” J. Mod. Opt. 35, 229–242 (1988).
[CrossRef]

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (2)

Lasers Med. Sci. (1)

B. C. Wilson, M. S. Patterson, D. M. Burns, “Effect of photosensitizer concentration in tissue on the penetration depth of photoactivating light,” Lasers Med. Sci. 1, 235–244 (1986).
[CrossRef]

Opt. Lett. (2)

Phys. Med. Biol. (1)

F. Martelli, M. Bassani, L. Alianelli, L. Zangheri, G. Zaccanti, “Accuracy of the diffusion equation to describe photon migration through an infinite medium: numerical and experimental investigation,” Phys. Med. Biol. 45, 1359–1373 (2000).
[CrossRef] [PubMed]

Phys. Rev. (1)

M. Lax, “Multiple scattering of waves. II. The effective field in dense systems,” Phys. Rev. 85, 621–629 (1952).
[CrossRef]

Waves Random Media (1)

G. Göbel, J. Kuhn, J. Fricke, “Dependent scattering effects in latex sphere suspensions and scattering powders,” Waves Random Media 5, 413–426 (1995).
[CrossRef]

Other (2)

A. Giusto, R. Saija, M. A. Iati, P. Denti, F. Borghese, O. I. Sindoni, “Optical properties of high-density dispersions of particles: application to Intralipid solutions,” Appl. Opt. (to be published).

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978), Vol. 2, Chap. 14.

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Figures (8)

Fig. 1
Fig. 1

Experimental setup for measurements of (a) extinction coefficient and (b) absorption and reduced scattering coefficients.

Fig. 2
Fig. 2

Examples of measurements of attenuation at low concentrations. Also shown is the straight line that best fits the results for ρ ≤ 0.00056. These results show that with the experimental setup used the extinction coefficient can be obtained with negligible error that is due to scattered received power until τ e is smaller than approximately 13.

Fig. 3
Fig. 3

Examples of measurements of attenuation at high concentrations. For each concentration measurements were repeated for several values of thickness d of the turbid medium. The extinction coefficient is equal to slope S of ln(P e /P r ) as a function of d.

Fig. 4
Fig. 4

Examples of measurements carried out to determine μeff. We show ln[rΦ(r)] as a function of r for three values of the Intralipid concentration. The straight lines that best fit the results are also shown.

Fig. 5
Fig. 5

Examples of measurements of (μeff)2 as a function of Δμ a . For each concentration the straight line that best fits the results is also reported. μ s ′ and μ a were obtained from the slope and from the intercept of this line.

Fig. 6
Fig. 6

Measured values of μ a , μ s , and μ s ′ as a function of volume concentration. The best-fit curves are also shown with the corresponding expressions. The error bars for μ s ′ are smaller than the marks.

Fig. 7
Fig. 7

Ratios μ s sIS and μ s ′/μ sIS′ and the asymmetry factor are shown as a function of ρ. μ sIS and μ sIS′ are the values expected if independent scattering occurs.

Fig. 8
Fig. 8

Comparison between the experimental results for μ s and the theoretical results expected with the model of Ref. 9.

Equations (8)

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

μa=εaρ, μs=εsρ,
Pb=Pe exp-μed,
Pr=Pb+Ps.
Φr=3μs4πrexp-μeffr,
lnrΦr=-μeffr+ln3μs/4π.
μeffΔμa2=3μsμa+3μsΔμa
μs=S/3, μa=I/S.
μa=εaρ+εaH2O1-ρ=εaH2O+εa-εaH2Oρ,

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