Abstract

A method of measuring the mean time of flight, ti, spent by photons inside a generic volume element of a highly diffusing medium is presented. The method comes from a general property of the radiative transfer equation and is based on relative measurements of cw attenuation that correspond to small variations of the absorption coefficient inside the volume element. By use of a liquid phantom and small gels with known optical properties it was possible to measure ti with good accuracy, even when it was only a few picoseconds long. The results were in good agreement with Monte Carlo results.

© 1999 Optical Society of America

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References

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  1. S. R. Arridge and J. C. Hebden, Phys. Med. Biol. 42, 841 (1997).
    [CrossRef] [PubMed]
  2. H. C. van de Hulst, Multiple Light Scattering Tables, Formulas, and Applications (Academic, New York, 1980), Vol. 2, Chap. 17.
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    [CrossRef] [PubMed]
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    [CrossRef]
  5. A. Sassaroli, C. Blumetti, F. Martelli, L. Alianelli, D. Contini, A. Ismaelli, and G. Zaccanti, Appl. Opt. 37, 7392 (1998).
    [CrossRef]
  6. G. Zaccanti, P. Bruscaglioni, and M. Dami, Appl. Opt. 29, 3938 (1990).
    [CrossRef] [PubMed]
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    [CrossRef]
  8. B. C. Wilson, M. S. Patterson, and D. M. Burns, Lasers Med. Sci. 1, 235 (1986).
    [CrossRef]

1998

1997

1993

P. Bruscaglioni, A. Ismaelli, and G. Zaccanti, Waves Random Media 3, 147 (1993).
[CrossRef]

1991

W. Cui, C. Kumar, and B. Chance, Proc. SPIE 1431, 180 (1991).
[CrossRef]

1990

1986

B. C. Wilson, M. S. Patterson, and D. M. Burns, Lasers Med. Sci. 1, 235 (1986).
[CrossRef]

Alianelli, L.

Arridge, S. R.

S. R. Arridge and J. C. Hebden, Phys. Med. Biol. 42, 841 (1997).
[CrossRef] [PubMed]

Blumetti, C.

Bruscaglioni, P.

P. Bruscaglioni, A. Ismaelli, and G. Zaccanti, Waves Random Media 3, 147 (1993).
[CrossRef]

G. Zaccanti, P. Bruscaglioni, and M. Dami, Appl. Opt. 29, 3938 (1990).
[CrossRef] [PubMed]

Burns, D. M.

B. C. Wilson, M. S. Patterson, and D. M. Burns, Lasers Med. Sci. 1, 235 (1986).
[CrossRef]

Chance, B.

W. Cui, C. Kumar, and B. Chance, Proc. SPIE 1431, 180 (1991).
[CrossRef]

Contini, D.

Cui, W.

W. Cui, C. Kumar, and B. Chance, Proc. SPIE 1431, 180 (1991).
[CrossRef]

Dami, M.

Hebden, J. C.

S. R. Arridge and J. C. Hebden, Phys. Med. Biol. 42, 841 (1997).
[CrossRef] [PubMed]

Ismaelli, A.

Kumar, C.

W. Cui, C. Kumar, and B. Chance, Proc. SPIE 1431, 180 (1991).
[CrossRef]

Martelli, F.

Patterson, M. S.

B. C. Wilson, M. S. Patterson, and D. M. Burns, Lasers Med. Sci. 1, 235 (1986).
[CrossRef]

Sassaroli, A.

van de Hulst, H. C.

H. C. van de Hulst, Multiple Light Scattering Tables, Formulas, and Applications (Academic, New York, 1980), Vol. 2, Chap. 17.

Wilson, B. C.

B. C. Wilson, M. S. Patterson, and D. M. Burns, Lasers Med. Sci. 1, 235 (1986).
[CrossRef]

Zaccanti, G.

Appl. Opt.

Lasers Med. Sci.

B. C. Wilson, M. S. Patterson, and D. M. Burns, Lasers Med. Sci. 1, 235 (1986).
[CrossRef]

Phys. Med. Biol.

S. R. Arridge and J. C. Hebden, Phys. Med. Biol. 42, 841 (1997).
[CrossRef] [PubMed]

Proc. SPIE

W. Cui, C. Kumar, and B. Chance, Proc. SPIE 1431, 180 (1991).
[CrossRef]

Waves Random Media

P. Bruscaglioni, A. Ismaelli, and G. Zaccanti, Waves Random Media 3, 147 (1993).
[CrossRef]

Other

H. C. van de Hulst, Multiple Light Scattering Tables, Formulas, and Applications (Academic, New York, 1980), Vol. 2, Chap. 17.

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Figures (1)

Fig. 1
Fig. 1

Examples of measurements of ti and te for a 40-mm-thick slab with μso=0.39 mm-1 and μao=3.8×10-4 mm-1. V is in the middle of the scattering cell. (a) ti versus the distance from the light beam for V=0.592 cm3, with μsi=0.39 mm-1 and μai=0.0073 mm-1. (b) ti versus V, with μsi=0.39 mm-1 and μai=0.0073 mm-1, when V is on the beam axis. (c) te traveled outside V=0.671 cm3, with μsi=0.39 mm-1 and μai=0.0195 mm-1, versus the distance of V from the light beam. The corresponding results of Monte Carlo simulations are also shown.

Equations (7)

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

Pμa=Pμa=00gtexp-μaνtdt,
tμa=0tgtexp-μaνtdt0gtexp-μaνtdt=-1ν ln Pμaμa.
tμa+Δμa/2-1νΔμalnPμa+ΔμaPμa.
Pμai=Pμai=00gitiexp-μaiνtidti,
tiμai+Δμai/2-1νΔμailnPμai+ΔμaiPμai.
teμae+Δμae/2-1νΔμaelnPμae+ΔμaePμae.
piμai=NiμaiNμai=Pμai-Pμai=Pμai,

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