Abstract

A procedure for retrieving the optical properties of a two-layered diffusive medium based on an exact analytical solution of the diffusion equation and on relative multidistance time-resolved reflectance measurements is presented. The method overcomes some limitations of previously developed procedures. Five parameters of the medium have been fitted: the absorption and the reduced scattering coefficients of both layers and the thickness of the first layer. The actual values of the parameters are correctly retrieved by the procedure. The inversion procedure does not require an initial guess for the unknown optical properties, but the starting value for the thickness of the first layer needs to be estimated with an error smaller than 50%.

© 2003 Optical Society of America

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2003 (1)

F. Martelli, A. Sassaroli, S. Del Bianco, Y. Yamada, and G. Zaccanti, Phys. Rev. E 67, 056623 (2003).
[CrossRef]

2002 (2)

F. Martelli, A. Sassaroli, Y. Yamada, and G. Zaccanti, J. Opt. Soc. Am. A 19, 71 (2002).
[CrossRef]

J. C. Hebden, A. Gibson, R. M. Yusof, N. Everdell, E. M. C. Hillman, D. T. Delpy, S. R. Arridge, T. Austin, J. H. Meek, and J. S. Wyatt, Phys. Med. Biol. 47, 4155 (2002).
[CrossRef] [PubMed]

2001 (1)

J. Ripoll, V. Ntziachristos, J. P. Culver, D. N. Pattanayak, A. G. Yodh, and M. Nieto-Vesperinas, J. Opt. Am. A 18, 821 (2001).
[CrossRef]

2000 (2)

1999 (1)

A. Kienle T. Glanzmann, Phys. Med. Biol. 44, 2689 (1999).
[CrossRef] [PubMed]

1998 (2)

1989 (1)

Arridge, S. R.

J. C. Hebden, A. Gibson, R. M. Yusof, N. Everdell, E. M. C. Hillman, D. T. Delpy, S. R. Arridge, T. Austin, J. H. Meek, and J. S. Wyatt, Phys. Med. Biol. 47, 4155 (2002).
[CrossRef] [PubMed]

Austin, T.

J. C. Hebden, A. Gibson, R. M. Yusof, N. Everdell, E. M. C. Hillman, D. T. Delpy, S. R. Arridge, T. Austin, J. H. Meek, and J. S. Wyatt, Phys. Med. Biol. 47, 4155 (2002).
[CrossRef] [PubMed]

Bays, R.

Chance, B.

Culver, J. P.

J. Ripoll, V. Ntziachristos, J. P. Culver, D. N. Pattanayak, A. G. Yodh, and M. Nieto-Vesperinas, J. Opt. Am. A 18, 821 (2001).
[CrossRef]

Del Bianco, S.

F. Martelli, A. Sassaroli, S. Del Bianco, Y. Yamada, and G. Zaccanti, Phys. Rev. E 67, 056623 (2003).
[CrossRef]

Delpy, D. T.

J. C. Hebden, A. Gibson, R. M. Yusof, N. Everdell, E. M. C. Hillman, D. T. Delpy, S. R. Arridge, T. Austin, J. H. Meek, and J. S. Wyatt, Phys. Med. Biol. 47, 4155 (2002).
[CrossRef] [PubMed]

Dognitz, N.

Everdell, N.

J. C. Hebden, A. Gibson, R. M. Yusof, N. Everdell, E. M. C. Hillman, D. T. Delpy, S. R. Arridge, T. Austin, J. H. Meek, and J. S. Wyatt, Phys. Med. Biol. 47, 4155 (2002).
[CrossRef] [PubMed]

Gibson, A.

J. C. Hebden, A. Gibson, R. M. Yusof, N. Everdell, E. M. C. Hillman, D. T. Delpy, S. R. Arridge, T. Austin, J. H. Meek, and J. S. Wyatt, Phys. Med. Biol. 47, 4155 (2002).
[CrossRef] [PubMed]

Glanzmann, T.

Hebden, J. C.

J. C. Hebden, A. Gibson, R. M. Yusof, N. Everdell, E. M. C. Hillman, D. T. Delpy, S. R. Arridge, T. Austin, J. H. Meek, and J. S. Wyatt, Phys. Med. Biol. 47, 4155 (2002).
[CrossRef] [PubMed]

Hillman, E. M. C.

J. C. Hebden, A. Gibson, R. M. Yusof, N. Everdell, E. M. C. Hillman, D. T. Delpy, S. R. Arridge, T. Austin, J. H. Meek, and J. S. Wyatt, Phys. Med. Biol. 47, 4155 (2002).
[CrossRef] [PubMed]

Kienle, A.

Martelli, F.

Meek, J. H.

J. C. Hebden, A. Gibson, R. M. Yusof, N. Everdell, E. M. C. Hillman, D. T. Delpy, S. R. Arridge, T. Austin, J. H. Meek, and J. S. Wyatt, Phys. Med. Biol. 47, 4155 (2002).
[CrossRef] [PubMed]

Nieto-Vesperinas, M.

J. Ripoll, V. Ntziachristos, J. P. Culver, D. N. Pattanayak, A. G. Yodh, and M. Nieto-Vesperinas, J. Opt. Am. A 18, 821 (2001).
[CrossRef]

Ntziachristos, V.

J. Ripoll, V. Ntziachristos, J. P. Culver, D. N. Pattanayak, A. G. Yodh, and M. Nieto-Vesperinas, J. Opt. Am. A 18, 821 (2001).
[CrossRef]

Pattanayak, D. N.

J. Ripoll, V. Ntziachristos, J. P. Culver, D. N. Pattanayak, A. G. Yodh, and M. Nieto-Vesperinas, J. Opt. Am. A 18, 821 (2001).
[CrossRef]

Patterson, M.

Patterson, M. S.

Pham, T. H.

Ripoll, J.

J. Ripoll, V. Ntziachristos, J. P. Culver, D. N. Pattanayak, A. G. Yodh, and M. Nieto-Vesperinas, J. Opt. Am. A 18, 821 (2001).
[CrossRef]

Sassaroli, A.

Spott, T.

Svaasand, L. O.

Tromberg, B. J.

van de Bergh, H.

Wagnieres, G.

Wilson, B. C.

Wyatt, J. S.

J. C. Hebden, A. Gibson, R. M. Yusof, N. Everdell, E. M. C. Hillman, D. T. Delpy, S. R. Arridge, T. Austin, J. H. Meek, and J. S. Wyatt, Phys. Med. Biol. 47, 4155 (2002).
[CrossRef] [PubMed]

Yamada, Y.

Yodh, A. G.

J. Ripoll, V. Ntziachristos, J. P. Culver, D. N. Pattanayak, A. G. Yodh, and M. Nieto-Vesperinas, J. Opt. Am. A 18, 821 (2001).
[CrossRef]

Yusof, R. M.

J. C. Hebden, A. Gibson, R. M. Yusof, N. Everdell, E. M. C. Hillman, D. T. Delpy, S. R. Arridge, T. Austin, J. H. Meek, and J. S. Wyatt, Phys. Med. Biol. 47, 4155 (2002).
[CrossRef] [PubMed]

Zaccanti, G.

Appl. Opt. (4)

J. Opt. Am. A (1)

J. Ripoll, V. Ntziachristos, J. P. Culver, D. N. Pattanayak, A. G. Yodh, and M. Nieto-Vesperinas, J. Opt. Am. A 18, 821 (2001).
[CrossRef]

J. Opt. Soc. Am. A (1)

Opt. Lett. (1)

Phys. Med. Biol. (2)

J. C. Hebden, A. Gibson, R. M. Yusof, N. Everdell, E. M. C. Hillman, D. T. Delpy, S. R. Arridge, T. Austin, J. H. Meek, and J. S. Wyatt, Phys. Med. Biol. 47, 4155 (2002).
[CrossRef] [PubMed]

A. Kienle T. Glanzmann, Phys. Med. Biol. 44, 2689 (1999).
[CrossRef] [PubMed]

Phys. Rev. E (1)

F. Martelli, A. Sassaroli, S. Del Bianco, Y. Yamada, and G. Zaccanti, Phys. Rev. E 67, 056623 (2003).
[CrossRef]

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Figures (1)

Fig. 1
Fig. 1

Example of fitting procedure for four measurements with four fitted amplitude factors. The data refer to the case μa0=0.004 mm-1, μa1=0.03 mm-1, μs0=1 mm-1, μs1=0.5 mm-1, s0=8 mm, nd=1.4. The refractive index of the external medium is ne=1.

Tables (2)

Tables Icon

Table 1 Fitting Results with a Single Fitted Amplitude Factora

Tables Icon

Table 2 Fitting Results with Four Fitted Amplitude Factorsa

Equations (3)

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

Rρ,t=l,n=1ν/Nln2D0Kln0J0Klρcos2AD0Kln0×sin*z0+2AD0Kln0×exp-Kl2+Kln02D0+μa0νt.
Nln2=πrJ1Klr2×f0+f1sinKln0l02/sinKln1l12, fi=sin2 ImKlnili/4 ImKlni-sin2 ReKlnili/4 ReKlni,    i=0,1.
D1Kln1 tanKln0l0=-D0Kln0 tanKln1l1.

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