Abstract

Spatially resolved reflectance measurements are widely used for determination of the optical properties of biological media. However, the influence of the phase function on these measurements has not been quantified. We show that errors in the derived reduced scattering and absorption coefficients are as great as 100% for both absolute and relative spatially resolved reflectance measurements if a standard solution of the diffusion equation is used in the analysis. In addition, we investigated nonlinear regressions, using Monte Carlo simulations and an additional fitting parameter that characterizes the phase function, and found that the errors in the obtained optical coefficients were 20%.

© 2001 Optical Society of America

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References

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  1. R. A. J. Groenhuis, H. A. Ferwerda, and J. J. ten Bosch, Appl. Opt. 22, 2456–2462 (1983).
    [CrossRef] [PubMed]
  2. T. J. Farrell, M. S. Patterson, and B. C. Wilson, Med. Phys. 19, 879–888 (1992).
    [CrossRef] [PubMed]
  3. E. L. Hull, M. G. Nichols, and T. H. Foster, Phys. Med. Biol. 43, 3381–3404 (1998).
    [CrossRef] [PubMed]
  4. A. Kienle, L. Lilge, M. S. Patterson, R. Hibst, R. Steiner, and B. C. Wilson, Appl. Opt. 35, 2304–2314 (1996).
    [CrossRef] [PubMed]
  5. F. Bevilacqua, D. Piquet, P. Marquet, J. D. Gross, B. J. Tromberg, and C. Depeursinge, Appl. Opt. 38, 4939–4950 (1999).
    [CrossRef]
  6. J. S. Dam, C. B. Pedersen, T. Dalgaard, P. E. Fabricius, P. Aruna, and S. Andersson-Engels, Appl. Opt. 40, 1155–1164 (2001).
    [CrossRef]
  7. T. H. Pham, F. Bevilacqua, T. Spott, J. S. Dam, B. J. Tromberg, and S. Andersson-Engels, Appl. Opt. 39, 6487–6497 (2000).
    [CrossRef]
  8. A. Kienle and M. S. Patterson, J. Opt. Soc. A 14, 246–254 (1997).
    [CrossRef]
  9. A. Kienle, “Lichtausbreitung in biologischem Gewebe” (University of Ulm, Ulm, Germany, 1995).
  10. J. R. Mourant, J. Boyer, A. H. Hielscher, and I. J. Bigio, Opt. Lett. 21, 546–548 (1996).
    [CrossRef] [PubMed]
  11. F. Bevilacqua and C. Depeursinge, J. Opt. Soc. A 16, 2935–2945 (1999).
    [CrossRef]
  12. D. Fried, R. E. Glena, J. D. B. Featherstone, and W. Seka, Appl. Opt. 7, 1278–1285 (1995).
    [CrossRef]
  13. S. L. Jacques, C. A. Alter, and S. A. Prahl, Lasers Life Sci. 1, 309–333 (1987).
  14. P. van der Zee, M. Essenpreis, and D. T. Delpy, Proc. SPIE 1888, 454–465 (1993).
    [CrossRef]
  15. H. J. van Staveren, C. J. M. Moes, J. van Marle, S. A. Prahl, and M. J. C. van Gemert, Appl. Opt. 30, 4507–4514 (1991).
    [CrossRef] [PubMed]
  16. G. Alexandrakis, D. R. Busch, G. W. Faris, and M. S. Patterson, Appl. Opt. 40, 3810 (2001).
    [CrossRef]
  17. T. J. Farrell, B. C. Wilson, and M. S. Patterson, Phys. Med. Biol. 37, 2281–2286 (1992).
    [CrossRef] [PubMed]
  18. A. Kienle and M. S. Patterson, Phys. Med. Biol. 41, 2221–2227 (1996).
    [CrossRef] [PubMed]

2001 (2)

2000 (1)

1999 (2)

1998 (1)

E. L. Hull, M. G. Nichols, and T. H. Foster, Phys. Med. Biol. 43, 3381–3404 (1998).
[CrossRef] [PubMed]

1997 (1)

A. Kienle and M. S. Patterson, J. Opt. Soc. A 14, 246–254 (1997).
[CrossRef]

1996 (3)

1995 (1)

D. Fried, R. E. Glena, J. D. B. Featherstone, and W. Seka, Appl. Opt. 7, 1278–1285 (1995).
[CrossRef]

1993 (1)

P. van der Zee, M. Essenpreis, and D. T. Delpy, Proc. SPIE 1888, 454–465 (1993).
[CrossRef]

1992 (2)

T. J. Farrell, B. C. Wilson, and M. S. Patterson, Phys. Med. Biol. 37, 2281–2286 (1992).
[CrossRef] [PubMed]

T. J. Farrell, M. S. Patterson, and B. C. Wilson, Med. Phys. 19, 879–888 (1992).
[CrossRef] [PubMed]

1991 (1)

1987 (1)

S. L. Jacques, C. A. Alter, and S. A. Prahl, Lasers Life Sci. 1, 309–333 (1987).

1983 (1)

Alexandrakis, G.

Alter, C. A.

S. L. Jacques, C. A. Alter, and S. A. Prahl, Lasers Life Sci. 1, 309–333 (1987).

Andersson-Engels, S.

Aruna, P.

Bevilacqua, F.

Bigio, I. J.

Boyer, J.

Busch, D. R.

Dalgaard, T.

Dam, J. S.

Delpy, D. T.

P. van der Zee, M. Essenpreis, and D. T. Delpy, Proc. SPIE 1888, 454–465 (1993).
[CrossRef]

Depeursinge, C.

Essenpreis, M.

P. van der Zee, M. Essenpreis, and D. T. Delpy, Proc. SPIE 1888, 454–465 (1993).
[CrossRef]

Fabricius, P. E.

Faris, G. W.

Farrell, T. J.

T. J. Farrell, B. C. Wilson, and M. S. Patterson, Phys. Med. Biol. 37, 2281–2286 (1992).
[CrossRef] [PubMed]

T. J. Farrell, M. S. Patterson, and B. C. Wilson, Med. Phys. 19, 879–888 (1992).
[CrossRef] [PubMed]

Featherstone, J. D. B.

D. Fried, R. E. Glena, J. D. B. Featherstone, and W. Seka, Appl. Opt. 7, 1278–1285 (1995).
[CrossRef]

Ferwerda, H. A.

Foster, T. H.

E. L. Hull, M. G. Nichols, and T. H. Foster, Phys. Med. Biol. 43, 3381–3404 (1998).
[CrossRef] [PubMed]

Fried, D.

D. Fried, R. E. Glena, J. D. B. Featherstone, and W. Seka, Appl. Opt. 7, 1278–1285 (1995).
[CrossRef]

Glena, R. E.

D. Fried, R. E. Glena, J. D. B. Featherstone, and W. Seka, Appl. Opt. 7, 1278–1285 (1995).
[CrossRef]

Groenhuis, R. A. J.

Gross, J. D.

Hibst, R.

Hielscher, A. H.

Hull, E. L.

E. L. Hull, M. G. Nichols, and T. H. Foster, Phys. Med. Biol. 43, 3381–3404 (1998).
[CrossRef] [PubMed]

Jacques, S. L.

S. L. Jacques, C. A. Alter, and S. A. Prahl, Lasers Life Sci. 1, 309–333 (1987).

Kienle, A.

A. Kienle and M. S. Patterson, J. Opt. Soc. A 14, 246–254 (1997).
[CrossRef]

A. Kienle, L. Lilge, M. S. Patterson, R. Hibst, R. Steiner, and B. C. Wilson, Appl. Opt. 35, 2304–2314 (1996).
[CrossRef] [PubMed]

A. Kienle and M. S. Patterson, Phys. Med. Biol. 41, 2221–2227 (1996).
[CrossRef] [PubMed]

A. Kienle, “Lichtausbreitung in biologischem Gewebe” (University of Ulm, Ulm, Germany, 1995).

Lilge, L.

Marquet, P.

Moes, C. J. M.

Mourant, J. R.

Nichols, M. G.

E. L. Hull, M. G. Nichols, and T. H. Foster, Phys. Med. Biol. 43, 3381–3404 (1998).
[CrossRef] [PubMed]

Patterson, M. S.

G. Alexandrakis, D. R. Busch, G. W. Faris, and M. S. Patterson, Appl. Opt. 40, 3810 (2001).
[CrossRef]

A. Kienle and M. S. Patterson, J. Opt. Soc. A 14, 246–254 (1997).
[CrossRef]

A. Kienle, L. Lilge, M. S. Patterson, R. Hibst, R. Steiner, and B. C. Wilson, Appl. Opt. 35, 2304–2314 (1996).
[CrossRef] [PubMed]

A. Kienle and M. S. Patterson, Phys. Med. Biol. 41, 2221–2227 (1996).
[CrossRef] [PubMed]

T. J. Farrell, B. C. Wilson, and M. S. Patterson, Phys. Med. Biol. 37, 2281–2286 (1992).
[CrossRef] [PubMed]

T. J. Farrell, M. S. Patterson, and B. C. Wilson, Med. Phys. 19, 879–888 (1992).
[CrossRef] [PubMed]

Pedersen, C. B.

Pham, T. H.

Piquet, D.

Prahl, S. A.

Seka, W.

D. Fried, R. E. Glena, J. D. B. Featherstone, and W. Seka, Appl. Opt. 7, 1278–1285 (1995).
[CrossRef]

Spott, T.

Steiner, R.

ten Bosch, J. J.

Tromberg, B. J.

van der Zee, P.

P. van der Zee, M. Essenpreis, and D. T. Delpy, Proc. SPIE 1888, 454–465 (1993).
[CrossRef]

van Gemert, M. J. C.

van Marle, J.

van Staveren, H. J.

Wilson, B. C.

A. Kienle, L. Lilge, M. S. Patterson, R. Hibst, R. Steiner, and B. C. Wilson, Appl. Opt. 35, 2304–2314 (1996).
[CrossRef] [PubMed]

T. J. Farrell, M. S. Patterson, and B. C. Wilson, Med. Phys. 19, 879–888 (1992).
[CrossRef] [PubMed]

T. J. Farrell, B. C. Wilson, and M. S. Patterson, Phys. Med. Biol. 37, 2281–2286 (1992).
[CrossRef] [PubMed]

Appl. Opt. (8)

J. Opt. Soc. A (2)

F. Bevilacqua and C. Depeursinge, J. Opt. Soc. A 16, 2935–2945 (1999).
[CrossRef]

A. Kienle and M. S. Patterson, J. Opt. Soc. A 14, 246–254 (1997).
[CrossRef]

Lasers Life Sci. (1)

S. L. Jacques, C. A. Alter, and S. A. Prahl, Lasers Life Sci. 1, 309–333 (1987).

Med. Phys. (1)

T. J. Farrell, M. S. Patterson, and B. C. Wilson, Med. Phys. 19, 879–888 (1992).
[CrossRef] [PubMed]

Opt. Lett. (1)

Phys. Med. Biol. (3)

E. L. Hull, M. G. Nichols, and T. H. Foster, Phys. Med. Biol. 43, 3381–3404 (1998).
[CrossRef] [PubMed]

T. J. Farrell, B. C. Wilson, and M. S. Patterson, Phys. Med. Biol. 37, 2281–2286 (1992).
[CrossRef] [PubMed]

A. Kienle and M. S. Patterson, Phys. Med. Biol. 41, 2221–2227 (1996).
[CrossRef] [PubMed]

Proc. SPIE (1)

P. van der Zee, M. Essenpreis, and D. T. Delpy, Proc. SPIE 1888, 454–465 (1993).
[CrossRef]

Other (1)

A. Kienle, “Lichtausbreitung in biologischem Gewebe” (University of Ulm, Ulm, Germany, 1995).

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Figures (2)

Fig. 1
Fig. 1

Spatially resolved reflectance simulations from semi-infinite homogeneous turbid media with several phase functions. The other optical properties are μs=1 mm-1, μa=0.01 mm-1, and n=1.4.

Fig. 2
Fig. 2

Relative errors of the absorption coefficients derived by nonlinear regressions of RDiffρ to RZeeρ. The start and end distances of the fitting range are varied. The optical properties are μs=1 mm-1, μa=0.01 mm-1, and n=1.4. Fitting of (a) absolute reflectance data and (b) relative reflectance data.

Tables (2)

Tables Icon

Table 1 Average Absolute Values of Relative Errors in Optical Coefficients Found by Fitting of RDiff(ρ) to RMC(ρ) Calculated with Various p(θ)

Tables Icon

Table 2 Optical Coefficients and Relative Errors (er) Derived by Fitting of Monte Carlo Simulations to RMC(ρ) Calculated with Several Values of p(θ) a

Equations (3)

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

pFried,Jacqθ=αpHGθ,gHG+1-α/4π,
pZeeθ=βpHGθ,gHG1+1-βpHGθ,gHG2
pθ=δpHGθ,gHG1+1-δ3 cos2θ/4π.

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