Abstract

We report high-precision measurements of the absorption and the reduced scattering coefficients for turbid media. Using a frequency-domain measurement technique for a point-source infinite-medium geometry, we find that the standard deviations of multiple measurements of the absorption coefficient μa and the reduced scattering coefficient μs are less than 0.6%, and three independently derived values for μa and μs agree to better than 1%. Measurements of μa agree with measurements of a nonscattering medium to within 1.2%. To obtain high precision requires attention to proper conditions for the spherical photon-density wave model, the detection linearity, and the ratio of the absorption rate to the source modulation rate. Frequency-domain amplitude and phase measurements deviate from fitted curves by 0.1% and 0.06° rms, respectively.

© 1999 Optical Society of America

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References

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  1. J. G. Fujimoto and M. S. Patterson, eds., Advances in Optical Imaging and Photon Migration, Vol. 21 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1998).
  2. B. Chance, R. R. Alfano, and B. J. Tromberg, eds., Optical Tomography and Spectroscopy of Tissue III, Proc. SPIE3597, (1999).
  3. B. Chance, M. Cope, E. Gratton, N. Ramanujam, and B. Tromberg, Rev. Sci. Instrum. 69, 3457 (1998).
    [CrossRef]
  4. S. Fantini, M. A. Franceschini, J. B. Fishkin, B. Barbieri, and E. Gratton, Appl. Opt. 33, 5204 (1994).
    [CrossRef] [PubMed]
  5. M. Gerken and G. W. Faris, Proc. SPIE 3597, xxx (1999).
  6. M. A. O’Leary, D. A. Boas, B. Chance, and A. G. Yodh, Phys. Rev. Lett. 69, 2658 (1992).
    [CrossRef] [PubMed]
  7. R. Aronson and N. Corngold, J. Opt. Soc. Am. A 16, 1066 (1999).
    [CrossRef]
  8. S. Fantini, M. A. Franceschini, and E. Gratton, Appl. Opt. 36, 156 (1997).
    [CrossRef] [PubMed]
  9. K. Rinzema, L. H. P. Murrer, and W. M. Star, J. Opt. Soc. Am. A 15, 2078 (1998).
    [CrossRef]
  10. G. M. Hale and M. R. Querry, Appl. Opt. 12, 555 (1973).
    [CrossRef] [PubMed]

1999 (2)

M. Gerken and G. W. Faris, Proc. SPIE 3597, xxx (1999).

R. Aronson and N. Corngold, J. Opt. Soc. Am. A 16, 1066 (1999).
[CrossRef]

1998 (2)

K. Rinzema, L. H. P. Murrer, and W. M. Star, J. Opt. Soc. Am. A 15, 2078 (1998).
[CrossRef]

B. Chance, M. Cope, E. Gratton, N. Ramanujam, and B. Tromberg, Rev. Sci. Instrum. 69, 3457 (1998).
[CrossRef]

1997 (1)

1994 (1)

1992 (1)

M. A. O’Leary, D. A. Boas, B. Chance, and A. G. Yodh, Phys. Rev. Lett. 69, 2658 (1992).
[CrossRef] [PubMed]

1973 (1)

Aronson, R.

Barbieri, B.

Boas, D. A.

M. A. O’Leary, D. A. Boas, B. Chance, and A. G. Yodh, Phys. Rev. Lett. 69, 2658 (1992).
[CrossRef] [PubMed]

Chance, B.

B. Chance, M. Cope, E. Gratton, N. Ramanujam, and B. Tromberg, Rev. Sci. Instrum. 69, 3457 (1998).
[CrossRef]

M. A. O’Leary, D. A. Boas, B. Chance, and A. G. Yodh, Phys. Rev. Lett. 69, 2658 (1992).
[CrossRef] [PubMed]

Cope, M.

B. Chance, M. Cope, E. Gratton, N. Ramanujam, and B. Tromberg, Rev. Sci. Instrum. 69, 3457 (1998).
[CrossRef]

Corngold, N.

Fantini, S.

Faris, G. W.

M. Gerken and G. W. Faris, Proc. SPIE 3597, xxx (1999).

Fishkin, J. B.

Franceschini, M. A.

Gerken, M.

M. Gerken and G. W. Faris, Proc. SPIE 3597, xxx (1999).

Gratton, E.

Hale, G. M.

Murrer, L. H. P.

O’Leary, M. A.

M. A. O’Leary, D. A. Boas, B. Chance, and A. G. Yodh, Phys. Rev. Lett. 69, 2658 (1992).
[CrossRef] [PubMed]

Querry, M. R.

Ramanujam, N.

B. Chance, M. Cope, E. Gratton, N. Ramanujam, and B. Tromberg, Rev. Sci. Instrum. 69, 3457 (1998).
[CrossRef]

Rinzema, K.

Star, W. M.

Tromberg, B.

B. Chance, M. Cope, E. Gratton, N. Ramanujam, and B. Tromberg, Rev. Sci. Instrum. 69, 3457 (1998).
[CrossRef]

Yodh, A. G.

M. A. O’Leary, D. A. Boas, B. Chance, and A. G. Yodh, Phys. Rev. Lett. 69, 2658 (1992).
[CrossRef] [PubMed]

Appl. Opt. (3)

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

Phys. Rev. Lett. (1)

M. A. O’Leary, D. A. Boas, B. Chance, and A. G. Yodh, Phys. Rev. Lett. 69, 2658 (1992).
[CrossRef] [PubMed]

Proc. SPIE (1)

M. Gerken and G. W. Faris, Proc. SPIE 3597, xxx (1999).

Rev. Sci. Instrum. (1)

B. Chance, M. Cope, E. Gratton, N. Ramanujam, and B. Tromberg, Rev. Sci. Instrum. 69, 3457 (1998).
[CrossRef]

Other (2)

J. G. Fujimoto and M. S. Patterson, eds., Advances in Optical Imaging and Photon Migration, Vol. 21 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1998).

B. Chance, R. R. Alfano, and B. J. Tromberg, eds., Optical Tomography and Spectroscopy of Tissue III, Proc. SPIE3597, (1999).

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Figures (2)

Fig. 1
Fig. 1

Variations of (a) dc and rf amplitudes and (b) phase as functions of source–detector distance (solid lines, data; dotted lines, linear fits). The residuals (data minus fits, shown under each graph) have rms values of 0.1% (amplitude) and 0.06° (phase).

Fig. 2
Fig. 2

(a) Slope ratios (phase slope in radians) and error factors for (b) μa and (c) μs as a function of the ratio of the absorption rate to the source angular modulation rate, ξ=cμa/2πνn. The dashed curves in (c) are approximate and assume equal errors in all independent quantities.

Tables (1)

Tables Icon

Table 1 Absorption and Reduced Scattering Coefficients Calculated from the Data in Fig. 1a

Equations (3)

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Δμsμs2=δ2-2μaμsφ2φ2+δ22Δδδ2+1+2μaμs2φ2+δ2φ2+δ22Δφφ2+41+μaμs2Δρρ2,
Δμsμs2=1-2μaμsφ2α2-φ22Δαα2+1+2μaμsα2α2-φ22Δφφ2+41+μaμs2Δρρ2,
Δμsμs2=δ2+2μaμsα2α2-δ22Δδδ2+1+2μaμs2α2-δ2α2-δ22Δαα2+41+μaμs2Δρρ2.

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