Abstract

Reflectance techniques are commonly used to characterize the optical properties of tissues. However, the precise determination of local chromophore concentrations in turbid media is usually difficult because of the nonlinear dependence of light intensity as a function of scattering and absorption coefficients. A technique is presented to easily determine absorbent compound concentration ratios in a turbid media from three optical reflectance spectra, in the visible range, measured for source–detector distances less than 1cm. The validity of the method is experimentally established, in cases of sets of diluted milk containing absorbent inks, over a relatively wide range of absorption (0.050.5cm1) and reduced scattering (1020cm1) coefficients.

© 2007 Optical Society of America

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References

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2006 (2)

2001 (1)

A. J. Jääskeläinen, K.-E Peiponen, and J. A. Räty, J. Dairy Sci. 84, 38 (2001).
[CrossRef] [PubMed]

2000 (1)

H. Obrig, R. Wenzel, M. Kohl, S. Horst, P. Wobst, J. Steinbrink, F. Thomas, and A. Villringer, Int. J. Psychophysiol 35, 125 (2000).
[CrossRef] [PubMed]

1998 (1)

M. Kohl, C. Nolte, H. R. Heekeren, S. Horst, U. Scholz, H. Obrig, and A. Villringer, Phys. Med. Biol. 43, 1771 (1998).
[CrossRef] [PubMed]

1997 (2)

X. Intes, B. Le Jeune, F. Pellen, Y. Guern, J. Cariou, and J. Lotrian, J. Opt. 28, 218 (1997).
[CrossRef]

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

1996 (1)

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

1995 (2)

L. H. Wang, S. L. Jacques, and L. Q. Zheng, Comput. Methods Programs Biomed. 47, 131 (1995).
[CrossRef] [PubMed]

H. Liu, D. A. Boas, Y. Zhang, A. G. Yodh, and B. Chance, Phys. Med. Biol. 40, 1983 (1995).
[CrossRef] [PubMed]

1992 (2)

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

S. R. Arridge, M. Cope, and D. T. Delpy, Phys. Med. Biol. 37, 1531 (1992).
[CrossRef] [PubMed]

1989 (1)

1983 (1)

Appl. Opt. (3)

Comput. Methods Programs Biomed. (1)

L. H. Wang, S. L. Jacques, and L. Q. Zheng, Comput. Methods Programs Biomed. 47, 131 (1995).
[CrossRef] [PubMed]

Int. J. Psychophysiol (1)

H. Obrig, R. Wenzel, M. Kohl, S. Horst, P. Wobst, J. Steinbrink, F. Thomas, and A. Villringer, Int. J. Psychophysiol 35, 125 (2000).
[CrossRef] [PubMed]

J. Dairy Sci. (1)

A. J. Jääskeläinen, K.-E Peiponen, and J. A. Räty, J. Dairy Sci. 84, 38 (2001).
[CrossRef] [PubMed]

J. Opt. (1)

X. Intes, B. Le Jeune, F. Pellen, Y. Guern, J. Cariou, and J. Lotrian, J. Opt. 28, 218 (1997).
[CrossRef]

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

Med. Phys. (1)

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

Opt. Express (1)

Phys. Med. Biol. (4)

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

H. Liu, D. A. Boas, Y. Zhang, A. G. Yodh, and B. Chance, Phys. Med. Biol. 40, 1983 (1995).
[CrossRef] [PubMed]

S. R. Arridge, M. Cope, and D. T. Delpy, Phys. Med. Biol. 37, 1531 (1992).
[CrossRef] [PubMed]

M. Kohl, C. Nolte, H. R. Heekeren, S. Horst, U. Scholz, H. Obrig, and A. Villringer, Phys. Med. Biol. 43, 1771 (1998).
[CrossRef] [PubMed]

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Figures (4)

Fig. 1
Fig. 1

Simulated offset corrected attenuation versus absorption coefficient in the range [ 0.05 0.5 ] cm 1 for distances of 0.5, 1.0, 2.0 and 3.0 cm , μ s = 20 cm 1 .

Fig. 2
Fig. 2

(a) Comparison between simulated CDR (solid curve) and the absorption spectra (dashed curve). The model considers a distance of 2 cm , a peak absorption of 0.5 cm 1 , and a value of μ s of 10 cm 1 . (b) Simulated evolution of coefficient K with distance, obtained by a slope measure of the CDR function for μ a [ 0.05 0.5 ] cm 1 and μ s of 10 cm 1 (solid curve) or 20 cm 1 (dashed curve). (c) Profiles of CDR as a function of μ a for μ s of 10 cm 1 and distances of 0.5, 1.0, 2.0, and 3.0 cm .

Fig. 3
Fig. 3

Experimental evolution of CDR in 1:2 (triangles) and a 1:4 (circles) diluted semi-skimmed milk as a function of the peak amplitude of the ink spectral absorption.

Fig. 4
Fig. 4

(a) Experimental reflectance spectra at 4.5, 5.0, and 5.5 mm from the lighting source (solid, dashed, and dash-dotted curves), in the case of 1:2 diluted milk with purple and turquoise absorbents. Peak amplitudes are, respectively, 0.2 and 0.3 cm 1 . (b) Spectral profile of CDR obtained from reflectance profiles (solid curve). Retrieved profile made up with absorption spectra (dashed curve). (c) Spectral profiles of purple (dashed curve) and turquoise (solid curve) inks weighted by fitting of CDR. (d) Comparison between retrieved turquoise ink ratios and expected values. The dashed line symbolizes a recovery identical to expectations.

Equations (9)

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R ( ρ ) = i { n , p } z i 4 π ( 1 r i + μ eff ) exp ( μ eff r i ) r i 2 ,
η 0.0636 n + 0.6681 + 0.7099 n 1 1.4399 n 2 ,
R ( ρ ) α ( 1 ρ + μ eff ) exp ( μ eff ρ ) ρ 2 ,
α = 1 2 π 1 μ a + μ s ( 1 + 2 3 A ) .
A tt ( ρ ) = log [ R ( ρ ) ] μ a ρ DPF ( ρ ) ln ( 10 ) + G ( ρ ) .
CDR ( ρ , λ ) = [ 1 R ( ρ , λ ) R ρ + 2 ρ ] 2 .
1 R ( ρ , λ ) R ρ = 2 ρ μ eff [ 1 ρ μ eff + 1 1 + 1 ( ρ μ eff ) ] .
CDR ( ρ , λ ) = μ eff 2 [ 1 ρ μ eff + 1 1 + 1 ( ρ μ eff ) ] 2 .
CDR ( ρ , λ ) K μ s μ a ( λ ) + ε ( ρ ) .

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