Abstract

Spectrophotometric measurements of scattering media are nontrivial owing to the nonlinear relationship between the observed attenuation A and the level of absorption coefficient μa. Presented is a method, utilizing frequency-domain measurements, capable of determining the validity of a measured change in μa based purely on the characteristics of a baseline temporal point-spread function. The order of cumulant used is shown to provide variation of the sensitivity of the method, and its use is demonstrated through Monte Carlo simulations of transmission measurements taken from a scattering slab.

© 2008 Optical Society of America

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References

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  1. R. N. Pittman and B. R. Duling, J. Appl. Physiol. 38, 315 (1975).
    [PubMed]
  2. C. E. Cooper, C. E. Elwell, J. H. Meek, S. J. Matcher, J. S. Wyatt, M. Cope, and D. T. Delpy, Pediatr. Res. 39, 32 (1996).
    [CrossRef] [PubMed]
  3. D. W. Lübbers and R. Wodick, in Oxygen Measurements in Biology and Medicine, J.P.Payne and D.W.Hill, eds. (Butterworths, 1975), pp. 85-110.
  4. J. Mayhew, Y. Zheng, Y. Hou, B. Vuksanovic, J. Berwick, S. Askew, and P. Coffey, Neuroimage 10, 304 (1999).
    [CrossRef] [PubMed]
  5. J. A. Crowe, D. E. Morris, M. S. Woolfson, P. E. Rodmell, and J. G. Walker, J. Opt. Soc. Am. A 24, 1969 (2007).
    [CrossRef]
  6. I. M. Stockford, L. Bo, J. A. Crowe, S. P. Morgan, and D. E. Morris, Appl. Spectrosc. 61, 1379 (2007).
    [CrossRef]
  7. M. S. Patterson, B. Chance, and B. C. Wilson, Appl. Opt. 28, 2331 (1989).
    [CrossRef] [PubMed]

2007 (2)

1999 (1)

J. Mayhew, Y. Zheng, Y. Hou, B. Vuksanovic, J. Berwick, S. Askew, and P. Coffey, Neuroimage 10, 304 (1999).
[CrossRef] [PubMed]

1996 (1)

C. E. Cooper, C. E. Elwell, J. H. Meek, S. J. Matcher, J. S. Wyatt, M. Cope, and D. T. Delpy, Pediatr. Res. 39, 32 (1996).
[CrossRef] [PubMed]

1989 (1)

1975 (1)

R. N. Pittman and B. R. Duling, J. Appl. Physiol. 38, 315 (1975).
[PubMed]

Askew, S.

J. Mayhew, Y. Zheng, Y. Hou, B. Vuksanovic, J. Berwick, S. Askew, and P. Coffey, Neuroimage 10, 304 (1999).
[CrossRef] [PubMed]

Berwick, J.

J. Mayhew, Y. Zheng, Y. Hou, B. Vuksanovic, J. Berwick, S. Askew, and P. Coffey, Neuroimage 10, 304 (1999).
[CrossRef] [PubMed]

Bo, L.

Chance, B.

Coffey, P.

J. Mayhew, Y. Zheng, Y. Hou, B. Vuksanovic, J. Berwick, S. Askew, and P. Coffey, Neuroimage 10, 304 (1999).
[CrossRef] [PubMed]

Cooper, C. E.

C. E. Cooper, C. E. Elwell, J. H. Meek, S. J. Matcher, J. S. Wyatt, M. Cope, and D. T. Delpy, Pediatr. Res. 39, 32 (1996).
[CrossRef] [PubMed]

Cope, M.

C. E. Cooper, C. E. Elwell, J. H. Meek, S. J. Matcher, J. S. Wyatt, M. Cope, and D. T. Delpy, Pediatr. Res. 39, 32 (1996).
[CrossRef] [PubMed]

Crowe, J. A.

Delpy, D. T.

C. E. Cooper, C. E. Elwell, J. H. Meek, S. J. Matcher, J. S. Wyatt, M. Cope, and D. T. Delpy, Pediatr. Res. 39, 32 (1996).
[CrossRef] [PubMed]

Duling, B. R.

R. N. Pittman and B. R. Duling, J. Appl. Physiol. 38, 315 (1975).
[PubMed]

Elwell, C. E.

C. E. Cooper, C. E. Elwell, J. H. Meek, S. J. Matcher, J. S. Wyatt, M. Cope, and D. T. Delpy, Pediatr. Res. 39, 32 (1996).
[CrossRef] [PubMed]

Hou, Y.

J. Mayhew, Y. Zheng, Y. Hou, B. Vuksanovic, J. Berwick, S. Askew, and P. Coffey, Neuroimage 10, 304 (1999).
[CrossRef] [PubMed]

Lübbers, D. W.

D. W. Lübbers and R. Wodick, in Oxygen Measurements in Biology and Medicine, J.P.Payne and D.W.Hill, eds. (Butterworths, 1975), pp. 85-110.

Matcher, S. J.

C. E. Cooper, C. E. Elwell, J. H. Meek, S. J. Matcher, J. S. Wyatt, M. Cope, and D. T. Delpy, Pediatr. Res. 39, 32 (1996).
[CrossRef] [PubMed]

Mayhew, J.

J. Mayhew, Y. Zheng, Y. Hou, B. Vuksanovic, J. Berwick, S. Askew, and P. Coffey, Neuroimage 10, 304 (1999).
[CrossRef] [PubMed]

Meek, J. H.

C. E. Cooper, C. E. Elwell, J. H. Meek, S. J. Matcher, J. S. Wyatt, M. Cope, and D. T. Delpy, Pediatr. Res. 39, 32 (1996).
[CrossRef] [PubMed]

Morgan, S. P.

Morris, D. E.

Patterson, M. S.

Pittman, R. N.

R. N. Pittman and B. R. Duling, J. Appl. Physiol. 38, 315 (1975).
[PubMed]

Rodmell, P. E.

Stockford, I. M.

Vuksanovic, B.

J. Mayhew, Y. Zheng, Y. Hou, B. Vuksanovic, J. Berwick, S. Askew, and P. Coffey, Neuroimage 10, 304 (1999).
[CrossRef] [PubMed]

Walker, J. G.

Wilson, B. C.

Wodick, R.

D. W. Lübbers and R. Wodick, in Oxygen Measurements in Biology and Medicine, J.P.Payne and D.W.Hill, eds. (Butterworths, 1975), pp. 85-110.

Woolfson, M. S.

Wyatt, J. S.

C. E. Cooper, C. E. Elwell, J. H. Meek, S. J. Matcher, J. S. Wyatt, M. Cope, and D. T. Delpy, Pediatr. Res. 39, 32 (1996).
[CrossRef] [PubMed]

Zheng, Y.

J. Mayhew, Y. Zheng, Y. Hou, B. Vuksanovic, J. Berwick, S. Askew, and P. Coffey, Neuroimage 10, 304 (1999).
[CrossRef] [PubMed]

Appl. Opt. (1)

Appl. Spectrosc. (1)

J. Appl. Physiol. (1)

R. N. Pittman and B. R. Duling, J. Appl. Physiol. 38, 315 (1975).
[PubMed]

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

Neuroimage (1)

J. Mayhew, Y. Zheng, Y. Hou, B. Vuksanovic, J. Berwick, S. Askew, and P. Coffey, Neuroimage 10, 304 (1999).
[CrossRef] [PubMed]

Pediatr. Res. (1)

C. E. Cooper, C. E. Elwell, J. H. Meek, S. J. Matcher, J. S. Wyatt, M. Cope, and D. T. Delpy, Pediatr. Res. 39, 32 (1996).
[CrossRef] [PubMed]

Other (1)

D. W. Lübbers and R. Wodick, in Oxygen Measurements in Biology and Medicine, J.P.Payne and D.W.Hill, eds. (Butterworths, 1975), pp. 85-110.

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Figures (3)

Fig. 1
Fig. 1

Absolute percentage error in the calculation of the change in attenuation using the truncated form of the cumulant generation function for a 1-cm-thick slab with μ a 0 = 0.1 mm 1 and μ s equal to (a) 0, (b) 5, (c) 10, and (d) 20 mm 1 . For clarity the graph is offset by 10 % , as each term is added with the number of terms used for each result given on the right.

Fig. 2
Fig. 2

Indication of the value of Δ μ a at which the conditions for a valid result are violated. This is performed for series of between four and eight terms in length for third-order derivatives and higher with μ s equal to (a) 5, (b) 10, and (c) 20 mm 1 .

Fig. 3
Fig. 3

The modeled A a versus μ a relationship of transmission through a 10-mm-thick slab showing the actual curve (dashed curve) and that resultant from truncation to six terms (solid curve). The points marked with pluses indicate where the truncated series becomes ill conditioned based on κ ̂ 3 for the marked base absorption ( μ a 0 = 1 mm 1 ) .

Tables (1)

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Table 1 Estimated Cumulants from Frequency-Domain Measurements a

Equations (5)

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A a ( ω , μ a ( λ ) ) = n = 1 1 n ! [ j ω μ a ( λ ) c ] n κ n ,
Δ A a ( 0 , μ a ( λ ) ) = n = 1 N 1 n ! ( Δ μ a c ) n κ ̂ n .
A = ln Φ ( r , t ) exp ( μ a c t ) d t ,
Φ ( r , t ) = c ( 4 π D c t ) 3 / 2 exp ( r 2 4 D c t μ a c t )
κ ̂ n = 2 ( 2 n 2 ) ! 4 n ( n 1 ) ! r c n μ a ( n 1 / 2 ) D .

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