Abstract

A model has been developed based on random walk theory that allows the diffusion of light along a principal axis to differ from that in orthogonal directions. We present expressions that describe the time-resolved intensity measured across a slab and on the surface of a semi-infinite medium for a principal axis oriented parallel or perpendicular to the surface. The model of time-resolved transmittance is compared with experimental data acquired by use of a phantom consisting of wax fibers arranged within a solid cube of resin. It is shown that a single set of optical parameters is sufficient to model the experimental measurements acquired across all three orientations of the cube.

© 2004 Optical Society of America

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2004 (1)

O. K. Dudko, G. H. Weiss, V. Chernomordik, and A. H. Gandjbakhche, Phys. Med. Biol. 49, 3979 (2004).
[CrossRef] [PubMed]

2003 (2)

J. Heino, S. R. Arridge, J. Sikora, and E. Somersalo, Phys. Rev. E 68, 031908 (2003).
[CrossRef]

L. Dagdug, G. H. Weiss, and A. H. Gandjbakhche, Phys. Med. Biol. 48, 1361 (2003).
[CrossRef] [PubMed]

2000 (1)

F. Schmidt, M. Fry, E. Hillman, J. Hebden, and D. Delpy, Rev. Sci. Instrum. 71, 256 (2000).
[CrossRef]

1999 (1)

V. Chernomordik, A. H. Gandjbakhche, J. C. Hebden, and G. Zaccanti, Med. Phys. 26, 1822 (1999).
[CrossRef] [PubMed]

1998 (1)

1997 (2)

1995 (1)

1994 (1)

1992 (1)

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

1989 (1)

Aronson, R.

Arridge, S. R.

J. Heino, S. R. Arridge, J. Sikora, and E. Somersalo, Phys. Rev. E 68, 031908 (2003).
[CrossRef]

S. R. Arridge and J. C. Hebden, Phys. Med. Biol. 42, 841 (1997).
[CrossRef] [PubMed]

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

Chance, B.

Chernomordik, V.

O. K. Dudko, G. H. Weiss, V. Chernomordik, and A. H. Gandjbakhche, Phys. Med. Biol. 49, 3979 (2004).
[CrossRef] [PubMed]

V. Chernomordik, A. H. Gandjbakhche, J. C. Hebden, and G. Zaccanti, Med. Phys. 26, 1822 (1999).
[CrossRef] [PubMed]

A. H. Gandjbakhche, V. Chernomordik, J. C. Hebden, and R. Nossal, Appl. Opt. 37, 1973 (1998).
[CrossRef]

Contini, D.

Cope, M.

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

Dagdug, L.

L. Dagdug, G. H. Weiss, and A. H. Gandjbakhche, Phys. Med. Biol. 48, 1361 (2003).
[CrossRef] [PubMed]

Delpy, D.

F. Schmidt, M. Fry, E. Hillman, J. Hebden, and D. Delpy, Rev. Sci. Instrum. 71, 256 (2000).
[CrossRef]

Delpy, D. T.

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

Dudko, O. K.

O. K. Dudko, G. H. Weiss, V. Chernomordik, and A. H. Gandjbakhche, Phys. Med. Biol. 49, 3979 (2004).
[CrossRef] [PubMed]

Fry, M.

F. Schmidt, M. Fry, E. Hillman, J. Hebden, and D. Delpy, Rev. Sci. Instrum. 71, 256 (2000).
[CrossRef]

Gandjbakhche, A. H.

O. K. Dudko, G. H. Weiss, V. Chernomordik, and A. H. Gandjbakhche, Phys. Med. Biol. 49, 3979 (2004).
[CrossRef] [PubMed]

L. Dagdug, G. H. Weiss, and A. H. Gandjbakhche, Phys. Med. Biol. 48, 1361 (2003).
[CrossRef] [PubMed]

V. Chernomordik, A. H. Gandjbakhche, J. C. Hebden, and G. Zaccanti, Med. Phys. 26, 1822 (1999).
[CrossRef] [PubMed]

A. H. Gandjbakhche, V. Chernomordik, J. C. Hebden, and R. Nossal, Appl. Opt. 37, 1973 (1998).
[CrossRef]

Hebden, J.

F. Schmidt, M. Fry, E. Hillman, J. Hebden, and D. Delpy, Rev. Sci. Instrum. 71, 256 (2000).
[CrossRef]

Hebden, J. C.

V. Chernomordik, A. H. Gandjbakhche, J. C. Hebden, and G. Zaccanti, Med. Phys. 26, 1822 (1999).
[CrossRef] [PubMed]

A. H. Gandjbakhche, V. Chernomordik, J. C. Hebden, and R. Nossal, Appl. Opt. 37, 1973 (1998).
[CrossRef]

S. R. Arridge and J. C. Hebden, Phys. Med. Biol. 42, 841 (1997).
[CrossRef] [PubMed]

Heino, J.

J. Heino, S. R. Arridge, J. Sikora, and E. Somersalo, Phys. Rev. E 68, 031908 (2003).
[CrossRef]

Hillman, E.

F. Schmidt, M. Fry, E. Hillman, J. Hebden, and D. Delpy, Rev. Sci. Instrum. 71, 256 (2000).
[CrossRef]

Kölzer, J.

Martelli, F.

Mitic, G.

Nossal, R.

Otto, J.

Patterson, M.

Plies, E.

Schmidt, F.

F. Schmidt, M. Fry, E. Hillman, J. Hebden, and D. Delpy, Rev. Sci. Instrum. 71, 256 (2000).
[CrossRef]

Sikora, J.

J. Heino, S. R. Arridge, J. Sikora, and E. Somersalo, Phys. Rev. E 68, 031908 (2003).
[CrossRef]

Sölkner, G.

Somersalo, E.

J. Heino, S. R. Arridge, J. Sikora, and E. Somersalo, Phys. Rev. E 68, 031908 (2003).
[CrossRef]

Weiss, G. H.

O. K. Dudko, G. H. Weiss, V. Chernomordik, and A. H. Gandjbakhche, Phys. Med. Biol. 49, 3979 (2004).
[CrossRef] [PubMed]

L. Dagdug, G. H. Weiss, and A. H. Gandjbakhche, Phys. Med. Biol. 48, 1361 (2003).
[CrossRef] [PubMed]

Wilson, B. C.

Zaccanti, G.

V. Chernomordik, A. H. Gandjbakhche, J. C. Hebden, and G. Zaccanti, Med. Phys. 26, 1822 (1999).
[CrossRef] [PubMed]

D. Contini, F. Martelli, and G. Zaccanti, Appl. Opt. 36, 4587 (1997).
[CrossRef] [PubMed]

Zinth, W.

Appl. Opt. (4)

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

Med. Phys. (1)

V. Chernomordik, A. H. Gandjbakhche, J. C. Hebden, and G. Zaccanti, Med. Phys. 26, 1822 (1999).
[CrossRef] [PubMed]

Phys. Med. Biol. (4)

L. Dagdug, G. H. Weiss, and A. H. Gandjbakhche, Phys. Med. Biol. 48, 1361 (2003).
[CrossRef] [PubMed]

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

S. R. Arridge and J. C. Hebden, Phys. Med. Biol. 42, 841 (1997).
[CrossRef] [PubMed]

O. K. Dudko, G. H. Weiss, V. Chernomordik, and A. H. Gandjbakhche, Phys. Med. Biol. 49, 3979 (2004).
[CrossRef] [PubMed]

Phys. Rev. E (1)

J. Heino, S. R. Arridge, J. Sikora, and E. Somersalo, Phys. Rev. E 68, 031908 (2003).
[CrossRef]

Rev. Sci. Instrum. (1)

F. Schmidt, M. Fry, E. Hillman, J. Hebden, and D. Delpy, Rev. Sci. Instrum. 71, 256 (2000).
[CrossRef]

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Figures (2)

Fig. 1
Fig. 1

Anisotropic scattering phantom consisting of aligned wax fibers in epoxy resin.

Fig. 2
Fig. 2

Time-of-flight measurements across the phantom in longitudinal and lateral orientations (discrete points) and corresponding fits of anisotropic model (solid curves).

Equations (6)

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

ΓT,longt=2BI02μsctB+2dμsB+2exp-μs+μact×m=1-1m+1sin22πmdμs×expBμctB+2cos2πmdμs,
ΓT,latt=2I0μsctB+2I0BμsctB+2dμsB+2×exp-μs+μactm=1-1m+1sin22πmdμs×expμctB+2cos2πmdμs.
ΓT,longt=B2πdμs2ctexp-μactm=1-1m+1×sin22πmdμsexp-Bπ2m2ctB+2d2μs,
ΓT,latt=12Bπdμs2ctexp-μactm=1-1m+1×sin22πmdμsexp-π2m2ctB+2d2μs.
ΓR,longt,X,Y=B2πdμs2ctexp-μact×exp-X2+Y2B+2μs4ctm=1sin22πmdμs×exp-Bπ2m2ctB+2d2μs,
ΓR,latt,X,Y=12Bπdμs2ctexp-μact×exp-BX2+Y2B+2μs4Bctm=1sin22πmdμs×exp-π2m2ctB+2d2μs.

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