Abstract

Imaging through highly scattering media with transmitted photons with the shortest flight times is limited ultimately by the available number of photons with sufficiently short paths. A method is described that enhances the performance of the time-resolved imaging technique. A least-squares fit was obtained between the measured temporal distributions of transmitted light and a model of photon transport based on the diffusion approximation to the radiative transfer theory. Images constructed from the model estimates of short-path-length photon intensities provide information on internal structure, with a significantly improved signal-to-noise ratio compared with those that would be obtained directly from the data.

© 1994 Optical Society of America

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References

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  1. B. Chance, R. R. Alfano, eds., Photon Migration and Imaging in Random Media and Tissues, Proc. Soc. Photo-Opt. Instrum. Eng.1888 (1993).
  2. E. Leith, C. Chen, H. Chen, D. Dilworth, J. Lopez, J. Rudd, P.-C. Sun, J. Valdmanis, G. Vossler, J. Opt. Soc. Am. A 9, 1148 (1992).
    [CrossRef]
  3. K. Yoo, Q. Xing, R. R. Alfano, Opt. Lett. 16, 1019 (1991).
    [CrossRef] [PubMed]
  4. L. Wang, P. P. Ho, C. Liu, G. Zhang, R. R. Alfano, Science 253, 769 (1991).
    [CrossRef] [PubMed]
  5. M. D. Duncan, R. Mahon, L. L. Tankersley, J. Reintjes, Opt. Lett. 16, 1868 (1991).
    [CrossRef] [PubMed]
  6. S. Andersson-Engels, R. Berg, S. Svanberg, O. Jarlman, Opt. Lett. 15, 1179 (1990).
    [CrossRef] [PubMed]
  7. D. A. Benaron, D. K. Stevenson, Science 259, 1463 (1993).
    [CrossRef] [PubMed]
  8. J. C. Hebden, Appl. Opt. 32, 3837 (1993).
    [CrossRef] [PubMed]
  9. J. C. Hebden, Med. Phys. 19, 1081 (1992).
    [CrossRef] [PubMed]
  10. S. R. Arridge, M. Schweiger, D. T. Delpy, Proc. Soc. Photo-Opt. Instrum. Eng. 1767, 372 (1992).
  11. M. S. Patterson, B. Chance, B. C. Wilson, Appl. Opt. 28, 2331 (1989).
    [CrossRef] [PubMed]
  12. V. G. Peters, D. R. Wyman, M. S. Patterson, G. L. Frank, Phys. Med. Biol. 35, 1317 (1990).
    [CrossRef] [PubMed]

1993 (2)

D. A. Benaron, D. K. Stevenson, Science 259, 1463 (1993).
[CrossRef] [PubMed]

J. C. Hebden, Appl. Opt. 32, 3837 (1993).
[CrossRef] [PubMed]

1992 (3)

E. Leith, C. Chen, H. Chen, D. Dilworth, J. Lopez, J. Rudd, P.-C. Sun, J. Valdmanis, G. Vossler, J. Opt. Soc. Am. A 9, 1148 (1992).
[CrossRef]

J. C. Hebden, Med. Phys. 19, 1081 (1992).
[CrossRef] [PubMed]

S. R. Arridge, M. Schweiger, D. T. Delpy, Proc. Soc. Photo-Opt. Instrum. Eng. 1767, 372 (1992).

1991 (3)

1990 (2)

V. G. Peters, D. R. Wyman, M. S. Patterson, G. L. Frank, Phys. Med. Biol. 35, 1317 (1990).
[CrossRef] [PubMed]

S. Andersson-Engels, R. Berg, S. Svanberg, O. Jarlman, Opt. Lett. 15, 1179 (1990).
[CrossRef] [PubMed]

1989 (1)

Alfano, R. R.

K. Yoo, Q. Xing, R. R. Alfano, Opt. Lett. 16, 1019 (1991).
[CrossRef] [PubMed]

L. Wang, P. P. Ho, C. Liu, G. Zhang, R. R. Alfano, Science 253, 769 (1991).
[CrossRef] [PubMed]

Andersson-Engels, S.

Arridge, S. R.

S. R. Arridge, M. Schweiger, D. T. Delpy, Proc. Soc. Photo-Opt. Instrum. Eng. 1767, 372 (1992).

Benaron, D. A.

D. A. Benaron, D. K. Stevenson, Science 259, 1463 (1993).
[CrossRef] [PubMed]

Berg, R.

Chance, B.

Chen, C.

Chen, H.

Delpy, D. T.

S. R. Arridge, M. Schweiger, D. T. Delpy, Proc. Soc. Photo-Opt. Instrum. Eng. 1767, 372 (1992).

Dilworth, D.

Duncan, M. D.

Frank, G. L.

V. G. Peters, D. R. Wyman, M. S. Patterson, G. L. Frank, Phys. Med. Biol. 35, 1317 (1990).
[CrossRef] [PubMed]

Hebden, J. C.

Ho, P. P.

L. Wang, P. P. Ho, C. Liu, G. Zhang, R. R. Alfano, Science 253, 769 (1991).
[CrossRef] [PubMed]

Jarlman, O.

Leith, E.

Liu, C.

L. Wang, P. P. Ho, C. Liu, G. Zhang, R. R. Alfano, Science 253, 769 (1991).
[CrossRef] [PubMed]

Lopez, J.

Mahon, R.

Patterson, M. S.

V. G. Peters, D. R. Wyman, M. S. Patterson, G. L. Frank, Phys. Med. Biol. 35, 1317 (1990).
[CrossRef] [PubMed]

M. S. Patterson, B. Chance, B. C. Wilson, Appl. Opt. 28, 2331 (1989).
[CrossRef] [PubMed]

Peters, V. G.

V. G. Peters, D. R. Wyman, M. S. Patterson, G. L. Frank, Phys. Med. Biol. 35, 1317 (1990).
[CrossRef] [PubMed]

Reintjes, J.

Rudd, J.

Schweiger, M.

S. R. Arridge, M. Schweiger, D. T. Delpy, Proc. Soc. Photo-Opt. Instrum. Eng. 1767, 372 (1992).

Stevenson, D. K.

D. A. Benaron, D. K. Stevenson, Science 259, 1463 (1993).
[CrossRef] [PubMed]

Sun, P.-C.

Svanberg, S.

Tankersley, L. L.

Valdmanis, J.

Vossler, G.

Wang, L.

L. Wang, P. P. Ho, C. Liu, G. Zhang, R. R. Alfano, Science 253, 769 (1991).
[CrossRef] [PubMed]

Wilson, B. C.

Wyman, D. R.

V. G. Peters, D. R. Wyman, M. S. Patterson, G. L. Frank, Phys. Med. Biol. 35, 1317 (1990).
[CrossRef] [PubMed]

Xing, Q.

Yoo, K.

Zhang, G.

L. Wang, P. P. Ho, C. Liu, G. Zhang, R. R. Alfano, Science 253, 769 (1991).
[CrossRef] [PubMed]

Appl. Opt. (2)

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

Med. Phys. (1)

J. C. Hebden, Med. Phys. 19, 1081 (1992).
[CrossRef] [PubMed]

Opt. Lett. (3)

Phys. Med. Biol. (1)

V. G. Peters, D. R. Wyman, M. S. Patterson, G. L. Frank, Phys. Med. Biol. 35, 1317 (1990).
[CrossRef] [PubMed]

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

S. R. Arridge, M. Schweiger, D. T. Delpy, Proc. Soc. Photo-Opt. Instrum. Eng. 1767, 372 (1992).

Science (2)

L. Wang, P. P. Ho, C. Liu, G. Zhang, R. R. Alfano, Science 253, 769 (1991).
[CrossRef] [PubMed]

D. A. Benaron, D. K. Stevenson, Science 259, 1463 (1993).
[CrossRef] [PubMed]

Other (1)

B. Chance, R. R. Alfano, eds., Photon Migration and Imaging in Random Media and Tissues, Proc. Soc. Photo-Opt. Instrum. Eng.1888 (1993).

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Figures (4)

Fig. 1
Fig. 1

Experimental time-resolved imaging system.

Fig. 2
Fig. 2

Highly scattering object consisting of six glass spheres suspended on a wire frame within a plastic box filled with a solution of latex microspheres.

Fig. 3
Fig. 3

Typical temporal distribution and a least-squares fit of the diffusion model.

Fig. 4
Fig. 4

Time-resolved images obtained from fits of the diffusion model and integration times of (a) 18 ps, (b)72 ps, (c) 400 ps, and (d) 1 ns.

Equations (2)

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T ( R , d , t ) = A D - 3 / 2 ( t - t 0 ) - 5 / 2 exp [ - μ a c ( t - t 0 ) ] × G ( d , t ) 0 R ρ exp [ - ρ 2 4 D c ( t - t 0 ) ] d ρ ,
G ( d , t ) = n = 1 , k = 2 n - 1 n = { ( k d - z 0 ) exp [ - ( k d - z 0 ) 2 4 D c ( t - t 0 ) ] - ( k d + z 0 ) exp [ - ( k d + z 0 ) 2 4 D c ( t - t 0 ) ] } .

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