Abstract

Diffuse optical tomography is a novel imaging technique that resolves and quantifies the optical properties of objects buried in turbid media. Typically, numerical solutions of the diffusion equation are employed to construct the tomographic problem when media of complex geometries are investigated. Numerical methods offer implementation simplicity but also significant computation burden, especially when large three-dimensional reconstructions are involved. We present an alternative method of performing tomography of diffuse media of arbitrary geometries by means of an analytical approach, the Kirchhoff approximation. We show that the method is extremely efficient in computation times and consider its potential as a real-time three-dimensional imaging tool.

© 2002 Optical Society of America

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References

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  1. V. Ntziachristos, A. G. Yodh, M. Schnall, and B. Chance, Proc. Nat. Acad. Sci. USA 97, 2767 (2000).
    [CrossRef]
  2. V. Ntziachristos and B. Chance, Breast Cancer Res. 3, 41 (2001).
    [CrossRef]
  3. T. O. McBride, B. W. Pogue, S. Jiang, U. L. Osterberg, K. D. Paulsen, and S. P. Poplack, Opt. Lett. 26, 822 (2001).
    [CrossRef]
  4. S. R. Arridge, Inverse Probl. 15, R41 (1999).
    [CrossRef]
  5. M. A. O’Leary, D. A. Boas, B. Chance, and A. G. Yodh, Opt. Lett. 20, 426 (1995).
    [CrossRef] [PubMed]
  6. M. Nieto-Vesperinas, Scattering and Diffraction in Physical Optics (Pergamon, New York, 1996).
  7. J. Ripoll, V. Ntziachristos, R. Carminati, and M. Nieto-Vesperinas, Phys. Rev. E 64, 051917 (2001).
    [CrossRef]
  8. M. S. Patterson, B. Chance, and B. C. Wilson, Appl. Opt. 28, 2331 (1989).
    [CrossRef] [PubMed]
  9. R. Aronson, J. Opt. Soc. Am. A 12, 2532 (1995).
    [CrossRef]
  10. J. Ripoll and M. Nieto-Vesperinas, Opt. Lett. 24, 796 (1999).
    [CrossRef]
  11. A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (Institute of Electrical and Electronics Engineers, New York, 1988).

2001 (3)

V. Ntziachristos and B. Chance, Breast Cancer Res. 3, 41 (2001).
[CrossRef]

T. O. McBride, B. W. Pogue, S. Jiang, U. L. Osterberg, K. D. Paulsen, and S. P. Poplack, Opt. Lett. 26, 822 (2001).
[CrossRef]

J. Ripoll, V. Ntziachristos, R. Carminati, and M. Nieto-Vesperinas, Phys. Rev. E 64, 051917 (2001).
[CrossRef]

2000 (1)

V. Ntziachristos, A. G. Yodh, M. Schnall, and B. Chance, Proc. Nat. Acad. Sci. USA 97, 2767 (2000).
[CrossRef]

1999 (2)

1995 (2)

1989 (1)

Aronson, R.

Arridge, S. R.

S. R. Arridge, Inverse Probl. 15, R41 (1999).
[CrossRef]

Boas, D. A.

Carminati, R.

J. Ripoll, V. Ntziachristos, R. Carminati, and M. Nieto-Vesperinas, Phys. Rev. E 64, 051917 (2001).
[CrossRef]

Chance, B.

V. Ntziachristos and B. Chance, Breast Cancer Res. 3, 41 (2001).
[CrossRef]

V. Ntziachristos, A. G. Yodh, M. Schnall, and B. Chance, Proc. Nat. Acad. Sci. USA 97, 2767 (2000).
[CrossRef]

M. A. O’Leary, D. A. Boas, B. Chance, and A. G. Yodh, Opt. Lett. 20, 426 (1995).
[CrossRef] [PubMed]

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

Jiang, S.

Kak, A. C.

A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (Institute of Electrical and Electronics Engineers, New York, 1988).

McBride, T. O.

Nieto-Vesperinas, M.

J. Ripoll, V. Ntziachristos, R. Carminati, and M. Nieto-Vesperinas, Phys. Rev. E 64, 051917 (2001).
[CrossRef]

J. Ripoll and M. Nieto-Vesperinas, Opt. Lett. 24, 796 (1999).
[CrossRef]

M. Nieto-Vesperinas, Scattering and Diffraction in Physical Optics (Pergamon, New York, 1996).

Ntziachristos, V.

V. Ntziachristos and B. Chance, Breast Cancer Res. 3, 41 (2001).
[CrossRef]

J. Ripoll, V. Ntziachristos, R. Carminati, and M. Nieto-Vesperinas, Phys. Rev. E 64, 051917 (2001).
[CrossRef]

V. Ntziachristos, A. G. Yodh, M. Schnall, and B. Chance, Proc. Nat. Acad. Sci. USA 97, 2767 (2000).
[CrossRef]

O’Leary, M. A.

Osterberg, U. L.

Patterson, M. S.

Paulsen, K. D.

Pogue, B. W.

Poplack, S. P.

Ripoll, J.

J. Ripoll, V. Ntziachristos, R. Carminati, and M. Nieto-Vesperinas, Phys. Rev. E 64, 051917 (2001).
[CrossRef]

J. Ripoll and M. Nieto-Vesperinas, Opt. Lett. 24, 796 (1999).
[CrossRef]

Schnall, M.

V. Ntziachristos, A. G. Yodh, M. Schnall, and B. Chance, Proc. Nat. Acad. Sci. USA 97, 2767 (2000).
[CrossRef]

Slaney, M.

A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (Institute of Electrical and Electronics Engineers, New York, 1988).

Wilson, B. C.

Yodh, A. G.

V. Ntziachristos, A. G. Yodh, M. Schnall, and B. Chance, Proc. Nat. Acad. Sci. USA 97, 2767 (2000).
[CrossRef]

M. A. O’Leary, D. A. Boas, B. Chance, and A. G. Yodh, Opt. Lett. 20, 426 (1995).
[CrossRef] [PubMed]

Appl. Opt. (1)

Breast Cancer Res. (1)

V. Ntziachristos and B. Chance, Breast Cancer Res. 3, 41 (2001).
[CrossRef]

Inverse Probl. (1)

S. R. Arridge, Inverse Probl. 15, R41 (1999).
[CrossRef]

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

Opt. Lett. (3)

Phys. Rev. E (1)

J. Ripoll, V. Ntziachristos, R. Carminati, and M. Nieto-Vesperinas, Phys. Rev. E 64, 051917 (2001).
[CrossRef]

Proc. Nat. Acad. Sci. USA (1)

V. Ntziachristos, A. G. Yodh, M. Schnall, and B. Chance, Proc. Nat. Acad. Sci. USA 97, 2767 (2000).
[CrossRef]

Other (2)

M. Nieto-Vesperinas, Scattering and Diffraction in Physical Optics (Pergamon, New York, 1996).

A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (Institute of Electrical and Electronics Engineers, New York, 1988).

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Figures (3)

Fig. 1
Fig. 1

Experimental setup: A ring with 12 sources (O’s) is placed at zs=0, and two rings with 12 detectors (X’s) each are located at zd=-0.5 cm and zd=0.5 cm.

Fig. 2
Fig. 2

Three-dimensional reconstructions of two absorbing tubes of μa=0.4 cm-1 and μs=5 cm-1, each 0.4 cm in diameter, 1 cm apart (white circles). 498 volume elements per plane were reconstructed at zd=-0.25 cm and zd=0.25 cm. Background optical properties: μa=0.1 cm-1 and μs=5 cm-1. Total computing time (including 3000 ART iterations), 5 min on a 650-MHz PC.

Fig. 3
Fig. 3

Number of volume elements versus computation time in seconds for weight matrix generation for 12×24 and 24×36 source–detector pairs (open squares and open circles, respectively). The total computing time (weight matrix and 3000 ART iterations) for 12×24 and 24×36 source–detector pairs (filled squares and filled circles, respectively) is also shown. All times were computed on a 650-MHz PC with 256 Mbytes of RAM.

Equations (1)

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UKArd=Uincrs-rd+14πp=1NCndDgκrp-rdnp+gκrp-rdUKArpnpΔSrp.

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