Abstract

The spatial structure of optically heterogeneous turbid media is probed with diffusive light. Projection images are obtained experimentally by deconvolution of the scattered diffuse-photon density waves on a planar boundary by use of a fast Fourier transform. The method is very fast, permitting object localization and characterization in 1000 volume-element samples on subsecond computational time scales. The optical properties of slice-shape inhomogeneities are accurately determined.

© 1997 Optical Society of America

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Corrections

X. D. Li, T. Durduran, A. G. Yodh, B. Chance, and D. N. Pattanayak, "Diffraction tomography for biomedical imaging with diffuse photon density waves: errata," Opt. Lett. 22, 1198-1198 (1997)
https://www.osapublishing.org/ol/abstract.cfm?uri=ol-22-15-1198

References

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  1. A. Yodh and B. Chance, Phys. Today 48(3), 34 (1995), and references therein.
    [CrossRef]
  2. See related studies in Advances in Optical Imaging and Photon Migration, R. Alfano, ed., Vol. 2 of Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1996).
  3. M. Tamura, O. Hazeki, S. Nioka, and B. Chance, Ann. Rev. Physiol. 51, 813 (1989).
    [CrossRef]
  4. S. R. Arridge, P. van der Zee, M. Cope, and D. T. Delpy, Proc. SPIE 1431, 204 (1991); R. L. Barbour, H. L. Graber, Y. Wang, J. H. Chang, and R. Aronson, in Medical Optical Tomography: Function Imaging and Monitoring, G. Müller, ed. (SPIE Optical Engineering Press, 1993), Vol. IS11, p. 87; M. A. O'Leary, D. A. Boass, B. Chance, and A. G. Yodh, Opt. Lett. 20, 426 (1995); C. P. Gonatas, M. Ishii, J. S. Leigh, and J. Schotland, Phys. Rev. E 52, 4361 (1995); B. M. Pogue, M. S. Patterson, H. Jiang, and K. D. Paulsen, Phys. Med. Biol. 40, 1709 (1995); H. B. Jiang, K. D. Paulsen, U. L. Osterberg, B. W. Pogue, and M. S. Patterson, Opt. Lett. 20, 2128 (1995).
    [CrossRef] [PubMed]
  5. S. Fantini, M. A. Franceschini, G. Gaida, E. Gratton, H. Jess, W. W. Mantulin, K. T. Moesta, P. M. Schlag, and M. Kaschke, Mod. Phys. 23, 149 (1996).
  6. A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (IEEE Press, New York, 1988), Chap. 7.
  7. E. Wolf, Opt. Commun.1, 153 (1969); E. Wolf, in Trends in Optics, A. Consortini, ed. (Academic, San Diego, Calif., 1996), p. 83; J. Devaney, Inverse Problems 2, 161 (1986).
    [CrossRef]
  8. D. N. Pattanayak, GE Tech. Info. Series91CRD241 General Electric; C. L. Matson, N. Clark, L. McMackin, and J. S. Fender, in Advances in Optical Imaging and Photon Migration, R. Alfano, ed., Vol. 2 of Trends in Optics and Photonics (Optical Society of America, Washington, D.C., 1996), p. 261.
  9. M. S. Patterson, B. Chance, and B. C. Wilson, Appl. Opt. 28, 2331 (1989).
    [CrossRef] [PubMed]
  10. A. Baños, Dipole Radiation in the Presence of a Con-ducting Half-Space (Pergamon, New York, 1996), p. 18.

1996 (1)

S. Fantini, M. A. Franceschini, G. Gaida, E. Gratton, H. Jess, W. W. Mantulin, K. T. Moesta, P. M. Schlag, and M. Kaschke, Mod. Phys. 23, 149 (1996).

1995 (1)

A. Yodh and B. Chance, Phys. Today 48(3), 34 (1995), and references therein.
[CrossRef]

1991 (1)

S. R. Arridge, P. van der Zee, M. Cope, and D. T. Delpy, Proc. SPIE 1431, 204 (1991); R. L. Barbour, H. L. Graber, Y. Wang, J. H. Chang, and R. Aronson, in Medical Optical Tomography: Function Imaging and Monitoring, G. Müller, ed. (SPIE Optical Engineering Press, 1993), Vol. IS11, p. 87; M. A. O'Leary, D. A. Boass, B. Chance, and A. G. Yodh, Opt. Lett. 20, 426 (1995); C. P. Gonatas, M. Ishii, J. S. Leigh, and J. Schotland, Phys. Rev. E 52, 4361 (1995); B. M. Pogue, M. S. Patterson, H. Jiang, and K. D. Paulsen, Phys. Med. Biol. 40, 1709 (1995); H. B. Jiang, K. D. Paulsen, U. L. Osterberg, B. W. Pogue, and M. S. Patterson, Opt. Lett. 20, 2128 (1995).
[CrossRef] [PubMed]

1989 (2)

M. Tamura, O. Hazeki, S. Nioka, and B. Chance, Ann. Rev. Physiol. 51, 813 (1989).
[CrossRef]

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

Arridge, S. R.

S. R. Arridge, P. van der Zee, M. Cope, and D. T. Delpy, Proc. SPIE 1431, 204 (1991); R. L. Barbour, H. L. Graber, Y. Wang, J. H. Chang, and R. Aronson, in Medical Optical Tomography: Function Imaging and Monitoring, G. Müller, ed. (SPIE Optical Engineering Press, 1993), Vol. IS11, p. 87; M. A. O'Leary, D. A. Boass, B. Chance, and A. G. Yodh, Opt. Lett. 20, 426 (1995); C. P. Gonatas, M. Ishii, J. S. Leigh, and J. Schotland, Phys. Rev. E 52, 4361 (1995); B. M. Pogue, M. S. Patterson, H. Jiang, and K. D. Paulsen, Phys. Med. Biol. 40, 1709 (1995); H. B. Jiang, K. D. Paulsen, U. L. Osterberg, B. W. Pogue, and M. S. Patterson, Opt. Lett. 20, 2128 (1995).
[CrossRef] [PubMed]

Baños, A.

A. Baños, Dipole Radiation in the Presence of a Con-ducting Half-Space (Pergamon, New York, 1996), p. 18.

Chance, B.

A. Yodh and B. Chance, Phys. Today 48(3), 34 (1995), and references therein.
[CrossRef]

M. Tamura, O. Hazeki, S. Nioka, and B. Chance, Ann. Rev. Physiol. 51, 813 (1989).
[CrossRef]

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

Cope, M.

S. R. Arridge, P. van der Zee, M. Cope, and D. T. Delpy, Proc. SPIE 1431, 204 (1991); R. L. Barbour, H. L. Graber, Y. Wang, J. H. Chang, and R. Aronson, in Medical Optical Tomography: Function Imaging and Monitoring, G. Müller, ed. (SPIE Optical Engineering Press, 1993), Vol. IS11, p. 87; M. A. O'Leary, D. A. Boass, B. Chance, and A. G. Yodh, Opt. Lett. 20, 426 (1995); C. P. Gonatas, M. Ishii, J. S. Leigh, and J. Schotland, Phys. Rev. E 52, 4361 (1995); B. M. Pogue, M. S. Patterson, H. Jiang, and K. D. Paulsen, Phys. Med. Biol. 40, 1709 (1995); H. B. Jiang, K. D. Paulsen, U. L. Osterberg, B. W. Pogue, and M. S. Patterson, Opt. Lett. 20, 2128 (1995).
[CrossRef] [PubMed]

Delpy, D. T.

S. R. Arridge, P. van der Zee, M. Cope, and D. T. Delpy, Proc. SPIE 1431, 204 (1991); R. L. Barbour, H. L. Graber, Y. Wang, J. H. Chang, and R. Aronson, in Medical Optical Tomography: Function Imaging and Monitoring, G. Müller, ed. (SPIE Optical Engineering Press, 1993), Vol. IS11, p. 87; M. A. O'Leary, D. A. Boass, B. Chance, and A. G. Yodh, Opt. Lett. 20, 426 (1995); C. P. Gonatas, M. Ishii, J. S. Leigh, and J. Schotland, Phys. Rev. E 52, 4361 (1995); B. M. Pogue, M. S. Patterson, H. Jiang, and K. D. Paulsen, Phys. Med. Biol. 40, 1709 (1995); H. B. Jiang, K. D. Paulsen, U. L. Osterberg, B. W. Pogue, and M. S. Patterson, Opt. Lett. 20, 2128 (1995).
[CrossRef] [PubMed]

Fantini, S.

S. Fantini, M. A. Franceschini, G. Gaida, E. Gratton, H. Jess, W. W. Mantulin, K. T. Moesta, P. M. Schlag, and M. Kaschke, Mod. Phys. 23, 149 (1996).

Franceschini, M. A.

S. Fantini, M. A. Franceschini, G. Gaida, E. Gratton, H. Jess, W. W. Mantulin, K. T. Moesta, P. M. Schlag, and M. Kaschke, Mod. Phys. 23, 149 (1996).

Gaida, G.

S. Fantini, M. A. Franceschini, G. Gaida, E. Gratton, H. Jess, W. W. Mantulin, K. T. Moesta, P. M. Schlag, and M. Kaschke, Mod. Phys. 23, 149 (1996).

Gratton, E.

S. Fantini, M. A. Franceschini, G. Gaida, E. Gratton, H. Jess, W. W. Mantulin, K. T. Moesta, P. M. Schlag, and M. Kaschke, Mod. Phys. 23, 149 (1996).

Hazeki, O.

M. Tamura, O. Hazeki, S. Nioka, and B. Chance, Ann. Rev. Physiol. 51, 813 (1989).
[CrossRef]

Jess, H.

S. Fantini, M. A. Franceschini, G. Gaida, E. Gratton, H. Jess, W. W. Mantulin, K. T. Moesta, P. M. Schlag, and M. Kaschke, Mod. Phys. 23, 149 (1996).

Kak, A. C.

A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (IEEE Press, New York, 1988), Chap. 7.

Kaschke, M.

S. Fantini, M. A. Franceschini, G. Gaida, E. Gratton, H. Jess, W. W. Mantulin, K. T. Moesta, P. M. Schlag, and M. Kaschke, Mod. Phys. 23, 149 (1996).

Mantulin, W. W.

S. Fantini, M. A. Franceschini, G. Gaida, E. Gratton, H. Jess, W. W. Mantulin, K. T. Moesta, P. M. Schlag, and M. Kaschke, Mod. Phys. 23, 149 (1996).

Moesta, K. T.

S. Fantini, M. A. Franceschini, G. Gaida, E. Gratton, H. Jess, W. W. Mantulin, K. T. Moesta, P. M. Schlag, and M. Kaschke, Mod. Phys. 23, 149 (1996).

Nioka, S.

M. Tamura, O. Hazeki, S. Nioka, and B. Chance, Ann. Rev. Physiol. 51, 813 (1989).
[CrossRef]

Patterson, M. S.

Schlag, P. M.

S. Fantini, M. A. Franceschini, G. Gaida, E. Gratton, H. Jess, W. W. Mantulin, K. T. Moesta, P. M. Schlag, and M. Kaschke, Mod. Phys. 23, 149 (1996).

Slaney, M.

A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (IEEE Press, New York, 1988), Chap. 7.

Tamura, M.

M. Tamura, O. Hazeki, S. Nioka, and B. Chance, Ann. Rev. Physiol. 51, 813 (1989).
[CrossRef]

van der Zee, P.

S. R. Arridge, P. van der Zee, M. Cope, and D. T. Delpy, Proc. SPIE 1431, 204 (1991); R. L. Barbour, H. L. Graber, Y. Wang, J. H. Chang, and R. Aronson, in Medical Optical Tomography: Function Imaging and Monitoring, G. Müller, ed. (SPIE Optical Engineering Press, 1993), Vol. IS11, p. 87; M. A. O'Leary, D. A. Boass, B. Chance, and A. G. Yodh, Opt. Lett. 20, 426 (1995); C. P. Gonatas, M. Ishii, J. S. Leigh, and J. Schotland, Phys. Rev. E 52, 4361 (1995); B. M. Pogue, M. S. Patterson, H. Jiang, and K. D. Paulsen, Phys. Med. Biol. 40, 1709 (1995); H. B. Jiang, K. D. Paulsen, U. L. Osterberg, B. W. Pogue, and M. S. Patterson, Opt. Lett. 20, 2128 (1995).
[CrossRef] [PubMed]

Wilson, B. C.

Wolf, E.

E. Wolf, Opt. Commun.1, 153 (1969); E. Wolf, in Trends in Optics, A. Consortini, ed. (Academic, San Diego, Calif., 1996), p. 83; J. Devaney, Inverse Problems 2, 161 (1986).
[CrossRef]

Yodh, A.

A. Yodh and B. Chance, Phys. Today 48(3), 34 (1995), and references therein.
[CrossRef]

Ann. Rev. Physiol. (1)

M. Tamura, O. Hazeki, S. Nioka, and B. Chance, Ann. Rev. Physiol. 51, 813 (1989).
[CrossRef]

Appl. Opt. (1)

Mod. Phys. (1)

S. Fantini, M. A. Franceschini, G. Gaida, E. Gratton, H. Jess, W. W. Mantulin, K. T. Moesta, P. M. Schlag, and M. Kaschke, Mod. Phys. 23, 149 (1996).

Phys. Today (1)

A. Yodh and B. Chance, Phys. Today 48(3), 34 (1995), and references therein.
[CrossRef]

Proc. SPIE (1)

S. R. Arridge, P. van der Zee, M. Cope, and D. T. Delpy, Proc. SPIE 1431, 204 (1991); R. L. Barbour, H. L. Graber, Y. Wang, J. H. Chang, and R. Aronson, in Medical Optical Tomography: Function Imaging and Monitoring, G. Müller, ed. (SPIE Optical Engineering Press, 1993), Vol. IS11, p. 87; M. A. O'Leary, D. A. Boass, B. Chance, and A. G. Yodh, Opt. Lett. 20, 426 (1995); C. P. Gonatas, M. Ishii, J. S. Leigh, and J. Schotland, Phys. Rev. E 52, 4361 (1995); B. M. Pogue, M. S. Patterson, H. Jiang, and K. D. Paulsen, Phys. Med. Biol. 40, 1709 (1995); H. B. Jiang, K. D. Paulsen, U. L. Osterberg, B. W. Pogue, and M. S. Patterson, Opt. Lett. 20, 2128 (1995).
[CrossRef] [PubMed]

Other (5)

See related studies in Advances in Optical Imaging and Photon Migration, R. Alfano, ed., Vol. 2 of Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1996).

A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (IEEE Press, New York, 1988), Chap. 7.

E. Wolf, Opt. Commun.1, 153 (1969); E. Wolf, in Trends in Optics, A. Consortini, ed. (Academic, San Diego, Calif., 1996), p. 83; J. Devaney, Inverse Problems 2, 161 (1986).
[CrossRef]

D. N. Pattanayak, GE Tech. Info. Series91CRD241 General Electric; C. L. Matson, N. Clark, L. McMackin, and J. S. Fender, in Advances in Optical Imaging and Photon Migration, R. Alfano, ed., Vol. 2 of Trends in Optics and Photonics (Optical Society of America, Washington, D.C., 1996), p. 261.

A. Baños, Dipole Radiation in the Presence of a Con-ducting Half-Space (Pergamon, New York, 1996), p. 18.

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Figures (2)

Fig. 1
Fig. 1

(a) Experimental geometry: The source is fixed at the origin, and the detector scans in a planar geometry at z = z d = 5.0   cm over a 9.3   cm × 9.3   cm region. (b) Setup: APD, avalanche photodiode; A, amplifier; SSB I/Q, single-sideband in-phase/quadrature-phase demodulator; LO, local port; RF, radiofrequency port; ADC, analog–digital converter; GPIB, general purpose interface bus.

Fig. 2
Fig. 2

(a) Slice showing the exact positions of the two slices; for experiments with scattering objects, two spheres are placed so that their centers coincide with the slice centers. (b) Projection image of slices. (c) Projection image of spheres. The recovered absorption (d) and scattering (e) properties of the slices and spheres, respectively, are also shown.

Equations (4)

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U 1 r d ,   r s ,   ω = V T U 0 r ,   r s ,   ω G r d - r d 3 r .
G r d - r = i 8 π 2 - d p d q m   exp ip x d - x + iq y d - y + im z d - z ,
U ˜ 1 p ,   q ,   z d ,   r s ,   ω = i 2 m z s z d T ˜ p ,   q ,   z ,   r s ,   ω × exp im z d - z d z .
j = 1 N T ˜ p ,   q ,   z j ,   r s ,   ω exp - mz j = 2 m i δ z   exp - imz d U ˜ 1 p ,   q ,   z d ,   r s ,   ω ,

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