Abstract

We present a model of the forward problem for diffuse photon-density waves in a turbid medium containing a spherical inhomogeneity, using diffraction tomographic (DT) methods. Recently, by use of DT methods, the forward problem was investigated [Opt.  Express 1, 6 (1997); www.osa.org] assuming weak perturbations from the background medium but an arbitrary inhomogeneity structure. We apply DT concepts to a forward problem solution that permits strong perturbations but requires a spherical inhomogeneity. We show that this model is consistent with previous DT results and discuss the application of this new model.

© 1998 Optical Society of America

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References

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  1. S. Feng, F. Zeng, and B. Chance, Appl. Opt. 34, 3826 (1995).
    [CrossRef] [PubMed]
  2. M. A. O'Leary, D. A. Boas, B. Chance, and A. G. Yodh, Opt. Lett. 20, 426 (1995).
    [CrossRef] [PubMed]
  3. H. B. Jiang, K. D. Paulsen, U. L. Osterberg, and M. S. Patterson, Appl. Opt. 36, 52 (1997).
    [CrossRef] [PubMed]
  4. D. A. Boas, M. A. O'Leary, B. Chance, and A. G. Yodh, Proc. Natl. Acad. Sci. USA 91, 4887 (1994).
    [CrossRef]
  5. C. L. Matson, Opt. Express 1, 6 (1997); www.osa.org .
    [CrossRef] [PubMed]
  6. A. Baños, Dipole Radiation in the Presence of a Conducting Half-Space (Pergamon, London, 1966).
  7. A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (Institute of Electrical and Electronics Engineers, New York, 1988).
  8. P. M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953), Vols. I and II.
  9. C. L. Matson, N. Clark, L. McMackin, and J. S. Fender, Appl. Opt. 36, 214 (1997).
    [CrossRef] [PubMed]

1997 (3)

1995 (2)

1994 (1)

D. A. Boas, M. A. O'Leary, B. Chance, and A. G. Yodh, Proc. Natl. Acad. Sci. USA 91, 4887 (1994).
[CrossRef]

Baños, A.

A. Baños, Dipole Radiation in the Presence of a Conducting Half-Space (Pergamon, London, 1966).

Boas, D. A.

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

D. A. Boas, M. A. O'Leary, B. Chance, and A. G. Yodh, Proc. Natl. Acad. Sci. USA 91, 4887 (1994).
[CrossRef]

Chance, B.

Clark, N.

Fender, J. S.

Feng, S.

Feshbach, H.

P. M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953), Vols. I and II.

Jiang, H. B.

Kak, A. C.

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

Matson, C. L.

McMackin, L.

Morse, P. M.

P. M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953), Vols. I and II.

O'Leary, M. A.

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

D. A. Boas, M. A. O'Leary, B. Chance, and A. G. Yodh, Proc. Natl. Acad. Sci. USA 91, 4887 (1994).
[CrossRef]

Osterberg, U. L.

Patterson, M. S.

Paulsen, K. D.

Slaney, M.

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

Yodh, A. G.

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

D. A. Boas, M. A. O'Leary, B. Chance, and A. G. Yodh, Proc. Natl. Acad. Sci. USA 91, 4887 (1994).
[CrossRef]

Zeng, F.

Appl. Opt. (3)

Opt. Express (1)

Opt. Lett. (1)

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

D. A. Boas, M. A. O'Leary, B. Chance, and A. G. Yodh, Proc. Natl. Acad. Sci. USA 91, 4887 (1994).
[CrossRef]

Other (3)

A. Baños, Dipole Radiation in the Presence of a Conducting Half-Space (Pergamon, London, 1966).

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

P. M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953), Vols. I and II.

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Figures (1)

Fig. 1
Fig. 1

Geometry for the DT forward problem solution. The source is situated along the z axis θs=π, allowing azimuthal symmetry to be exploited. A spherical inhomogeneity is situated at the origin, and the radial distances for the source and the detector are indicated.4

Equations (7)

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uBx, y, z0=18π2expixξ+iyη-iz0γiγ×Ouγξ, η, -γidξdη,
UBξ, η, z0=12exp-iz0γiγOuγξ, η, -γi,
ΦSCr=l=0Alhl1krYl0θ, ϕ,  ra,
ΦSCr=l=02l+14π1/2Al2πil02πdβBexpik·r×Plcos αsin αdα,
ΦSCr=l=02l+14π1/2Al2πkil+1×02πdβ0exp-γz+ixλcos β+yλsin βγ×Pliγkλdλ.
ΦSCr=l=02l+14π1/2Al2πkil+1Pliγk×exp-γz+iξx+ηyγdξdη.
USCξ, η; z0=12exp-iγiz0γl=0π2l+11/2×2Alkil+1Pliγkexp-γrz0.

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