Abstract

The effects of the approximation D=0 that is often used in frequency-resolved optical diffusion imaging are examined. It is shown that this approximation can affect the performance of integral-equation-based approaches to optical diffusion imaging, such as the Born iterative method and the distorted Born iterative method. The approximation introduces errors into the calculation of data used in simulations, which can lead to misleading evaluations of reconstruction algorithms. Numerical calculations show the magnitude of these effects and the appearance of artifacts in reconstructed images when conventional inversion algorithms are applied to more accurately calculated data.

© 1998 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
  4. J. J. Duderstadt and L. J. Hamilton, Nuclear Reactor Analysis (Wiley, New York, 1976).
  5. U. Tautenhahn, Inverse Probl. 13, 1427 (1997).
    [CrossRef]
  6. M. Schweige, S. R. Arridge, M. Hiraoka, M. Fairbank, and D. T. Delpy, Proc. SPIE 1888, 179 (1993).
    [CrossRef]
  7. M. O’Leary, D. Boas, B. Chance, and A. Yodh, Opt. Lett. 20, 426 (1995).
    [CrossRef] [PubMed]
  8. J. C. Ye, K. J. Webb, T. J. Downar, and R. P. Millane, Proc. SPIE 3171, 118 (1997).
    [CrossRef]
  9. A. W. Naylor and G. R. Sell, Linear Operator Theory in Engineering and Science, 2nd ed. (Springer-Verlag, Berlin, 1982).
    [CrossRef]
  10. W. Chew, Waves and Fields in Inhomogeneous Media (Van Nostrand Reinhold, New York, 1990).
  11. N. Joachimowicz, C. Pichot, and J. Hugonin, IEEE Trans. Antennas Propag. 39, 1742 (1991).
    [CrossRef]
  12. J. E. Dennis, Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Prentice-Hall, Englewood Cliffs, N.J., 1983).

1997 (3)

U. Tautenhahn, Inverse Probl. 13, 1427 (1997).
[CrossRef]

J. C. Ye, K. J. Webb, T. J. Downar, and R. P. Millane, Proc. SPIE 3171, 118 (1997).
[CrossRef]

Y. Yao, Y. Wang, Y. Pei, W. Zhu, and R. L. Barbour, J. Opt. Soc. Am. A 14, 325 (1997).
[CrossRef]

1996 (1)

1995 (1)

1993 (1)

M. Schweige, S. R. Arridge, M. Hiraoka, M. Fairbank, and D. T. Delpy, Proc. SPIE 1888, 179 (1993).
[CrossRef]

1992 (1)

T. J. Farrell, M. S. Patterson, and B. Wilson, Med. Phys. 19, 879 (1992).
[CrossRef] [PubMed]

1991 (1)

N. Joachimowicz, C. Pichot, and J. Hugonin, IEEE Trans. Antennas Propag. 39, 1742 (1991).
[CrossRef]

Arridge, S. R.

M. Schweige, S. R. Arridge, M. Hiraoka, M. Fairbank, and D. T. Delpy, Proc. SPIE 1888, 179 (1993).
[CrossRef]

Barbour, R. L.

Boas, D.

Chance, B.

Chew, W.

W. Chew, Waves and Fields in Inhomogeneous Media (Van Nostrand Reinhold, New York, 1990).

Delpy, D. T.

M. Schweige, S. R. Arridge, M. Hiraoka, M. Fairbank, and D. T. Delpy, Proc. SPIE 1888, 179 (1993).
[CrossRef]

Dennis, J. E.

J. E. Dennis, Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Prentice-Hall, Englewood Cliffs, N.J., 1983).

Downar, T. J.

J. C. Ye, K. J. Webb, T. J. Downar, and R. P. Millane, Proc. SPIE 3171, 118 (1997).
[CrossRef]

Duderstadt, J. J.

J. J. Duderstadt and L. J. Hamilton, Nuclear Reactor Analysis (Wiley, New York, 1976).

Fairbank, M.

M. Schweige, S. R. Arridge, M. Hiraoka, M. Fairbank, and D. T. Delpy, Proc. SPIE 1888, 179 (1993).
[CrossRef]

Farrell, T. J.

T. J. Farrell, M. S. Patterson, and B. Wilson, Med. Phys. 19, 879 (1992).
[CrossRef] [PubMed]

Hamilton, L. J.

J. J. Duderstadt and L. J. Hamilton, Nuclear Reactor Analysis (Wiley, New York, 1976).

Hiraoka, M.

M. Schweige, S. R. Arridge, M. Hiraoka, M. Fairbank, and D. T. Delpy, Proc. SPIE 1888, 179 (1993).
[CrossRef]

Hugonin, J.

N. Joachimowicz, C. Pichot, and J. Hugonin, IEEE Trans. Antennas Propag. 39, 1742 (1991).
[CrossRef]

Jiang, H.

Joachimowicz, N.

N. Joachimowicz, C. Pichot, and J. Hugonin, IEEE Trans. Antennas Propag. 39, 1742 (1991).
[CrossRef]

Millane, R. P.

J. C. Ye, K. J. Webb, T. J. Downar, and R. P. Millane, Proc. SPIE 3171, 118 (1997).
[CrossRef]

Naylor, A. W.

A. W. Naylor and G. R. Sell, Linear Operator Theory in Engineering and Science, 2nd ed. (Springer-Verlag, Berlin, 1982).
[CrossRef]

O’Leary, M.

Osterberg, U. L.

Patterson, M. S.

Paulsen, K. D.

Pei, Y.

Pichot, C.

N. Joachimowicz, C. Pichot, and J. Hugonin, IEEE Trans. Antennas Propag. 39, 1742 (1991).
[CrossRef]

Pogue, B. W.

Schweige, M.

M. Schweige, S. R. Arridge, M. Hiraoka, M. Fairbank, and D. T. Delpy, Proc. SPIE 1888, 179 (1993).
[CrossRef]

Sell, G. R.

A. W. Naylor and G. R. Sell, Linear Operator Theory in Engineering and Science, 2nd ed. (Springer-Verlag, Berlin, 1982).
[CrossRef]

Tautenhahn, U.

U. Tautenhahn, Inverse Probl. 13, 1427 (1997).
[CrossRef]

Wang, Y.

Webb, K. J.

J. C. Ye, K. J. Webb, T. J. Downar, and R. P. Millane, Proc. SPIE 3171, 118 (1997).
[CrossRef]

Wilson, B.

T. J. Farrell, M. S. Patterson, and B. Wilson, Med. Phys. 19, 879 (1992).
[CrossRef] [PubMed]

Yao, Y.

Ye, J. C.

J. C. Ye, K. J. Webb, T. J. Downar, and R. P. Millane, Proc. SPIE 3171, 118 (1997).
[CrossRef]

Yodh, A.

Zhu, W.

IEEE Trans. Antennas Propag. (1)

N. Joachimowicz, C. Pichot, and J. Hugonin, IEEE Trans. Antennas Propag. 39, 1742 (1991).
[CrossRef]

Inverse Probl. (1)

U. Tautenhahn, Inverse Probl. 13, 1427 (1997).
[CrossRef]

J. Opt. Soc. Am. A (2)

Med. Phys. (1)

T. J. Farrell, M. S. Patterson, and B. Wilson, Med. Phys. 19, 879 (1992).
[CrossRef] [PubMed]

Opt. Lett. (1)

Proc. SPIE (2)

M. Schweige, S. R. Arridge, M. Hiraoka, M. Fairbank, and D. T. Delpy, Proc. SPIE 1888, 179 (1993).
[CrossRef]

J. C. Ye, K. J. Webb, T. J. Downar, and R. P. Millane, Proc. SPIE 3171, 118 (1997).
[CrossRef]

Other (4)

A. W. Naylor and G. R. Sell, Linear Operator Theory in Engineering and Science, 2nd ed. (Springer-Verlag, Berlin, 1982).
[CrossRef]

W. Chew, Waves and Fields in Inhomogeneous Media (Van Nostrand Reinhold, New York, 1990).

J. J. Duderstadt and L. J. Hamilton, Nuclear Reactor Analysis (Wiley, New York, 1976).

J. E. Dennis, Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Prentice-Hall, Englewood Cliffs, N.J., 1983).

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Figures (3)

Fig. 1
Fig. 1

Arrangement of the source (0) and detectors × for the simulations. A, source used for the results shown in Figs. 2(c) and 2(d).

Fig. 2
Fig. 2

Actual absorption (a) and scattering (b) coefficients. The magnitude (c) and phase (d) of the flux on the x axis for a source at A in Fig. 1 are shown with - and without the D term and for a homogeneous background medium only (--).

Fig. 3
Fig. 3

Reconstructed absorption and scattering coefficients using data calculated without [(a), (b)] and with [(c), (d)] the D term.

Equations (8)

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

·Dϕ+-μa+iω/cϕ=-s in Ω,
Bϕ,V=ΩDϕ·V+-μa+iω/cϕVdr
B˜ϕ,ϕ=ΩDϕ·ϕ-μaϕ2+1cϕ2tdr.
·Dϕ=D2ϕ+D·ϕD2ϕ,
2ϕ+k2μa,μsϕ=-sˆ  in Ω,    ϕ=0 on Ω,
k2μa,μs=3μa+μs-μa+iω/c,sˆ=3μa+μss.
ϕr;μa,μs=ϕr;μab,μsb+Ωgr,r;μab,μsb×ϕr;μa,μsΔk2rdr
Δμar=-wcRekb r2+Δk2rImkb r2+Δk2r-μabr,  Δμsr=c3wImΔk2r-Δμar,

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