Abstract

We present a solution to this problem in the form of a fast algorithm with computational complexity that scales as N log N, where N is the number of spatial measurements of the scattered field.

© 2002 Optical Society of America

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References

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  1. S. Arridge, Inv. Prob. 15, R41 (1999).
    [CrossRef]
  2. M. Franceschini, K. Moesta, S. Fantini, G. Gaida, E. Gratton, H. Jess, W. Mantulin, M. Seeber, P. Schlag, and M. Kaschke, Proc. Natl. Acad. Sci. USA 94, 6468 (1997).
    [CrossRef]
  3. V. Ntziachristos, A. Yodh, M. Schnall, and B. Chance, Proc. Natl. Acad. Sci. USA 97, 2769 (1999).
  4. V. Markel and J. Schotland, Phys. Rev. E 64, 035601(R) (2001).
    [CrossRef]
  5. V. Markel and J. Schotland, J. Opt. Soc. Am. A 19, 558 (2002).
    [CrossRef]

2002 (1)

2001 (1)

V. Markel and J. Schotland, Phys. Rev. E 64, 035601(R) (2001).
[CrossRef]

1999 (2)

V. Ntziachristos, A. Yodh, M. Schnall, and B. Chance, Proc. Natl. Acad. Sci. USA 97, 2769 (1999).

S. Arridge, Inv. Prob. 15, R41 (1999).
[CrossRef]

1997 (1)

M. Franceschini, K. Moesta, S. Fantini, G. Gaida, E. Gratton, H. Jess, W. Mantulin, M. Seeber, P. Schlag, and M. Kaschke, Proc. Natl. Acad. Sci. USA 94, 6468 (1997).
[CrossRef]

Arridge, S.

S. Arridge, Inv. Prob. 15, R41 (1999).
[CrossRef]

Chance, B.

V. Ntziachristos, A. Yodh, M. Schnall, and B. Chance, Proc. Natl. Acad. Sci. USA 97, 2769 (1999).

Fantini, S.

M. Franceschini, K. Moesta, S. Fantini, G. Gaida, E. Gratton, H. Jess, W. Mantulin, M. Seeber, P. Schlag, and M. Kaschke, Proc. Natl. Acad. Sci. USA 94, 6468 (1997).
[CrossRef]

Franceschini, M.

M. Franceschini, K. Moesta, S. Fantini, G. Gaida, E. Gratton, H. Jess, W. Mantulin, M. Seeber, P. Schlag, and M. Kaschke, Proc. Natl. Acad. Sci. USA 94, 6468 (1997).
[CrossRef]

Gaida, G.

M. Franceschini, K. Moesta, S. Fantini, G. Gaida, E. Gratton, H. Jess, W. Mantulin, M. Seeber, P. Schlag, and M. Kaschke, Proc. Natl. Acad. Sci. USA 94, 6468 (1997).
[CrossRef]

Gratton, E.

M. Franceschini, K. Moesta, S. Fantini, G. Gaida, E. Gratton, H. Jess, W. Mantulin, M. Seeber, P. Schlag, and M. Kaschke, Proc. Natl. Acad. Sci. USA 94, 6468 (1997).
[CrossRef]

Jess, H.

M. Franceschini, K. Moesta, S. Fantini, G. Gaida, E. Gratton, H. Jess, W. Mantulin, M. Seeber, P. Schlag, and M. Kaschke, Proc. Natl. Acad. Sci. USA 94, 6468 (1997).
[CrossRef]

Kaschke, M.

M. Franceschini, K. Moesta, S. Fantini, G. Gaida, E. Gratton, H. Jess, W. Mantulin, M. Seeber, P. Schlag, and M. Kaschke, Proc. Natl. Acad. Sci. USA 94, 6468 (1997).
[CrossRef]

Mantulin, W.

M. Franceschini, K. Moesta, S. Fantini, G. Gaida, E. Gratton, H. Jess, W. Mantulin, M. Seeber, P. Schlag, and M. Kaschke, Proc. Natl. Acad. Sci. USA 94, 6468 (1997).
[CrossRef]

Markel, V.

V. Markel and J. Schotland, J. Opt. Soc. Am. A 19, 558 (2002).
[CrossRef]

V. Markel and J. Schotland, Phys. Rev. E 64, 035601(R) (2001).
[CrossRef]

Moesta, K.

M. Franceschini, K. Moesta, S. Fantini, G. Gaida, E. Gratton, H. Jess, W. Mantulin, M. Seeber, P. Schlag, and M. Kaschke, Proc. Natl. Acad. Sci. USA 94, 6468 (1997).
[CrossRef]

Ntziachristos, V.

V. Ntziachristos, A. Yodh, M. Schnall, and B. Chance, Proc. Natl. Acad. Sci. USA 97, 2769 (1999).

Schlag, P.

M. Franceschini, K. Moesta, S. Fantini, G. Gaida, E. Gratton, H. Jess, W. Mantulin, M. Seeber, P. Schlag, and M. Kaschke, Proc. Natl. Acad. Sci. USA 94, 6468 (1997).
[CrossRef]

Schnall, M.

V. Ntziachristos, A. Yodh, M. Schnall, and B. Chance, Proc. Natl. Acad. Sci. USA 97, 2769 (1999).

Schotland, J.

V. Markel and J. Schotland, J. Opt. Soc. Am. A 19, 558 (2002).
[CrossRef]

V. Markel and J. Schotland, Phys. Rev. E 64, 035601(R) (2001).
[CrossRef]

Seeber, M.

M. Franceschini, K. Moesta, S. Fantini, G. Gaida, E. Gratton, H. Jess, W. Mantulin, M. Seeber, P. Schlag, and M. Kaschke, Proc. Natl. Acad. Sci. USA 94, 6468 (1997).
[CrossRef]

Yodh, A.

V. Ntziachristos, A. Yodh, M. Schnall, and B. Chance, Proc. Natl. Acad. Sci. USA 97, 2769 (1999).

Inv. Prob. (1)

S. Arridge, Inv. Prob. 15, R41 (1999).
[CrossRef]

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

Phys. Rev. E (1)

V. Markel and J. Schotland, Phys. Rev. E 64, 035601(R) (2001).
[CrossRef]

Proc. Natl. Acad. Sci. USA (2)

M. Franceschini, K. Moesta, S. Fantini, G. Gaida, E. Gratton, H. Jess, W. Mantulin, M. Seeber, P. Schlag, and M. Kaschke, Proc. Natl. Acad. Sci. USA 94, 6468 (1997).
[CrossRef]

V. Ntziachristos, A. Yodh, M. Schnall, and B. Chance, Proc. Natl. Acad. Sci. USA 97, 2769 (1999).

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Figures (2)

Fig. 1
Fig. 1

Illustration of the geometries corresponding to the (a) axial, (b) paraxial, and (c) complete-data problems. Also illustrated in (d) is the relationship between the window size, W, and the linear dimension of the field of view, L.

Fig. 2
Fig. 2

Tomographic images of the slab at different depths z and window sizes W. The images are calibrated from -1 (blue) to 1 (red) all on the same linear color scale. Here red corresponds to the maximum value of δα obtained for a point absorber located in the center of the field of view at a particular depth.

Equations (9)

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

ϕρ1,ρ2=d3rΓρ1,ρ2;rδαr.
Γρ1,ρ2;r=12π4d2q1d2q2κq1,q2;z×exp-iq1-q2·r+iq1·ρ1-q2·ρ2,
κq1,q2;z=sinhQq1L-zsinhQq2zsinhQq1LsinhQq2L,
ψnρ=d3rmcnmΓρ,ρ+δρm;rδαr.
ψˆnω;q=0LdzpKnω,z;q-pδα˜q-p,z,
Knω,z;q=d2q2πa2mcnmκq+q,q;z×expiq·δρm,
δα˜q-p,z=ω,ωn,mKn*ω,z;q-p×Mnm-1ω,ω;qψ^mω,q,
Mnmω,ω;q=0LdzpKnω,z;q-p×Km*ω,z;q-p.
δαr=FBZd2q2π2exp-iq·rω,ωn,mp×expip·rKn*ω,z;q-p×Mnm-1ω,ω;qψˆmω,q,

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