Abstract

We consider the image reconstruction problem for optical tomography with structured illumination. A fast image reconstruction algorithm is proposed that reduces the required number of measurements of the optical field compared to methods that utilize point-source illumination. The results are illustrated with numerical simulations.

© 2009 Optical Society of America

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References

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  1. S. R. Arridge, Inverse Probl. 15, R41 (1999).
    [CrossRef]
  2. R. Schulz, J. Ripoll, and V. Ntziachristos, Opt. Lett. 28, 1701 (2003).
    [CrossRef] [PubMed]
  3. G. Turner, G. Zacharakis, A. Soubret, J. Ripoll, and V. Ntziachristos, Opt. Lett. 30, 409 (2005).
    [CrossRef] [PubMed]
  4. Z.-M. Wang, G. Y. Panasyuk, V. A. Markel, and J. C. Schotland, Opt. Lett. 30, 3338 (2005).
    [CrossRef]
  5. V. A. Markel and J. C. Schotland, Appl. Phys. Lett. 81, 1180 (2002).
    [CrossRef]
  6. V. A. Markel and J. C. Schotland, Phys. Rev. E 70, 056616 (2004).
    [CrossRef]
  7. S. D. Konecky, G. Y. Panasyuk, K. Lee, V. Markel, A. G. Yodh, and J. C. Schotland, Opt. Express 16, 5049 (2008).
    [CrossRef]
  8. D. Cuccia, F. Bevilacqua, A. Durkin, and B. Tromberg, Opt. Lett. 30, 1354 (2005).
    [CrossRef] [PubMed]
  9. The FBZ is defined to be [−π/h,π/h]×[−π/h,π/h], where h is the spacing of the detector lattice.
  10. A. R. Fisher, A. J. Schissler, and J. C. Schotland, Phys. Rev. E 76, 036604 (2007).
    [CrossRef]
  11. V. A. Markel, V. Mital, and J. C. Schotland, J. Opt. Soc. Am. A 20, 890 (2003).
    [CrossRef]

2008 (1)

S. D. Konecky, G. Y. Panasyuk, K. Lee, V. Markel, A. G. Yodh, and J. C. Schotland, Opt. Express 16, 5049 (2008).
[CrossRef]

2007 (1)

A. R. Fisher, A. J. Schissler, and J. C. Schotland, Phys. Rev. E 76, 036604 (2007).
[CrossRef]

2005 (3)

2004 (1)

V. A. Markel and J. C. Schotland, Phys. Rev. E 70, 056616 (2004).
[CrossRef]

2003 (2)

2002 (1)

V. A. Markel and J. C. Schotland, Appl. Phys. Lett. 81, 1180 (2002).
[CrossRef]

1999 (1)

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

Arridge, S. R.

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

Bevilacqua, F.

Cuccia, D.

Durkin, A.

Fisher, A. R.

A. R. Fisher, A. J. Schissler, and J. C. Schotland, Phys. Rev. E 76, 036604 (2007).
[CrossRef]

Konecky, S. D.

S. D. Konecky, G. Y. Panasyuk, K. Lee, V. Markel, A. G. Yodh, and J. C. Schotland, Opt. Express 16, 5049 (2008).
[CrossRef]

Lee, K.

S. D. Konecky, G. Y. Panasyuk, K. Lee, V. Markel, A. G. Yodh, and J. C. Schotland, Opt. Express 16, 5049 (2008).
[CrossRef]

Markel, V.

S. D. Konecky, G. Y. Panasyuk, K. Lee, V. Markel, A. G. Yodh, and J. C. Schotland, Opt. Express 16, 5049 (2008).
[CrossRef]

Markel, V. A.

Mital, V.

Ntziachristos, V.

Panasyuk, G. Y.

S. D. Konecky, G. Y. Panasyuk, K. Lee, V. Markel, A. G. Yodh, and J. C. Schotland, Opt. Express 16, 5049 (2008).
[CrossRef]

Z.-M. Wang, G. Y. Panasyuk, V. A. Markel, and J. C. Schotland, Opt. Lett. 30, 3338 (2005).
[CrossRef]

Ripoll, J.

Schissler, A. J.

A. R. Fisher, A. J. Schissler, and J. C. Schotland, Phys. Rev. E 76, 036604 (2007).
[CrossRef]

Schotland, J. C.

S. D. Konecky, G. Y. Panasyuk, K. Lee, V. Markel, A. G. Yodh, and J. C. Schotland, Opt. Express 16, 5049 (2008).
[CrossRef]

A. R. Fisher, A. J. Schissler, and J. C. Schotland, Phys. Rev. E 76, 036604 (2007).
[CrossRef]

Z.-M. Wang, G. Y. Panasyuk, V. A. Markel, and J. C. Schotland, Opt. Lett. 30, 3338 (2005).
[CrossRef]

V. A. Markel and J. C. Schotland, Phys. Rev. E 70, 056616 (2004).
[CrossRef]

V. A. Markel, V. Mital, and J. C. Schotland, J. Opt. Soc. Am. A 20, 890 (2003).
[CrossRef]

V. A. Markel and J. C. Schotland, Appl. Phys. Lett. 81, 1180 (2002).
[CrossRef]

Schulz, R.

Soubret, A.

Tromberg, B.

Turner, G.

Wang, Z.-M.

Yodh, A. G.

S. D. Konecky, G. Y. Panasyuk, K. Lee, V. Markel, A. G. Yodh, and J. C. Schotland, Opt. Express 16, 5049 (2008).
[CrossRef]

Zacharakis, G.

Appl. Phys. Lett. (1)

V. A. Markel and J. C. Schotland, Appl. Phys. Lett. 81, 1180 (2002).
[CrossRef]

Inverse Probl. (1)

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

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

Opt. Express (1)

S. D. Konecky, G. Y. Panasyuk, K. Lee, V. Markel, A. G. Yodh, and J. C. Schotland, Opt. Express 16, 5049 (2008).
[CrossRef]

Opt. Lett. (4)

Phys. Rev. E (2)

V. A. Markel and J. C. Schotland, Phys. Rev. E 70, 056616 (2004).
[CrossRef]

A. R. Fisher, A. J. Schissler, and J. C. Schotland, Phys. Rev. E 76, 036604 (2007).
[CrossRef]

Other (1)

The FBZ is defined to be [−π/h,π/h]×[−π/h,π/h], where h is the spacing of the detector lattice.

Cited By

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Figures (2)

Fig. 1
Fig. 1

Reconstruction of δ α in the slab geometry. All images are plotted on the same linear color scale.

Fig. 2
Fig. 2

Reconstruction of δ α in the half-space geometry. All images are plotted on the same linear color scale.

Equations (15)

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D 2 u ( r ) + α ( r ) u ( r ) = S ( r ) ,
u ( r ) + l n ̂ u ( r ) = 0
I ( r ) = c 4 π ( 1 + l * l ) G ( r , r ) S ( r ) d 3 r ,
G ( r , r ) = G 0 ( r , r ) G 0 ( r , r ) δ α ( r ) G 0 ( r , r ) d 3 r ,
S ( r ) = S 0 ( 1 + A cos ( Q ρ + ϕ ) ) δ ( z ) ,
φ ( r ) = d 3 r d 2 ρ e i Q ρ G 0 ( r , r ) G 0 ( r ; ρ , 0 ) δ α ( r ) ,
φ ̃ ( q , z ) = ρ exp ( i q ρ ) φ ( ρ , z ) ,
G 0 ( r , r ) = d 2 q ( 2 π ) 2 e i q ( ρ ρ ) g ( z , z ; q ) .
g ( z , z ; q ) = l D sinh [ Q ( q ) ( L z z ) ] + Q ( q ) l cosh [ Q ( q ) ( L z z ) ] sinh ( Q ( q ) L ) + 2 Q ( q ) l cosh ( Q ( q ) L ) + ( Q ( q ) l ) 2 sinh ( Q ( q ) L ) ,
φ ̃ ( q , Q ) = 1 h 2 0 L g ( 0 , z ; Q ) g ( z , z d ; q ) δ α ˜ ( q + Q , z ) d z ,
ψ ( Q , q ) = 0 L K ( Q , z ; q ) δ α ˜ ( q , z ) d z ,
K ( Q , z ; q ) = 1 h 2 g ( 0 , z ; Q ) g ( z , z d ; Q q ) ,
ψ ( Q , q ) = φ ̃ ( q Q , Q ) .
δ α ( r ) = FBZ d 2 q ( 2 π ) 2 e i q ρ Q , Q K * ( Q , z ; q ) M Q Q 1 ( q ) ψ ( Q , q ) .
M Q Q ( q ) = 0 L K ( Q , z ; q ) K * ( Q , z ; q ) d z

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