Abstract

We show that the source location problem can be solved in a scattering medium using the fluorescence lifetime and realistic a priori information. The intrinsic ill-posedness of the problem is reduced when the level of scattering increases. This work is a proof of principle demonstrating the high potential of quantitative lifetime imaging in complex media.

© 2012 Optical Society of America

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References

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  1. R. R. Chance, A. Prock, and R. Sylbey, Adv. Chem. Phys. 37, 1 (1978).
    [CrossRef]
  2. E. A. Donley and T. Plakhotnik, J. Chem. Phys. 114, 9993 (2001).
    [CrossRef]
  3. R. A. L. Vallée, N. Tomczak, L. Kuipers, G. J. Vancso, and N. F. van Hulst, Phys. Rev. Lett. 91, 038301 (2003).
    [CrossRef]
  4. L. S. Froufe-Pérez, R. Carminati, and J. J. Sáenz, Phys. Rev. A 76, 013835 (2007).
    [CrossRef]
  5. M. D. Birowosuto, S. E. Skipetrov, W. L. Vos, and A. P. Mosk, Phys. Rev. Lett. 105, 013904 (2010).
    [CrossRef]
  6. V. Krachmalnicoff, E. Castanié, Y. De Wilde, and R. Carminati, Phys. Rev. Lett. 105, 183901 (2010).
    [CrossRef]
  7. R. Sapienza, P. Bondareff, R. Pierrat, B. Habert, R. Carminati, and N. F. van Hulst, Phys. Rev. Lett. 106, 163902 (2011).
    [CrossRef]
  8. R. Pierrat and R. Carminati, Phys. Rev. A 81, 063802 (2010).
    [CrossRef]
  9. A. Cazé, R. Pierrat, and R. Carminati, Phys. Rev. A 82, 043823 (2010).
    [CrossRef]
  10. K. Suhling, P. W. French, and D. Philipps, Photochem. Photobiol. Sci. 4, 13 (2005).
    [CrossRef]
  11. P. S. Carney, V. A. Markel, and J. C. Schotland, Phys. Rev. Lett. 86, 5874 (2001).
    [CrossRef]
  12. J. C. Schotland, Opt. Lett. 35, 3309 (2010).
    [CrossRef]
  13. J. M. Wylie and J. E. Sipe, Phys. Rev. A 30, 1185 (1984).
    [CrossRef]
  14. Since Γ0 is proportional to |peg|2, the prefactor in Eq. (1) is independent on peg. The knowledge of the transition dipole is not required to solve the inverse problem.
  15. L. L. Foldy, Phys. Rev. 67, 107 (1945).
    [CrossRef]
  16. M. Lax, Rev. Mod. Phys. 23, 287 (1951).
    [CrossRef]

2011 (1)

R. Sapienza, P. Bondareff, R. Pierrat, B. Habert, R. Carminati, and N. F. van Hulst, Phys. Rev. Lett. 106, 163902 (2011).
[CrossRef]

2010 (5)

R. Pierrat and R. Carminati, Phys. Rev. A 81, 063802 (2010).
[CrossRef]

A. Cazé, R. Pierrat, and R. Carminati, Phys. Rev. A 82, 043823 (2010).
[CrossRef]

M. D. Birowosuto, S. E. Skipetrov, W. L. Vos, and A. P. Mosk, Phys. Rev. Lett. 105, 013904 (2010).
[CrossRef]

V. Krachmalnicoff, E. Castanié, Y. De Wilde, and R. Carminati, Phys. Rev. Lett. 105, 183901 (2010).
[CrossRef]

J. C. Schotland, Opt. Lett. 35, 3309 (2010).
[CrossRef]

2007 (1)

L. S. Froufe-Pérez, R. Carminati, and J. J. Sáenz, Phys. Rev. A 76, 013835 (2007).
[CrossRef]

2005 (1)

K. Suhling, P. W. French, and D. Philipps, Photochem. Photobiol. Sci. 4, 13 (2005).
[CrossRef]

2003 (1)

R. A. L. Vallée, N. Tomczak, L. Kuipers, G. J. Vancso, and N. F. van Hulst, Phys. Rev. Lett. 91, 038301 (2003).
[CrossRef]

2001 (2)

E. A. Donley and T. Plakhotnik, J. Chem. Phys. 114, 9993 (2001).
[CrossRef]

P. S. Carney, V. A. Markel, and J. C. Schotland, Phys. Rev. Lett. 86, 5874 (2001).
[CrossRef]

1984 (1)

J. M. Wylie and J. E. Sipe, Phys. Rev. A 30, 1185 (1984).
[CrossRef]

1978 (1)

R. R. Chance, A. Prock, and R. Sylbey, Adv. Chem. Phys. 37, 1 (1978).
[CrossRef]

1951 (1)

M. Lax, Rev. Mod. Phys. 23, 287 (1951).
[CrossRef]

1945 (1)

L. L. Foldy, Phys. Rev. 67, 107 (1945).
[CrossRef]

Birowosuto, M. D.

M. D. Birowosuto, S. E. Skipetrov, W. L. Vos, and A. P. Mosk, Phys. Rev. Lett. 105, 013904 (2010).
[CrossRef]

Bondareff, P.

R. Sapienza, P. Bondareff, R. Pierrat, B. Habert, R. Carminati, and N. F. van Hulst, Phys. Rev. Lett. 106, 163902 (2011).
[CrossRef]

Carminati, R.

R. Sapienza, P. Bondareff, R. Pierrat, B. Habert, R. Carminati, and N. F. van Hulst, Phys. Rev. Lett. 106, 163902 (2011).
[CrossRef]

V. Krachmalnicoff, E. Castanié, Y. De Wilde, and R. Carminati, Phys. Rev. Lett. 105, 183901 (2010).
[CrossRef]

R. Pierrat and R. Carminati, Phys. Rev. A 81, 063802 (2010).
[CrossRef]

A. Cazé, R. Pierrat, and R. Carminati, Phys. Rev. A 82, 043823 (2010).
[CrossRef]

L. S. Froufe-Pérez, R. Carminati, and J. J. Sáenz, Phys. Rev. A 76, 013835 (2007).
[CrossRef]

Carney, P. S.

P. S. Carney, V. A. Markel, and J. C. Schotland, Phys. Rev. Lett. 86, 5874 (2001).
[CrossRef]

Castanié, E.

V. Krachmalnicoff, E. Castanié, Y. De Wilde, and R. Carminati, Phys. Rev. Lett. 105, 183901 (2010).
[CrossRef]

Cazé, A.

A. Cazé, R. Pierrat, and R. Carminati, Phys. Rev. A 82, 043823 (2010).
[CrossRef]

Chance, R. R.

R. R. Chance, A. Prock, and R. Sylbey, Adv. Chem. Phys. 37, 1 (1978).
[CrossRef]

De Wilde, Y.

V. Krachmalnicoff, E. Castanié, Y. De Wilde, and R. Carminati, Phys. Rev. Lett. 105, 183901 (2010).
[CrossRef]

Donley, E. A.

E. A. Donley and T. Plakhotnik, J. Chem. Phys. 114, 9993 (2001).
[CrossRef]

Foldy, L. L.

L. L. Foldy, Phys. Rev. 67, 107 (1945).
[CrossRef]

French, P. W.

K. Suhling, P. W. French, and D. Philipps, Photochem. Photobiol. Sci. 4, 13 (2005).
[CrossRef]

Froufe-Pérez, L. S.

L. S. Froufe-Pérez, R. Carminati, and J. J. Sáenz, Phys. Rev. A 76, 013835 (2007).
[CrossRef]

Habert, B.

R. Sapienza, P. Bondareff, R. Pierrat, B. Habert, R. Carminati, and N. F. van Hulst, Phys. Rev. Lett. 106, 163902 (2011).
[CrossRef]

Krachmalnicoff, V.

V. Krachmalnicoff, E. Castanié, Y. De Wilde, and R. Carminati, Phys. Rev. Lett. 105, 183901 (2010).
[CrossRef]

Kuipers, L.

R. A. L. Vallée, N. Tomczak, L. Kuipers, G. J. Vancso, and N. F. van Hulst, Phys. Rev. Lett. 91, 038301 (2003).
[CrossRef]

Lax, M.

M. Lax, Rev. Mod. Phys. 23, 287 (1951).
[CrossRef]

Markel, V. A.

P. S. Carney, V. A. Markel, and J. C. Schotland, Phys. Rev. Lett. 86, 5874 (2001).
[CrossRef]

Mosk, A. P.

M. D. Birowosuto, S. E. Skipetrov, W. L. Vos, and A. P. Mosk, Phys. Rev. Lett. 105, 013904 (2010).
[CrossRef]

Philipps, D.

K. Suhling, P. W. French, and D. Philipps, Photochem. Photobiol. Sci. 4, 13 (2005).
[CrossRef]

Pierrat, R.

R. Sapienza, P. Bondareff, R. Pierrat, B. Habert, R. Carminati, and N. F. van Hulst, Phys. Rev. Lett. 106, 163902 (2011).
[CrossRef]

A. Cazé, R. Pierrat, and R. Carminati, Phys. Rev. A 82, 043823 (2010).
[CrossRef]

R. Pierrat and R. Carminati, Phys. Rev. A 81, 063802 (2010).
[CrossRef]

Plakhotnik, T.

E. A. Donley and T. Plakhotnik, J. Chem. Phys. 114, 9993 (2001).
[CrossRef]

Prock, A.

R. R. Chance, A. Prock, and R. Sylbey, Adv. Chem. Phys. 37, 1 (1978).
[CrossRef]

Sáenz, J. J.

L. S. Froufe-Pérez, R. Carminati, and J. J. Sáenz, Phys. Rev. A 76, 013835 (2007).
[CrossRef]

Sapienza, R.

R. Sapienza, P. Bondareff, R. Pierrat, B. Habert, R. Carminati, and N. F. van Hulst, Phys. Rev. Lett. 106, 163902 (2011).
[CrossRef]

Schotland, J. C.

J. C. Schotland, Opt. Lett. 35, 3309 (2010).
[CrossRef]

P. S. Carney, V. A. Markel, and J. C. Schotland, Phys. Rev. Lett. 86, 5874 (2001).
[CrossRef]

Sipe, J. E.

J. M. Wylie and J. E. Sipe, Phys. Rev. A 30, 1185 (1984).
[CrossRef]

Skipetrov, S. E.

M. D. Birowosuto, S. E. Skipetrov, W. L. Vos, and A. P. Mosk, Phys. Rev. Lett. 105, 013904 (2010).
[CrossRef]

Suhling, K.

K. Suhling, P. W. French, and D. Philipps, Photochem. Photobiol. Sci. 4, 13 (2005).
[CrossRef]

Sylbey, R.

R. R. Chance, A. Prock, and R. Sylbey, Adv. Chem. Phys. 37, 1 (1978).
[CrossRef]

Tomczak, N.

R. A. L. Vallée, N. Tomczak, L. Kuipers, G. J. Vancso, and N. F. van Hulst, Phys. Rev. Lett. 91, 038301 (2003).
[CrossRef]

Vallée, R. A. L.

R. A. L. Vallée, N. Tomczak, L. Kuipers, G. J. Vancso, and N. F. van Hulst, Phys. Rev. Lett. 91, 038301 (2003).
[CrossRef]

van Hulst, N. F.

R. Sapienza, P. Bondareff, R. Pierrat, B. Habert, R. Carminati, and N. F. van Hulst, Phys. Rev. Lett. 106, 163902 (2011).
[CrossRef]

R. A. L. Vallée, N. Tomczak, L. Kuipers, G. J. Vancso, and N. F. van Hulst, Phys. Rev. Lett. 91, 038301 (2003).
[CrossRef]

Vancso, G. J.

R. A. L. Vallée, N. Tomczak, L. Kuipers, G. J. Vancso, and N. F. van Hulst, Phys. Rev. Lett. 91, 038301 (2003).
[CrossRef]

Vos, W. L.

M. D. Birowosuto, S. E. Skipetrov, W. L. Vos, and A. P. Mosk, Phys. Rev. Lett. 105, 013904 (2010).
[CrossRef]

Wylie, J. M.

J. M. Wylie and J. E. Sipe, Phys. Rev. A 30, 1185 (1984).
[CrossRef]

Adv. Chem. Phys. (1)

R. R. Chance, A. Prock, and R. Sylbey, Adv. Chem. Phys. 37, 1 (1978).
[CrossRef]

J. Chem. Phys. (1)

E. A. Donley and T. Plakhotnik, J. Chem. Phys. 114, 9993 (2001).
[CrossRef]

Opt. Lett. (1)

Photochem. Photobiol. Sci. (1)

K. Suhling, P. W. French, and D. Philipps, Photochem. Photobiol. Sci. 4, 13 (2005).
[CrossRef]

Phys. Rev. (1)

L. L. Foldy, Phys. Rev. 67, 107 (1945).
[CrossRef]

Phys. Rev. A (4)

J. M. Wylie and J. E. Sipe, Phys. Rev. A 30, 1185 (1984).
[CrossRef]

R. Pierrat and R. Carminati, Phys. Rev. A 81, 063802 (2010).
[CrossRef]

A. Cazé, R. Pierrat, and R. Carminati, Phys. Rev. A 82, 043823 (2010).
[CrossRef]

L. S. Froufe-Pérez, R. Carminati, and J. J. Sáenz, Phys. Rev. A 76, 013835 (2007).
[CrossRef]

Phys. Rev. Lett. (5)

M. D. Birowosuto, S. E. Skipetrov, W. L. Vos, and A. P. Mosk, Phys. Rev. Lett. 105, 013904 (2010).
[CrossRef]

V. Krachmalnicoff, E. Castanié, Y. De Wilde, and R. Carminati, Phys. Rev. Lett. 105, 183901 (2010).
[CrossRef]

R. Sapienza, P. Bondareff, R. Pierrat, B. Habert, R. Carminati, and N. F. van Hulst, Phys. Rev. Lett. 106, 163902 (2011).
[CrossRef]

R. A. L. Vallée, N. Tomczak, L. Kuipers, G. J. Vancso, and N. F. van Hulst, Phys. Rev. Lett. 91, 038301 (2003).
[CrossRef]

P. S. Carney, V. A. Markel, and J. C. Schotland, Phys. Rev. Lett. 86, 5874 (2001).
[CrossRef]

Rev. Mod. Phys. (1)

M. Lax, Rev. Mod. Phys. 23, 287 (1951).
[CrossRef]

Other (1)

Since Γ0 is proportional to |peg|2, the prefactor in Eq. (1) is independent on peg. The knowledge of the transition dipole is not required to solve the inverse problem.

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Figures (3)

Fig. 1.
Fig. 1.

Top row: maps of Im[Es(r0,ω)] in one realization of the disordered medium with 63 scatterers indicated by dots. From left to right: 1/(ks)=0.28, 0.15, and 0.06 (s=0.5, 1, and 2.4 μm). Bottom row: cross sections at x=1.7μm. Size of domain: 2μm×2μm.

Fig. 2.
Fig. 2.

Top row: reconstructions inside a 1μm×1μm DOI (black square) in the same disordered medium as in Fig. 1, for three scattering strength regimes. Left: (ks)-1=0.22-0.28, (ks)-1=0.13-0.17, and (ks)-1=0.06-0.08. Two-frequency data are used for the reconstruction. Bottom row: residuals along the y directions.

Fig. 3.
Fig. 3.

Number of solutions with the same decay rate as r0 scans the medium. Left column: (ks)-1=0.20-0.25. Right column: (ks)-1=0.05-0.06. Top row: two-frequency data without noise. Middle row: two-frequency data with 8% noise. Bottom row: six-frequency data with 8% noise.

Equations (4)

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

Γ(r0,ω)-Γ0Γ0=2μ0ω2|peg|2Γ0Im[Gs(r0,r0,ω)].
Es(r,ω)=k2jG0(r,rj,ω)α(ω)Eexc(rj,ω),
Eexc(rj,ω)=Einc(rj,ω)+k2mjG0(rj,rm,ω)α(ω)Eexc(rm,ω),
Γ(x,y,ωi)=d(ωi)i=1,2,.

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