Abstract

The time-resolved propagation of spatial frequencies in turbid media is investigated. We discuss the relevant information content in terms of the spatial Fourier component of the propagating pulse. We present a method to record and analyze the time-gated spatial frequency response of highly scattering media. We demonstrate that high spatial frequency information appears in the early time-gated signal, whereas low frequencies persist for longer times.

© 2008 Optical Society of America

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References

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2007

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2003

2001

2000

F. Martelli, M. Bassani, L. Alianelli, L. Zangheri, and G. Zaccanti, Phys. Med. Biol. 45, 1359 (2000).
[CrossRef] [PubMed]

1998

N. Dognitz and G. Wagnieres, Lasers Med. Sci. 13, 55 (1998).
[CrossRef]

1997

M. A. A. Neil, R. Juskaitis, and T. Wilson, Opt. Lett. 22, 019057 (1997).
[CrossRef]

1989

1984

D. M. Jameson, E. Gratton, and R. D. Hall, Appl. Spectrosc. Rev. 20, 55 (1984).
[CrossRef]

Alianelli, L.

F. Martelli, M. Bassani, L. Alianelli, L. Zangheri, and G. Zaccanti, Phys. Med. Biol. 45, 1359 (2000).
[CrossRef] [PubMed]

Andersson-Engels, S.

Bangerth, W.

Bassani, M.

F. Martelli, M. Bassani, L. Alianelli, L. Zangheri, and G. Zaccanti, Phys. Med. Biol. 45, 1359 (2000).
[CrossRef] [PubMed]

Bassi, A.

Bevilacqua, F.

Carlson, A. B.

A. B. Carlson, Communication Systems (McGraw-Hill, 1988).

Chance, B.

Cubeddu, R.

Cuccia, D. J.

Dam, J. S.

D'Andrea, C.

Dognitz, N.

N. Dognitz and G. Wagnieres, Lasers Med. Sci. 13, 55 (1998).
[CrossRef]

Durkin, A. J.

Farina, A.

Gratton, E.

D. M. Jameson, E. Gratton, and R. D. Hall, Appl. Spectrosc. Rev. 20, 55 (1984).
[CrossRef]

Hall, R. D.

D. M. Jameson, E. Gratton, and R. D. Hall, Appl. Spectrosc. Rev. 20, 55 (1984).
[CrossRef]

Jameson, D. M.

D. M. Jameson, E. Gratton, and R. D. Hall, Appl. Spectrosc. Rev. 20, 55 (1984).
[CrossRef]

Joshi, A.

Juskaitis, R.

M. A. A. Neil, R. Juskaitis, and T. Wilson, Opt. Lett. 22, 019057 (1997).
[CrossRef]

Markel, V.

Martelli, F.

F. Martelli, M. Bassani, L. Alianelli, L. Zangheri, and G. Zaccanti, Phys. Med. Biol. 45, 1359 (2000).
[CrossRef] [PubMed]

Neil, M. A. A.

M. A. A. Neil, R. Juskaitis, and T. Wilson, Opt. Lett. 22, 019057 (1997).
[CrossRef]

Patterson, M. S.

Pifferi, A.

Schotland, J. C.

Sevick-Muraca, E. M.

Swartling, J.

Tromberg, B. J.

Valentini, G.

Wagnieres, G.

N. Dognitz and G. Wagnieres, Lasers Med. Sci. 13, 55 (1998).
[CrossRef]

Wilson, B. C.

Wilson, T.

M. A. A. Neil, R. Juskaitis, and T. Wilson, Opt. Lett. 22, 019057 (1997).
[CrossRef]

Zaccanti, G.

F. Martelli, M. Bassani, L. Alianelli, L. Zangheri, and G. Zaccanti, Phys. Med. Biol. 45, 1359 (2000).
[CrossRef] [PubMed]

Zangheri, L.

F. Martelli, M. Bassani, L. Alianelli, L. Zangheri, and G. Zaccanti, Phys. Med. Biol. 45, 1359 (2000).
[CrossRef] [PubMed]

Appl. Opt.

Appl. Spectrosc. Rev.

D. M. Jameson, E. Gratton, and R. D. Hall, Appl. Spectrosc. Rev. 20, 55 (1984).
[CrossRef]

J. Opt. Soc. Am. A

Lasers Med. Sci.

N. Dognitz and G. Wagnieres, Lasers Med. Sci. 13, 55 (1998).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Med. Biol.

F. Martelli, M. Bassani, L. Alianelli, L. Zangheri, and G. Zaccanti, Phys. Med. Biol. 45, 1359 (2000).
[CrossRef] [PubMed]

Other

A. B. Carlson, Communication Systems (McGraw-Hill, 1988).

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Figures (3)

Fig. 1
Fig. 1

Experimental setup.

Fig. 2
Fig. 2

Measured Fourier components A k x as a function of time and spatial frequency (top). Error Δ A k x between the theory and the experiment (bottom). The theoretical curve is not shown.

Fig. 3
Fig. 3

(a) Experimental and theoretical (curves) normalized Fourier components as a function of spatial frequency at three temporal gates; the circles represent the steady-state value, calculated by integrating over all times. (b) Comparison between experiments and theory as a function of time at different spatial frequencies.

Equations (6)

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J in ( ρ 1 ) = 1 + exp [ i k ρ 1 ] ,
J out ( ρ 2 , t ) = A 0 ( d , t ) + A k ( d , t ) exp [ i k ρ 2 ] ,
1 c ϕ t = ( D 2 + μ a ) ϕ ,
ϕ ̃ = A k ( z , t ) = c exp ( z 2 4 D c t D ( k k ) c t μ a c t ) ( 4 π D c t ) 1 2 .
lim t d d t ln ( ϕ ̃ ) = c [ μ a + D ( k x 2 + k y 2 ) ] .
A k x ( ρ 2 , t ) = 2 n p p = 0 n p 1 J out p ( ρ 2 , t ) exp [ i ( 2 π p n p ) ] .

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