Abstract

We show that the temporal broadening of a pulsed, tightly focused TEM00 beam propagating in a scattering medium can be accurately modeled as a convolution between the initial pulse profile and an effective impulse response that is given by the propagation behavior of an infinitely thin pulse in the said medium. The impulse response is obtained with a Monte Carlo (MC) analysis of the propagating photons in the impulse. Our algorithm is 2 orders of magnitude less complex than the full MC solution of the pulse propagation problem. The accuracies, however, are comparable even for scattering path lengths that are 20 times the mean free path.

© 1999 Optical Society of America

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References

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    [CrossRef]
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1999

M. van Rossum, Th. M. Nieuwenhuizen, “Multiple scattering of classical waves: microscopy, mesoscopy, and diffusion,” Rev. Mod. Phys. 71, 313–372 (1999).
[CrossRef]

1998

M. Lim, C. Saloma, “Direct signal recovery from threshold crossings,” Phys. Rev. E 58, 6759–6765 (1998).
[CrossRef]

W. Cai, B. Luo, M. Lax, R. Alfano, “Time-resolved optical backscattering model in highly scattering media,” Opt. Lett. 23, 983–985 (1998).
[CrossRef]

M. Zevallos, A. Polischuck, B. Das, F. Liu, R. Alfano, “Time-resolved photon-scattering measurements from scattering media fitted to non-Euclidean and conventional diffusion models,” Phys. Rev. E 57, 7244–7253 (1998).
[CrossRef]

C. Saloma, C. Palmes-Saloma, H. Kondoh, “Site-specific confocal fluorescence imaging of biological microstructures in turbid medium,” Phys. Med. Biol. 43, 1741–1759 (1998).
[CrossRef] [PubMed]

V. Daria, C. Blanca, O. Nakamura, S. Kawata, C. Saloma, “Image contrast enhancement for two-photon fluorescence microscopy in turbid medium,” Appl. Opt. 37, 7960–7967 (1998).
[CrossRef]

C. Blanca, C. Saloma, “Monte Carlo analysis of two-photon fluorescence imaging through a scattering medium,” Appl. Opt. 37, 8092–8102 (1998).
[CrossRef]

1997

1996

1995

1994

1990

K. Yoo, F. Liu, R. Alfano, “Time-resolved coherent and incoherent components of forward light scattering in random media,” Phys. Rev. Lett. 64, 2647–2650 (1990).
[CrossRef] [PubMed]

Alfano, R.

W. Cai, B. Luo, M. Lax, R. Alfano, “Time-resolved optical backscattering model in highly scattering media,” Opt. Lett. 23, 983–985 (1998).
[CrossRef]

M. Zevallos, A. Polischuck, B. Das, F. Liu, R. Alfano, “Time-resolved photon-scattering measurements from scattering media fitted to non-Euclidean and conventional diffusion models,” Phys. Rev. E 57, 7244–7253 (1998).
[CrossRef]

S. Demos, R. Alfano, “Optical polarization imaging,” Appl. Opt. 36, 150–155 (1997).
[CrossRef] [PubMed]

Y. Guo, P. Ho, H. Savage, D. Harris, P. Sacks, S. Schantz, F. Liu, N. Zhadin, R. Alfano, “Second-harmonic tomography of tissues,” Opt. Lett. 22, 1323–1325 (1997).
[CrossRef]

S. Gayen, R. Alfano, “Emerging optical biomedical imaging techniques,” Opt. Photon. News, 16–20 (March1996).

K. Yoo, F. Liu, R. Alfano, “Time-resolved coherent and incoherent components of forward light scattering in random media,” Phys. Rev. Lett. 64, 2647–2650 (1990).
[CrossRef] [PubMed]

Blanca, C.

Cai, W.

Cambaliza, M.

Daria, V.

Das, B.

M. Zevallos, A. Polischuck, B. Das, F. Liu, R. Alfano, “Time-resolved photon-scattering measurements from scattering media fitted to non-Euclidean and conventional diffusion models,” Phys. Rev. E 57, 7244–7253 (1998).
[CrossRef]

Demos, S.

Flannery, S.

W. Press, S. Flannery, S. Teukolsky, W. Vetterling, Numerical Recipes: The Art of Scientific Computing (Cambridge U Press, New York, 1986).

Gayen, S.

S. Gayen, R. Alfano, “Emerging optical biomedical imaging techniques,” Opt. Photon. News, 16–20 (March1996).

Guo, Y.

Harris, D.

Ho, P.

Kawata, S.

Knuttel, A.

Kondoh, H.

C. Saloma, C. Palmes-Saloma, H. Kondoh, “Site-specific confocal fluorescence imaging of biological microstructures in turbid medium,” Phys. Med. Biol. 43, 1741–1759 (1998).
[CrossRef] [PubMed]

Lax, M.

Lim, M.

M. Lim, C. Saloma, “Direct signal recovery from threshold crossings,” Phys. Rev. E 58, 6759–6765 (1998).
[CrossRef]

Liu, F.

M. Zevallos, A. Polischuck, B. Das, F. Liu, R. Alfano, “Time-resolved photon-scattering measurements from scattering media fitted to non-Euclidean and conventional diffusion models,” Phys. Rev. E 57, 7244–7253 (1998).
[CrossRef]

Y. Guo, P. Ho, H. Savage, D. Harris, P. Sacks, S. Schantz, F. Liu, N. Zhadin, R. Alfano, “Second-harmonic tomography of tissues,” Opt. Lett. 22, 1323–1325 (1997).
[CrossRef]

K. Yoo, F. Liu, R. Alfano, “Time-resolved coherent and incoherent components of forward light scattering in random media,” Phys. Rev. Lett. 64, 2647–2650 (1990).
[CrossRef] [PubMed]

Luo, B.

Nakamura, O.

Nieuwenhuizen, Th. M.

M. van Rossum, Th. M. Nieuwenhuizen, “Multiple scattering of classical waves: microscopy, mesoscopy, and diffusion,” Rev. Mod. Phys. 71, 313–372 (1999).
[CrossRef]

Palmes-Saloma, C.

C. Saloma, C. Palmes-Saloma, H. Kondoh, “Site-specific confocal fluorescence imaging of biological microstructures in turbid medium,” Phys. Med. Biol. 43, 1741–1759 (1998).
[CrossRef] [PubMed]

Polischuck, A.

M. Zevallos, A. Polischuck, B. Das, F. Liu, R. Alfano, “Time-resolved photon-scattering measurements from scattering media fitted to non-Euclidean and conventional diffusion models,” Phys. Rev. E 57, 7244–7253 (1998).
[CrossRef]

Press, W.

W. Press, S. Flannery, S. Teukolsky, W. Vetterling, Numerical Recipes: The Art of Scientific Computing (Cambridge U Press, New York, 1986).

Sacks, P.

Saloma, C.

Savage, H.

Schantz, S.

Schmitt, J.

Siegman, A.

A. Siegman, Lasers (University Science Books, Mill Valley, Calif., 1986).

Teukolsky, S.

W. Press, S. Flannery, S. Teukolsky, W. Vetterling, Numerical Recipes: The Art of Scientific Computing (Cambridge U Press, New York, 1986).

van Rossum, M.

M. van Rossum, Th. M. Nieuwenhuizen, “Multiple scattering of classical waves: microscopy, mesoscopy, and diffusion,” Rev. Mod. Phys. 71, 313–372 (1999).
[CrossRef]

Vetterling, W.

W. Press, S. Flannery, S. Teukolsky, W. Vetterling, Numerical Recipes: The Art of Scientific Computing (Cambridge U Press, New York, 1986).

Webb, W.

Xu, C.

Yadlowsky, M.

Yoo, K.

K. Yoo, F. Liu, R. Alfano, “Time-resolved coherent and incoherent components of forward light scattering in random media,” Phys. Rev. Lett. 64, 2647–2650 (1990).
[CrossRef] [PubMed]

Zevallos, M.

M. Zevallos, A. Polischuck, B. Das, F. Liu, R. Alfano, “Time-resolved photon-scattering measurements from scattering media fitted to non-Euclidean and conventional diffusion models,” Phys. Rev. E 57, 7244–7253 (1998).
[CrossRef]

Zhadin, N.

Appl. Opt.

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

Opt. Lett.

Opt. Photon. News

S. Gayen, R. Alfano, “Emerging optical biomedical imaging techniques,” Opt. Photon. News, 16–20 (March1996).

Phys. Med. Biol.

C. Saloma, C. Palmes-Saloma, H. Kondoh, “Site-specific confocal fluorescence imaging of biological microstructures in turbid medium,” Phys. Med. Biol. 43, 1741–1759 (1998).
[CrossRef] [PubMed]

Phys. Rev. E

M. Zevallos, A. Polischuck, B. Das, F. Liu, R. Alfano, “Time-resolved photon-scattering measurements from scattering media fitted to non-Euclidean and conventional diffusion models,” Phys. Rev. E 57, 7244–7253 (1998).
[CrossRef]

M. Lim, C. Saloma, “Direct signal recovery from threshold crossings,” Phys. Rev. E 58, 6759–6765 (1998).
[CrossRef]

Phys. Rev. Lett.

K. Yoo, F. Liu, R. Alfano, “Time-resolved coherent and incoherent components of forward light scattering in random media,” Phys. Rev. Lett. 64, 2647–2650 (1990).
[CrossRef] [PubMed]

Rev. Mod. Phys.

M. van Rossum, Th. M. Nieuwenhuizen, “Multiple scattering of classical waves: microscopy, mesoscopy, and diffusion,” Rev. Mod. Phys. 71, 313–372 (1999).
[CrossRef]

Other

A. Siegman, Lasers (University Science Books, Mill Valley, Calif., 1986).

W. Press, S. Flannery, S. Teukolsky, W. Vetterling, Numerical Recipes: The Art of Scientific Computing (Cambridge U Press, New York, 1986).

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Figures (5)

Fig. 1
Fig. 1

Confocal setup to simulate the temporal broadening of I o (t) in the scattering medium of refractive index n = 1.4. The profile of pulse I d (t) detected by the photodetector, PD, is obtained with the IR method. It is compared with the full MC solution. Lenses L 1 and L 2 are identical (numerical aperture = 0.7) where e n is a unit normal vector, S is a point light source, and f is the focal length.

Fig. 2
Fig. 2

Normalized I d (t) profiles obtained with the IR (dark curve) and the full MC, FMC, methods: (a) g = 0.9 (anisotropic) and (b) g = 0.0001 (isotropic). Predictions of the diffusion approximation are also presented for R = 10.

Fig. 3
Fig. 3

Error plot of IR-calculated I d (t) profiles: circle (g = 0.9) and square (g = 0.0001). The best-fit curves are described by e(R) = 2.744 × 10-6 exp (0.506R) for g = 0.9, and e(R) = 1.1892 × 10-6 R 4.967 (0.506R) for g = 0.0001.

Fig. 4
Fig. 4

Normalized I d (t) profiles of I o (t) as function of R: (a) g = 0.9 and (b) g = 0.0001. All profiles were calculated with the IR method.

Fig. 5
Fig. 5

Complexity as function of photon number N e for IR (square) and full MC (circle) methods (M = N = 200).

Equations (10)

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st=n sn-0.5Δδt-n-0.5Δ,
Iot-t0=exp-4 ln 2t-to2/τp2,
dj=-ds ln Ξ,
cos θj=2g-11+g2-1-g222g-1×1-g+2gσ2,
Nek=Ne exp-4 ln 2tk-to22/τp2,
ε=mIdMCmΔ-IdIRmΔ2m IdMC2mΔ,
ΔR=1=0.1,ΔR=2, 3=0.125,ΔR=4, 5=0.15,ΔR=6=0.175,ΔR=7, 8=0.2,ΔR=9, 10=0.225.
ΔR=1=0.1,ΔR=2=0.125,ΔR=3=0.15,ΔR=4=0.4ΔR=5 to 10=1.5.
CIR=αNeR+2MNe+8M2,
CMC=γNeR2K+γ2MNe.

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