Abstract

An efficient and fast simulation technique is presented to calculate characteristic features of confocal imaging through scattering media. The simulation can predict the time-resolved confocal response to pulsed illumination that allows optimizing of imaging contrast when time-gating techniques are applied. Modest computational effort is sufficient to obtain contrast predictions for arbitrary numerical aperture, focus depth, pinhole size, and scattering density, while the simulation accuracy is independent of scattering density and pinhole size. In the case of isotropic scattering, our results indicate that reflection-mode confocal imaging through scattering media is limited to μd3.5 optical thicknesses for continuous-wave illumination. If time-gating is applied, imaging through scattering densities of μd8 is theoretically possible.

© 2001 Optical Society of America

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References

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1999 (2)

J. M. Schmitt, “Optical coherence tomography (OCT): a review,” IEEE J. Sel. Top. Quantum Electron. 5, 1205–1215 (1999).
[CrossRef]

C. M. Blanca and C. Saloma, “Efficient analysis of temporal broadening of a pulsed focused Gaussian beam in scattering media,” Appl. Opt. 38, 5433–5437 (1999).
[CrossRef]

1998 (1)

E. Baiger, C. Hauger, and W. Zinth, “Imaging within highly scattering media using time-resolved backscattering of femtosecond pulses,” Appl. Phys. B 67, 257–261 (1998).
[CrossRef]

1997 (2)

1996 (3)

1995 (1)

1994 (1)

1993 (1)

1990 (1)

1989 (2)

M. S. Patterson, B. Chance, and B. C. Wilson, “Time resolved reflectance and transmittance for the non-invasive measurement of tissue optical properties,” Appl. Opt. 28, 2331–2336 (1989).
[CrossRef] [PubMed]

S. T. Flock, M. S. Patterson, B. C. Wilson, and D. R. Wyman, “Monte Carlo modeling of light propagation in highly scattering tissue I: Model predictions and comparison with diffusion theory,” IEEE Trans. Biomed. Eng. 36, 1162–1167 (1989).
[CrossRef] [PubMed]

1988 (1)

R. Vreeker, M. P. Van Albada, R. Sprik, and A. Lagendijk, “Femtosecond time-resolved measurements of weak localization of light,” Phys. Lett. A 132, 51–54 (1988).
[CrossRef]

1986 (1)

Alfano, R. R.

Avrillier, S.

Baiger, E.

E. Baiger, C. Hauger, and W. Zinth, “Imaging within highly scattering media using time-resolved backscattering of femtosecond pulses,” Appl. Phys. B 67, 257–261 (1998).
[CrossRef]

Ben-Letaief, K.

Blanca, C. M.

Chance, B.

Corey, R.

de Silvestri, S.

Dorn, P.

Flock, S. T.

S. T. Flock, M. S. Patterson, B. C. Wilson, and D. R. Wyman, “Monte Carlo modeling of light propagation in highly scattering tissue I: Model predictions and comparison with diffusion theory,” IEEE Trans. Biomed. Eng. 36, 1162–1167 (1989).
[CrossRef] [PubMed]

Fujimoto, J. G.

Genack, A. Z.

Hauger, C.

E. Baiger, C. Hauger, and W. Zinth, “Imaging within highly scattering media using time-resolved backscattering of femtosecond pulses,” Appl. Phys. B 67, 257–261 (1998).
[CrossRef]

Hee, M. R.

Ippen, E. P.

Izatt, J. A.

Jacobson, J. M.

Kempe, M.

Knüttel, A.

Lagendijk, A.

R. Vreeker, M. P. Van Albada, R. Sprik, and A. Lagendijk, “Femtosecond time-resolved measurements of weak localization of light,” Phys. Lett. A 132, 51–54 (1988).
[CrossRef]

Liu, Feng

Patterson, M. S.

S. T. Flock, M. S. Patterson, B. C. Wilson, and D. R. Wyman, “Monte Carlo modeling of light propagation in highly scattering tissue I: Model predictions and comparison with diffusion theory,” IEEE Trans. Biomed. Eng. 36, 1162–1167 (1989).
[CrossRef] [PubMed]

M. S. Patterson, B. Chance, and B. C. Wilson, “Time resolved reflectance and transmittance for the non-invasive measurement of tissue optical properties,” Appl. Opt. 28, 2331–2336 (1989).
[CrossRef] [PubMed]

Rudolph, W.

Saloma, C.

Saulnier, P.

Schmidt, A.

Schmitt, J. M.

Sprik, R.

R. Vreeker, M. P. Van Albada, R. Sprik, and A. Lagendijk, “Femtosecond time-resolved measurements of weak localization of light,” Phys. Lett. A 132, 51–54 (1988).
[CrossRef]

Tinet, E.

Tualle, J. M.

Van Albada, M. P.

R. Vreeker, M. P. Van Albada, R. Sprik, and A. Lagendijk, “Femtosecond time-resolved measurements of weak localization of light,” Phys. Lett. A 132, 51–54 (1988).
[CrossRef]

Vreeker, R.

R. Vreeker, M. P. Van Albada, R. Sprik, and A. Lagendijk, “Femtosecond time-resolved measurements of weak localization of light,” Phys. Lett. A 132, 51–54 (1988).
[CrossRef]

Welsch, E.

Wilson, B. C.

M. S. Patterson, B. Chance, and B. C. Wilson, “Time resolved reflectance and transmittance for the non-invasive measurement of tissue optical properties,” Appl. Opt. 28, 2331–2336 (1989).
[CrossRef] [PubMed]

S. T. Flock, M. S. Patterson, B. C. Wilson, and D. R. Wyman, “Monte Carlo modeling of light propagation in highly scattering tissue I: Model predictions and comparison with diffusion theory,” IEEE Trans. Biomed. Eng. 36, 1162–1167 (1989).
[CrossRef] [PubMed]

Wyman, D. R.

S. T. Flock, M. S. Patterson, B. C. Wilson, and D. R. Wyman, “Monte Carlo modeling of light propagation in highly scattering tissue I: Model predictions and comparison with diffusion theory,” IEEE Trans. Biomed. Eng. 36, 1162–1167 (1989).
[CrossRef] [PubMed]

Yadlowsky, M.

Yoo, K. M.

Zinth, W.

E. Baiger, C. Hauger, and W. Zinth, “Imaging within highly scattering media using time-resolved backscattering of femtosecond pulses,” Appl. Phys. B 67, 257–261 (1998).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. B (1)

E. Baiger, C. Hauger, and W. Zinth, “Imaging within highly scattering media using time-resolved backscattering of femtosecond pulses,” Appl. Phys. B 67, 257–261 (1998).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

J. M. Schmitt, “Optical coherence tomography (OCT): a review,” IEEE J. Sel. Top. Quantum Electron. 5, 1205–1215 (1999).
[CrossRef]

IEEE Trans. Biomed. Eng. (1)

S. T. Flock, M. S. Patterson, B. C. Wilson, and D. R. Wyman, “Monte Carlo modeling of light propagation in highly scattering tissue I: Model predictions and comparison with diffusion theory,” IEEE Trans. Biomed. Eng. 36, 1162–1167 (1989).
[CrossRef] [PubMed]

J. Opt. Soc. Am. A (6)

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

Opt. Lett. (3)

Phys. Lett. A (1)

R. Vreeker, M. P. Van Albada, R. Sprik, and A. Lagendijk, “Femtosecond time-resolved measurements of weak localization of light,” Phys. Lett. A 132, 51–54 (1988).
[CrossRef]

Other (3)

T. Wilson, ed., Confocal Microscopy (Academic, San Diego Calif., 1990), p. 11.

H. C. Van De Hulst, Multiple Light Scattering: Tables, Formulas, and Applications (Academic, San Diego, Calif., 1980), Vol. 1, p. 9.

M. Magnor, “Reflection mode confocal microscopy through scattering media,” M.S. thesis (University of New Mexico, Albuquerque, New Mexico, 1997), p. 63.

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Figures (9)

Fig. 1
Fig. 1

Schematic diagram of confocal imaging through scattering layers. The volume region from which light can be scattered into the pinhole is subdivided into voxels.

Fig. 2
Fig. 2

Experimental measurements and simulation results of the confocal signal when imaging through a scatterer. A mirror in the focal plane reflects ballistic and scattered photons.

Fig. 3
Fig. 3

Confocal imaging contrast C as a function of the optical thickness μd for different numerical apertures NA.

Fig. 4
Fig. 4

Normalized confocal signal versus depth for different scattering densities (NA=0.4).

Fig. 5
Fig. 5

Confocal imaging with time gating (NA=0.4). The normalized signal is shown as a function of the position of the time gate for different scattering densities. The oscillations around t=0 originate from the large voxel sizes on the sample surface.

Fig. 6
Fig. 6

Same as Fig. 4, depicting the time around focus in detail. The singly scattered signal contribution is shown in addition to the total signal.

Fig. 7
Fig. 7

Comparison of the confocal imaging contrast without (cw) and with time-gating for NA=0.4. The contrast is determined for 10-fs and 200-fs time-gate widths and for a time-gate width equal to the transit time of light through the focal region (Δu=5.6).

Fig. 8
Fig. 8

Confocal imaging contrast using a 10-fs time gate for different numerical apertures.

Fig. 9
Fig. 9

Confocal imaging without and with a 10-fs time gate. The curves describe the parameter combination at which the contrast C=1. Confocal imaging is possible to the left of the respective curves.

Equations (11)

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

u=8πzλ sin2 α2,
v=2πrλ sin α,
R(z)=r0+|d-z|tan arcsin NAn,
z(1)=-ln(1-qz)μ cos arctan qrtan α-r0d,
r(1)=qrr0+|d-z(1)|tan α-r0d,
pesc(z(1))=12[exp(-μz(1))-μz(1)E1(μz(1))],
E1(x)-(ln x+γ)+x-x24+x318x<1.618exp(-x)x 1-1x+2x2x>1.618
l=-ln(1-Kq)μ,
K=1-exp(-μz/sin θ)0<θπ/210θ-π/2.
C=ΣsignalΣnoise.
C(g)2µ(1-g)sinh [2µ(1-g)].

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