Abstract

Photon pathlength distributions as a function of the number of scattering events in cylindrical turbid samples are studied using a polarization-sensitive Monte Carlo model with linearly polarized light input. Sample scattering causes extensive depolarization, yielding a photon field comprised of polarized and depolarized sub-populations. It is found that the pathlength of polarization-preserving photons is distributed within a defined spatial range with strong angular dependence. This pathlength, averaged over the range, is 2-3X smaller than the one averaged over the widely-spread range of all (polarized + depolarized) collected photons. It is also demonstrated that changes in optical properties of the media affect the pathlength distributions.

© 2007 Optical Society of America

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  1. G. H. Weiss, R. Nossal, and R. F. Bonner, "Statistics of penetration depth of photons re-emitted from irradiated tissue," J. Mod. Opt. 36, 349-359 (1989).
    [CrossRef]
  2. M. Dogariu and T. Asakura, "Photon pathlength distribution from polarized backscattering in random media," Opt. Eng. 35, 2234-2239 (1996).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  5. 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]
  6. S. R. Arridge, M. Cope, and D. T. Delpy, "The theoretical basis for the determination of optical pathlengths in tissue: temporal and frequency analysis," Phys. Med. Biol. 37, 1531-1560 (1992).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
  9. S. T. Flock, M. S. Patterson, B. C. Wilson, and D. R. Wyman, "Monte Carlo modeling of light propagation in highly scattering tissues-I: model predictions and comparison with diffusion theory," IEEE Trans. Biomed. Eng. 36, 1162-1168 (1989).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  11. X. Wang, L. V. Wang, C. Sun, and C. Yang, "Polarized light propagation through scattering media:time-resolved Monte Carlo simulations and experiments," J. Biomed. Opt. 8, 608-617 (2003).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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2006 (1)

X. Guo, M. F. G. Wood, and I. A. Vitkin, "Angular measurements of light scattered by turbid chiral media using linear Stokes polarimeter," J. Biomed. Opt. 11, 041105 (2006).
[CrossRef] [PubMed]

2005 (2)

2004 (1)

D. Côté and I. A. Vitkin, "Balanced detection for low-noise precision polarimetric measurements of optically active, multiply scattering tissue phantoms," J. Biomed. Opt. 9, 213-220 (2004).
[CrossRef] [PubMed]

2003 (2)

F. Jaillon and H. Saint-Jalmes, "Description and time reduction of a Monte Carlo code to simulate propagation of polarized light through scattering media," Appl. Opt. 42, 3290-3296 (2003).
[CrossRef] [PubMed]

X. Wang, L. V. Wang, C. Sun, and C. Yang, "Polarized light propagation through scattering media:time-resolved Monte Carlo simulations and experiments," J. Biomed. Opt. 8, 608-617 (2003).
[CrossRef] [PubMed]

2002 (1)

2001 (3)

2000 (1)

R. J. McNichols and G. L. Coté, "Optical glucose sensing in biological fluids: an overview," J. Biomed. Opt. 5, 5-16 (2000).
[CrossRef] [PubMed]

1998 (1)

1996 (1)

M. Dogariu and T. Asakura, "Photon pathlength distribution from polarized backscattering in random media," Opt. Eng. 35, 2234-2239 (1996).
[CrossRef]

1993 (1)

1992 (3)

J. M. Schmitt, A. H. Gandjbakhche, and R. F. Bonner, "Use of polarized light to discriminate short-path photons in a multiply scattering medium," Appl. Opt. 31, 6535-6546 (1992).
[CrossRef] [PubMed]

S. R. Arridge, M. Cope, and D. T. Delpy, "The theoretical basis for the determination of optical pathlengths in tissue: temporal and frequency analysis," Phys. Med. Biol. 37, 1531-1560 (1992).
[CrossRef] [PubMed]

G. L. Coté, M. D. Fox, and R. B. Northrop, "Noninvasive optical polarimetric glucose sensing using a true phase measurement technique," IEEE Trans. Biomed. Eng. 39, 752-756 (1992).
[CrossRef] [PubMed]

1989 (3)

G. H. Weiss, R. Nossal, and R. F. Bonner, "Statistics of penetration depth of photons re-emitted from irradiated tissue," J. Mod. Opt. 36, 349-359 (1989).
[CrossRef]

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]

S. T. Flock, M. S. Patterson, B. C. Wilson, and D. R. Wyman, "Monte Carlo modeling of light propagation in highly scattering tissues-I: model predictions and comparison with diffusion theory," IEEE Trans. Biomed. Eng. 36, 1162-1168 (1989).
[CrossRef] [PubMed]

1983 (1)

B. C. Wilson and G. Adam, "A Monte Carlo model for the absorption and flux distributions of light in tissue," Med. Phys. 10, 824-830 (1983).
[CrossRef] [PubMed]

Adam, G.

B. C. Wilson and G. Adam, "A Monte Carlo model for the absorption and flux distributions of light in tissue," Med. Phys. 10, 824-830 (1983).
[CrossRef] [PubMed]

Arridge, S. R.

S. R. Arridge, M. Cope, and D. T. Delpy, "The theoretical basis for the determination of optical pathlengths in tissue: temporal and frequency analysis," Phys. Med. Biol. 37, 1531-1560 (1992).
[CrossRef] [PubMed]

Asakura, T.

M. Dogariu and T. Asakura, "Photon pathlength distribution from polarized backscattering in random media," Opt. Eng. 35, 2234-2239 (1996).
[CrossRef]

Backman, V.

Bonner, R. F.

J. M. Schmitt, A. H. Gandjbakhche, and R. F. Bonner, "Use of polarized light to discriminate short-path photons in a multiply scattering medium," Appl. Opt. 31, 6535-6546 (1992).
[CrossRef] [PubMed]

G. H. Weiss, R. Nossal, and R. F. Bonner, "Statistics of penetration depth of photons re-emitted from irradiated tissue," J. Mod. Opt. 36, 349-359 (1989).
[CrossRef]

Chance, B.

Cope, M.

S. R. Arridge, M. Cope, and D. T. Delpy, "The theoretical basis for the determination of optical pathlengths in tissue: temporal and frequency analysis," Phys. Med. Biol. 37, 1531-1560 (1992).
[CrossRef] [PubMed]

Coté, G. L.

R. J. McNichols and G. L. Coté, "Optical glucose sensing in biological fluids: an overview," J. Biomed. Opt. 5, 5-16 (2000).
[CrossRef] [PubMed]

G. L. Coté, M. D. Fox, and R. B. Northrop, "Noninvasive optical polarimetric glucose sensing using a true phase measurement technique," IEEE Trans. Biomed. Eng. 39, 752-756 (1992).
[CrossRef] [PubMed]

Côté, D.

D. Côté and I. A. Vitkin, "Robust concentration determination of optically active molecules in turbid media with validated three-dimensional polarization sensitive Monte Carlo calculations," Opt. Express 13, 148-163 (2005).
[CrossRef] [PubMed]

D. Côté and I. A. Vitkin, "Balanced detection for low-noise precision polarimetric measurements of optically active, multiply scattering tissue phantoms," J. Biomed. Opt. 9, 213-220 (2004).
[CrossRef] [PubMed]

Delpy, D. T.

S. R. Arridge, M. Cope, and D. T. Delpy, "The theoretical basis for the determination of optical pathlengths in tissue: temporal and frequency analysis," Phys. Med. Biol. 37, 1531-1560 (1992).
[CrossRef] [PubMed]

Dogariu, A.

Dogariu, M.

M. Dogariu and T. Asakura, "Photon pathlength distribution from polarized backscattering in random media," Opt. Eng. 35, 2234-2239 (1996).
[CrossRef]

Drévillon, B.

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 tissues-I: model predictions and comparison with diffusion theory," IEEE Trans. Biomed. Eng. 36, 1162-1168 (1989).
[CrossRef] [PubMed]

Fox, M. D.

G. L. Coté, M. D. Fox, and R. B. Northrop, "Noninvasive optical polarimetric glucose sensing using a true phase measurement technique," IEEE Trans. Biomed. Eng. 39, 752-756 (1992).
[CrossRef] [PubMed]

Gandjbakhche, A. H.

Guo, X.

X. Guo, M. F. G. Wood, and I. A. Vitkin, "Angular measurements of light scattered by turbid chiral media using linear Stokes polarimeter," J. Biomed. Opt. 11, 041105 (2006).
[CrossRef] [PubMed]

Jacques, S. L.

Jaillon, F.

Kaplan, B.

Kehtarnavaz, N.

Kim, Y. L.

Ledanois, G.

Li, X.

Liu, Y.

McNichols, R. J.

R. J. McNichols and G. L. Coté, "Optical glucose sensing in biological fluids: an overview," J. Biomed. Opt. 5, 5-16 (2000).
[CrossRef] [PubMed]

Mehrübeoglu, M.

Northrop, R. B.

G. L. Coté, M. D. Fox, and R. B. Northrop, "Noninvasive optical polarimetric glucose sensing using a true phase measurement technique," IEEE Trans. Biomed. Eng. 39, 752-756 (1992).
[CrossRef] [PubMed]

Nossal, R.

G. H. Weiss, R. Nossal, and R. F. Bonner, "Statistics of penetration depth of photons re-emitted from irradiated tissue," J. Mod. Opt. 36, 349-359 (1989).
[CrossRef]

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 tissues-I: model predictions and comparison with diffusion theory," IEEE Trans. Biomed. Eng. 36, 1162-1168 (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]

Popescu, G.

Rastegar, S.

Saint-Jalmes, H.

Schmitt, J. M.

Sun, C.

X. Wang, L. V. Wang, C. Sun, and C. Yang, "Polarized light propagation through scattering media:time-resolved Monte Carlo simulations and experiments," J. Biomed. Opt. 8, 608-617 (2003).
[CrossRef] [PubMed]

Tsuchiya, Y.

Y. Tsuchiya, "Photon path distribution and optical responses of turbid media: theoretical analysis based on the microscopic Beer-Lambert law," Phys. Med. Biol. 46, 2067-2084 (2001).
[CrossRef] [PubMed]

Vitkin, I. A.

X. Guo, M. F. G. Wood, and I. A. Vitkin, "Angular measurements of light scattered by turbid chiral media using linear Stokes polarimeter," J. Biomed. Opt. 11, 041105 (2006).
[CrossRef] [PubMed]

D. Côté and I. A. Vitkin, "Robust concentration determination of optically active molecules in turbid media with validated three-dimensional polarization sensitive Monte Carlo calculations," Opt. Express 13, 148-163 (2005).
[CrossRef] [PubMed]

D. Côté and I. A. Vitkin, "Balanced detection for low-noise precision polarimetric measurements of optically active, multiply scattering tissue phantoms," J. Biomed. Opt. 9, 213-220 (2004).
[CrossRef] [PubMed]

Wang, L.

Wang, L. V.

Wang, X.

X. Wang, L. V. Wang, C. Sun, and C. Yang, "Polarized light propagation through scattering media:time-resolved Monte Carlo simulations and experiments," J. Biomed. Opt. 8, 608-617 (2003).
[CrossRef] [PubMed]

X. Wang, G. Yao, and L. V. Wang, "Monte Carlo model and single-scattering approximation of the propagation of polarized light in turbid media containing glucose," Appl. Opt. 41, 792-801 (2002).
[CrossRef] [PubMed]

Weiss, G. H.

G. H. Weiss, R. Nossal, and R. F. Bonner, "Statistics of penetration depth of photons re-emitted from irradiated tissue," J. Mod. Opt. 36, 349-359 (1989).
[CrossRef]

Wilson, B. C.

S. T. Flock, M. S. Patterson, B. C. Wilson, and D. R. Wyman, "Monte Carlo modeling of light propagation in highly scattering tissues-I: model predictions and comparison with diffusion theory," IEEE Trans. Biomed. Eng. 36, 1162-1168 (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]

B. C. Wilson and G. Adam, "A Monte Carlo model for the absorption and flux distributions of light in tissue," Med. Phys. 10, 824-830 (1983).
[CrossRef] [PubMed]

Wood, M. F. G.

X. Guo, M. F. G. Wood, and I. A. Vitkin, "Angular measurements of light scattered by turbid chiral media using linear Stokes polarimeter," J. Biomed. Opt. 11, 041105 (2006).
[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 tissues-I: model predictions and comparison with diffusion theory," IEEE Trans. Biomed. Eng. 36, 1162-1168 (1989).
[CrossRef] [PubMed]

Yang, C.

X. Wang, L. V. Wang, C. Sun, and C. Yang, "Polarized light propagation through scattering media:time-resolved Monte Carlo simulations and experiments," J. Biomed. Opt. 8, 608-617 (2003).
[CrossRef] [PubMed]

Yao, G.

Appl. Opt. (6)

IEEE Trans. Biomed. Eng. (2)

S. T. Flock, M. S. Patterson, B. C. Wilson, and D. R. Wyman, "Monte Carlo modeling of light propagation in highly scattering tissues-I: model predictions and comparison with diffusion theory," IEEE Trans. Biomed. Eng. 36, 1162-1168 (1989).
[CrossRef] [PubMed]

G. L. Coté, M. D. Fox, and R. B. Northrop, "Noninvasive optical polarimetric glucose sensing using a true phase measurement technique," IEEE Trans. Biomed. Eng. 39, 752-756 (1992).
[CrossRef] [PubMed]

J. Biomed. Opt. (4)

X. Guo, M. F. G. Wood, and I. A. Vitkin, "Angular measurements of light scattered by turbid chiral media using linear Stokes polarimeter," J. Biomed. Opt. 11, 041105 (2006).
[CrossRef] [PubMed]

R. J. McNichols and G. L. Coté, "Optical glucose sensing in biological fluids: an overview," J. Biomed. Opt. 5, 5-16 (2000).
[CrossRef] [PubMed]

X. Wang, L. V. Wang, C. Sun, and C. Yang, "Polarized light propagation through scattering media:time-resolved Monte Carlo simulations and experiments," J. Biomed. Opt. 8, 608-617 (2003).
[CrossRef] [PubMed]

D. Côté and I. A. Vitkin, "Balanced detection for low-noise precision polarimetric measurements of optically active, multiply scattering tissue phantoms," J. Biomed. Opt. 9, 213-220 (2004).
[CrossRef] [PubMed]

J. Mod. Opt. (1)

G. H. Weiss, R. Nossal, and R. F. Bonner, "Statistics of penetration depth of photons re-emitted from irradiated tissue," J. Mod. Opt. 36, 349-359 (1989).
[CrossRef]

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

Med. Phys. (1)

B. C. Wilson and G. Adam, "A Monte Carlo model for the absorption and flux distributions of light in tissue," Med. Phys. 10, 824-830 (1983).
[CrossRef] [PubMed]

Opt. Eng. (1)

M. Dogariu and T. Asakura, "Photon pathlength distribution from polarized backscattering in random media," Opt. Eng. 35, 2234-2239 (1996).
[CrossRef]

Opt. Express (3)

Phys. Med. Biol. (2)

Y. Tsuchiya, "Photon path distribution and optical responses of turbid media: theoretical analysis based on the microscopic Beer-Lambert law," Phys. Med. Biol. 46, 2067-2084 (2001).
[CrossRef] [PubMed]

S. R. Arridge, M. Cope, and D. T. Delpy, "The theoretical basis for the determination of optical pathlengths in tissue: temporal and frequency analysis," Phys. Med. Biol. 37, 1531-1560 (1992).
[CrossRef] [PubMed]

Other (1)

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

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Figures (8)

Fig. 1.
Fig. 1.

Cylindrical simulation geometry. Linearly polarized light incidents at O on the vertically oriented cylindrical sample. The scattered light is detected at P(z, θ) on the surface of the cylinder, with an acceptance angle ψ. z is the distance of the detector off the horizontal incident plane and θ is the detection direction (the angle between the transmission direction Y and the normal to the detection element).

Fig. 2.
Fig. 2.

Intensity distribution within the incident plane (z=0) for 109 incident (linearly polarized) photons. (a) summed number of photons in each bin IN as a function of the number of scattering events N. (b) angular dependence of total collected photon intensity. The symbols are MC calculation results and the line is a guide for the eye.

Fig. 3.
Fig. 3.

Distribution of surviving linearly polarized photons within incident plane (z=0). (a) indexed surviving polarization fraction distribution at different detection angles θ; the numbers in brackets following the θ-values are the βLtotal results. (b) angular dependence of indexed surviving polarization fraction. The symbols are MC calculation results and the lines are a guide for the eye.

Fig. 4.
Fig. 4.

Distribution of surviving linearly polarized photons within incident plane (z=0). (a) ratio of indexed polarized photon to total collected photons at different detection angles. (b) total surviving linear polarization fraction vs. detection angle θ for g=0.88 [see bracketed percentage values in fig. 3(a)]. The symbols are MC calculation results and the lines are a guide for the eye. The inset is the plot of total surviving linear polarization fraction against detection angle for different g values: 0.5 (blue symbol+line), 0.75 (brown symbol+line) and 0.93 (red symbol+line).

Fig. 5.
Fig. 5.

Indexed pathlength distribution within the incident plane (z=0). (a) indexed average pathlength distribution at different detection angles θ. (b) angular dependence of indexed pathlength. The symbols are MC calculation results and the lines are a guide for the eye. The blue reference line is the direct distance between sample entrance O and exit P, as shown in the inset, at different detection angles.

Fig. 6.
Fig. 6.

(LN/N) distributions. The solid reference line is the mean free path (mfp) calculated from 1/μs.

Fig. 7.
Fig. 7.

Pathlength distribution of polarized photons within incident plane (z=0). (a) polarized photon distribution as a function of pathlength. (b) angular dependence of characteristic polarization pathlength LCP and total average pathlength Ltotal. The inset is the plot of Ltotal to LCP ratio (Ltotal/LCP). The symbols are MC calculation results and the lines are a guide for the eye.

Fig. 8.
Fig. 8.

Effect of optical properties (g, μs and μs’) on pathlength distributions for a fixed number of scattering events (N=30). The symbols are MC calculation results and the lines are a guide for the eye.

Equations (4)

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N total = N = 1 N I N I total .
R N = β LN I N I total .
L CP = N = i j I N L N N = i j I N ,
L total = N = 1 I N L N N = 1 I N ,

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