Abstract

Monte Carlo simulations were performed in order to obtain reflectance measurements from phantoms typically used in biomedical optics when either unpolarized or circularly polarized incident light is used. Phantoms contain spherical targets of different diameters, placed at different depths, with higher absorption than the surrounding medium, which are detected using a coaxial setup of laser and detector. The considered turbid media have highly anisotropic scattering phase functions, so detected light for the considered times of flight is not diffuse, but rather in the multiple-scattering regime. Therefore, the target reconstruction methods typically used in diffuse optical imaging cannot be employed. However, spatially resolved reflectance measurements in the time domain allow use of a novel reconstruction method based on the approximation of average photon trajectories, which are functions of the separation distance from the point of incidence and of the time of flight. With the approximated average photon trajectories, one can estimate the depth of the target.

© 2012 Optical Society of America

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  1. D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
    [CrossRef]
  2. A. M. Zysk, F. T. Nguyen, A. L. Oldenburg, D. L. Marks, and S. A. Boppart, “Optical coherence tomography: a review of clinical development from bench to bedside,” J. Biomed. Opt. 12, 051403 (2007).
    [CrossRef]
  3. A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, “Optical coherence tomography-principles and applications,” Rep. Prog. Phys. 66, 239–303 (2003).
    [CrossRef]
  4. A. Torricelli, A. Pifferi, L. Spinelli, R. Cubeddu, F. Martelli, S. Del Bianco, and G. Zaccanti, “Time-resolved reflectance at null source-detector separation: improving contrast and resolution in diffuse optical imaging,” Phys. Rev. Lett. 95, 078101 (2005).
    [CrossRef]
  5. M. Schweiger, A. Gibson, and S. R. Arridge, “Computational aspects of diffuse optical tomography,” Comput. Sci. Eng. 5, 33–41 (2003).
    [CrossRef]
  6. A. P. Gibson, J. C. Hebden, and S. R. Arridge, “Recent advances in diffuse optical imaging,” Phys. Med. Biol. 50, R1–R43(2005).
    [CrossRef]
  7. C. Niclass, C. Favi, T. Kluter, M. Gersbach, and E. Charbon, “A 128×128 single-photon image sensor with column-level 10 bit time-to-digital converter array,” IEEE J. Solid-State Circuits 43, 2977–2989 (2008).
    [CrossRef]
  8. X. Ni and R. R. Alfano, “Time-resolved backscattering of circularly and linearly polarized light in a turbid medium,” Opt. Lett. 29, 2773–2775 (2004).
    [CrossRef]
  9. S. A. Kartazayeva, X. Ni, and R. R. Alfano, “Backscattering target detection in a turbid medium by use of circularly and linearly polarized light,” Opt. Lett. 30, 1168–1170 (2005).
    [CrossRef]
  10. M. Šormaz and P. Jenny, “Contrast improvement by selecting ballistic-photons using polarization gating,” Opt. Express 18, 23746–23755 (2010).
    [CrossRef]
  11. M. Šormaz, T. Stamm, and P. Jenny, “Stochastic modeling of polarized light scattering using a Monte Carlo-based stencil method,” J. Opt. Soc. Am. A 27, 1100–1110 (2010).
    [CrossRef]
  12. M. Šormaz and P. Jenny, “Subsurface imaging with NIR light using polarization gating,” PIERS Online 7, 595–600 (2011).
    [CrossRef]
  13. P. Jenny, S. Mourad, T. Stamm, M. Vöge, and K. Simon, “Computing light statistics in heterogeneous media based on a mass weighted probability density function method,” J. Opt. Soc. Am. A 24, 2206–2219 (2007).
    [CrossRef]
  14. M. Šormaz, T. Stamm, S. Mourad, and P. Jenny, “Stochastic modeling of light scattering with fluorescence using a Monte Carlo-based multiscale approach,” J. Opt. Soc. Am. A 26, 1403–1413 (2009).
    [CrossRef]
  15. M. Šormaz, T. Stamm, and P. Jenny, “Influence of linear birefringence in the computation of scattering phase functions,” J. Biomed. Opt. 15, 055010 (2010).
    [CrossRef]
  16. A. D. Kim and M. Moscoso, “Backscattering of circularly polarized pulses,” Opt. Lett. 27, 181589 (2002).
    [CrossRef]
  17. W. Cai, X. Ni, S. K. Gayen, and R. R. Alfano, “Analytical cumulant solution of the vector radiative transfer equation investigates backscattering of circularly polarized light from turbid media,” Phys. Rev. E 74, 056605 (2006).
    [CrossRef]
  18. A. D. Kim and M. Moscoso, “Backscattering of beams by forward-peaked scattering media,” Opt. Lett. 29, 010074 (2004).
    [CrossRef]
  19. K. G. Phillips, M. Xu, S. K. Gayen, and R. R. Alfano, “Time-resolved ring structure of circularly polarized beams backscattered from forward scattering media,” Opt. Express 13, 7954–7969 (2005).
    [CrossRef]

2011

M. Šormaz and P. Jenny, “Subsurface imaging with NIR light using polarization gating,” PIERS Online 7, 595–600 (2011).
[CrossRef]

2010

2009

2008

C. Niclass, C. Favi, T. Kluter, M. Gersbach, and E. Charbon, “A 128×128 single-photon image sensor with column-level 10 bit time-to-digital converter array,” IEEE J. Solid-State Circuits 43, 2977–2989 (2008).
[CrossRef]

2007

P. Jenny, S. Mourad, T. Stamm, M. Vöge, and K. Simon, “Computing light statistics in heterogeneous media based on a mass weighted probability density function method,” J. Opt. Soc. Am. A 24, 2206–2219 (2007).
[CrossRef]

A. M. Zysk, F. T. Nguyen, A. L. Oldenburg, D. L. Marks, and S. A. Boppart, “Optical coherence tomography: a review of clinical development from bench to bedside,” J. Biomed. Opt. 12, 051403 (2007).
[CrossRef]

2006

W. Cai, X. Ni, S. K. Gayen, and R. R. Alfano, “Analytical cumulant solution of the vector radiative transfer equation investigates backscattering of circularly polarized light from turbid media,” Phys. Rev. E 74, 056605 (2006).
[CrossRef]

2005

S. A. Kartazayeva, X. Ni, and R. R. Alfano, “Backscattering target detection in a turbid medium by use of circularly and linearly polarized light,” Opt. Lett. 30, 1168–1170 (2005).
[CrossRef]

K. G. Phillips, M. Xu, S. K. Gayen, and R. R. Alfano, “Time-resolved ring structure of circularly polarized beams backscattered from forward scattering media,” Opt. Express 13, 7954–7969 (2005).
[CrossRef]

A. Torricelli, A. Pifferi, L. Spinelli, R. Cubeddu, F. Martelli, S. Del Bianco, and G. Zaccanti, “Time-resolved reflectance at null source-detector separation: improving contrast and resolution in diffuse optical imaging,” Phys. Rev. Lett. 95, 078101 (2005).
[CrossRef]

A. P. Gibson, J. C. Hebden, and S. R. Arridge, “Recent advances in diffuse optical imaging,” Phys. Med. Biol. 50, R1–R43(2005).
[CrossRef]

2004

A. D. Kim and M. Moscoso, “Backscattering of beams by forward-peaked scattering media,” Opt. Lett. 29, 010074 (2004).
[CrossRef]

X. Ni and R. R. Alfano, “Time-resolved backscattering of circularly and linearly polarized light in a turbid medium,” Opt. Lett. 29, 2773–2775 (2004).
[CrossRef]

2003

M. Schweiger, A. Gibson, and S. R. Arridge, “Computational aspects of diffuse optical tomography,” Comput. Sci. Eng. 5, 33–41 (2003).
[CrossRef]

A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, “Optical coherence tomography-principles and applications,” Rep. Prog. Phys. 66, 239–303 (2003).
[CrossRef]

2002

A. D. Kim and M. Moscoso, “Backscattering of circularly polarized pulses,” Opt. Lett. 27, 181589 (2002).
[CrossRef]

1991

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef]

Alfano, R. R.

Arridge, S. R.

A. P. Gibson, J. C. Hebden, and S. R. Arridge, “Recent advances in diffuse optical imaging,” Phys. Med. Biol. 50, R1–R43(2005).
[CrossRef]

M. Schweiger, A. Gibson, and S. R. Arridge, “Computational aspects of diffuse optical tomography,” Comput. Sci. Eng. 5, 33–41 (2003).
[CrossRef]

Boppart, S. A.

A. M. Zysk, F. T. Nguyen, A. L. Oldenburg, D. L. Marks, and S. A. Boppart, “Optical coherence tomography: a review of clinical development from bench to bedside,” J. Biomed. Opt. 12, 051403 (2007).
[CrossRef]

Cai, W.

W. Cai, X. Ni, S. K. Gayen, and R. R. Alfano, “Analytical cumulant solution of the vector radiative transfer equation investigates backscattering of circularly polarized light from turbid media,” Phys. Rev. E 74, 056605 (2006).
[CrossRef]

Chang, W.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef]

Charbon, E.

C. Niclass, C. Favi, T. Kluter, M. Gersbach, and E. Charbon, “A 128×128 single-photon image sensor with column-level 10 bit time-to-digital converter array,” IEEE J. Solid-State Circuits 43, 2977–2989 (2008).
[CrossRef]

Cubeddu, R.

A. Torricelli, A. Pifferi, L. Spinelli, R. Cubeddu, F. Martelli, S. Del Bianco, and G. Zaccanti, “Time-resolved reflectance at null source-detector separation: improving contrast and resolution in diffuse optical imaging,” Phys. Rev. Lett. 95, 078101 (2005).
[CrossRef]

Del Bianco, S.

A. Torricelli, A. Pifferi, L. Spinelli, R. Cubeddu, F. Martelli, S. Del Bianco, and G. Zaccanti, “Time-resolved reflectance at null source-detector separation: improving contrast and resolution in diffuse optical imaging,” Phys. Rev. Lett. 95, 078101 (2005).
[CrossRef]

Drexler, W.

A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, “Optical coherence tomography-principles and applications,” Rep. Prog. Phys. 66, 239–303 (2003).
[CrossRef]

Favi, C.

C. Niclass, C. Favi, T. Kluter, M. Gersbach, and E. Charbon, “A 128×128 single-photon image sensor with column-level 10 bit time-to-digital converter array,” IEEE J. Solid-State Circuits 43, 2977–2989 (2008).
[CrossRef]

Fercher, A. F.

A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, “Optical coherence tomography-principles and applications,” Rep. Prog. Phys. 66, 239–303 (2003).
[CrossRef]

Flotte, T.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef]

Fujimoto, J. G.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef]

Gayen, S. K.

W. Cai, X. Ni, S. K. Gayen, and R. R. Alfano, “Analytical cumulant solution of the vector radiative transfer equation investigates backscattering of circularly polarized light from turbid media,” Phys. Rev. E 74, 056605 (2006).
[CrossRef]

K. G. Phillips, M. Xu, S. K. Gayen, and R. R. Alfano, “Time-resolved ring structure of circularly polarized beams backscattered from forward scattering media,” Opt. Express 13, 7954–7969 (2005).
[CrossRef]

Gersbach, M.

C. Niclass, C. Favi, T. Kluter, M. Gersbach, and E. Charbon, “A 128×128 single-photon image sensor with column-level 10 bit time-to-digital converter array,” IEEE J. Solid-State Circuits 43, 2977–2989 (2008).
[CrossRef]

Gibson, A.

M. Schweiger, A. Gibson, and S. R. Arridge, “Computational aspects of diffuse optical tomography,” Comput. Sci. Eng. 5, 33–41 (2003).
[CrossRef]

Gibson, A. P.

A. P. Gibson, J. C. Hebden, and S. R. Arridge, “Recent advances in diffuse optical imaging,” Phys. Med. Biol. 50, R1–R43(2005).
[CrossRef]

Gregory, K.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef]

Hebden, J. C.

A. P. Gibson, J. C. Hebden, and S. R. Arridge, “Recent advances in diffuse optical imaging,” Phys. Med. Biol. 50, R1–R43(2005).
[CrossRef]

Hee, M. R.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef]

Hitzenberger, C. K.

A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, “Optical coherence tomography-principles and applications,” Rep. Prog. Phys. 66, 239–303 (2003).
[CrossRef]

Huang, D.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef]

Jenny, P.

Kartazayeva, S. A.

Kim, A. D.

A. D. Kim and M. Moscoso, “Backscattering of beams by forward-peaked scattering media,” Opt. Lett. 29, 010074 (2004).
[CrossRef]

A. D. Kim and M. Moscoso, “Backscattering of circularly polarized pulses,” Opt. Lett. 27, 181589 (2002).
[CrossRef]

Kluter, T.

C. Niclass, C. Favi, T. Kluter, M. Gersbach, and E. Charbon, “A 128×128 single-photon image sensor with column-level 10 bit time-to-digital converter array,” IEEE J. Solid-State Circuits 43, 2977–2989 (2008).
[CrossRef]

Lasser, T.

A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, “Optical coherence tomography-principles and applications,” Rep. Prog. Phys. 66, 239–303 (2003).
[CrossRef]

Lin, C. P.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef]

Marks, D. L.

A. M. Zysk, F. T. Nguyen, A. L. Oldenburg, D. L. Marks, and S. A. Boppart, “Optical coherence tomography: a review of clinical development from bench to bedside,” J. Biomed. Opt. 12, 051403 (2007).
[CrossRef]

Martelli, F.

A. Torricelli, A. Pifferi, L. Spinelli, R. Cubeddu, F. Martelli, S. Del Bianco, and G. Zaccanti, “Time-resolved reflectance at null source-detector separation: improving contrast and resolution in diffuse optical imaging,” Phys. Rev. Lett. 95, 078101 (2005).
[CrossRef]

Moscoso, M.

A. D. Kim and M. Moscoso, “Backscattering of beams by forward-peaked scattering media,” Opt. Lett. 29, 010074 (2004).
[CrossRef]

A. D. Kim and M. Moscoso, “Backscattering of circularly polarized pulses,” Opt. Lett. 27, 181589 (2002).
[CrossRef]

Mourad, S.

Nguyen, F. T.

A. M. Zysk, F. T. Nguyen, A. L. Oldenburg, D. L. Marks, and S. A. Boppart, “Optical coherence tomography: a review of clinical development from bench to bedside,” J. Biomed. Opt. 12, 051403 (2007).
[CrossRef]

Ni, X.

Niclass, C.

C. Niclass, C. Favi, T. Kluter, M. Gersbach, and E. Charbon, “A 128×128 single-photon image sensor with column-level 10 bit time-to-digital converter array,” IEEE J. Solid-State Circuits 43, 2977–2989 (2008).
[CrossRef]

Oldenburg, A. L.

A. M. Zysk, F. T. Nguyen, A. L. Oldenburg, D. L. Marks, and S. A. Boppart, “Optical coherence tomography: a review of clinical development from bench to bedside,” J. Biomed. Opt. 12, 051403 (2007).
[CrossRef]

Phillips, K. G.

Pifferi, A.

A. Torricelli, A. Pifferi, L. Spinelli, R. Cubeddu, F. Martelli, S. Del Bianco, and G. Zaccanti, “Time-resolved reflectance at null source-detector separation: improving contrast and resolution in diffuse optical imaging,” Phys. Rev. Lett. 95, 078101 (2005).
[CrossRef]

Puliafito, C. A.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef]

Schuman, J. S.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef]

Schweiger, M.

M. Schweiger, A. Gibson, and S. R. Arridge, “Computational aspects of diffuse optical tomography,” Comput. Sci. Eng. 5, 33–41 (2003).
[CrossRef]

Simon, K.

Šormaz, M.

Spinelli, L.

A. Torricelli, A. Pifferi, L. Spinelli, R. Cubeddu, F. Martelli, S. Del Bianco, and G. Zaccanti, “Time-resolved reflectance at null source-detector separation: improving contrast and resolution in diffuse optical imaging,” Phys. Rev. Lett. 95, 078101 (2005).
[CrossRef]

Stamm, T.

Stinson, W. G.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef]

Swanson, E. A.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef]

Torricelli, A.

A. Torricelli, A. Pifferi, L. Spinelli, R. Cubeddu, F. Martelli, S. Del Bianco, and G. Zaccanti, “Time-resolved reflectance at null source-detector separation: improving contrast and resolution in diffuse optical imaging,” Phys. Rev. Lett. 95, 078101 (2005).
[CrossRef]

Vöge, M.

Xu, M.

Zaccanti, G.

A. Torricelli, A. Pifferi, L. Spinelli, R. Cubeddu, F. Martelli, S. Del Bianco, and G. Zaccanti, “Time-resolved reflectance at null source-detector separation: improving contrast and resolution in diffuse optical imaging,” Phys. Rev. Lett. 95, 078101 (2005).
[CrossRef]

Zysk, A. M.

A. M. Zysk, F. T. Nguyen, A. L. Oldenburg, D. L. Marks, and S. A. Boppart, “Optical coherence tomography: a review of clinical development from bench to bedside,” J. Biomed. Opt. 12, 051403 (2007).
[CrossRef]

Comput. Sci. Eng.

M. Schweiger, A. Gibson, and S. R. Arridge, “Computational aspects of diffuse optical tomography,” Comput. Sci. Eng. 5, 33–41 (2003).
[CrossRef]

IEEE J. Solid-State Circuits

C. Niclass, C. Favi, T. Kluter, M. Gersbach, and E. Charbon, “A 128×128 single-photon image sensor with column-level 10 bit time-to-digital converter array,” IEEE J. Solid-State Circuits 43, 2977–2989 (2008).
[CrossRef]

J. Biomed. Opt.

M. Šormaz, T. Stamm, and P. Jenny, “Influence of linear birefringence in the computation of scattering phase functions,” J. Biomed. Opt. 15, 055010 (2010).
[CrossRef]

A. M. Zysk, F. T. Nguyen, A. L. Oldenburg, D. L. Marks, and S. A. Boppart, “Optical coherence tomography: a review of clinical development from bench to bedside,” J. Biomed. Opt. 12, 051403 (2007).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Express

Opt. Lett.

Phys. Med. Biol.

A. P. Gibson, J. C. Hebden, and S. R. Arridge, “Recent advances in diffuse optical imaging,” Phys. Med. Biol. 50, R1–R43(2005).
[CrossRef]

Phys. Rev. E

W. Cai, X. Ni, S. K. Gayen, and R. R. Alfano, “Analytical cumulant solution of the vector radiative transfer equation investigates backscattering of circularly polarized light from turbid media,” Phys. Rev. E 74, 056605 (2006).
[CrossRef]

Phys. Rev. Lett.

A. Torricelli, A. Pifferi, L. Spinelli, R. Cubeddu, F. Martelli, S. Del Bianco, and G. Zaccanti, “Time-resolved reflectance at null source-detector separation: improving contrast and resolution in diffuse optical imaging,” Phys. Rev. Lett. 95, 078101 (2005).
[CrossRef]

PIERS Online

M. Šormaz and P. Jenny, “Subsurface imaging with NIR light using polarization gating,” PIERS Online 7, 595–600 (2011).
[CrossRef]

Rep. Prog. Phys.

A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, “Optical coherence tomography-principles and applications,” Rep. Prog. Phys. 66, 239–303 (2003).
[CrossRef]

Science

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef]

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Figures (9)

Fig. 1.
Fig. 1.

Simulation setup with the semi-infinite phantom and the spherical target with diameter D and the center placed at depth zc on the line along the incident laser beam. Average photon trajectories t1 and t2 have the same length. Point of incidence of the laser beam is denoted by O, while points P1 and P2 represent depths along the incident laser beam at which the contrast gradient is plotted. The reached depth of trajectories t1 and t2 is zit, while d is the distance from the point of incidence till the outgoing position of detected light.

Fig. 2.
Fig. 2.

Trajectories generated using model 1, which satisfy the condition ϵl<1%. Only trajectories which pass through the target are plotted. The target is placed in phantom 1 at zc=30ls with D=4ls.

Fig. 3.
Fig. 3.

Trajectories generated using model 2, which satisfy the condition ϵl<1%. Only trajectories which pass through the target are plotted. The target is placed in phantom 1 at zc=10ls with D=2ls.

Fig. 4.
Fig. 4.

Photon trajectories contributing to the (|d|, t)-bins for which ϵl<1% using model 1. The turbid medium is phantom 1 and the light incident at point (0, 0, 0) is un-polarized. The trajectories of detected photons coming out of the sample within 10ls<|d|30ls and 0ps<t400ps are plotted. Only trajectories with reached depths between 2.49–2.5 cm are shown. The number of simulated particles is 105. Note that different but arbitrary colors were assigned to the individual trajectories in order to better distinguish them among each other.

Fig. 5.
Fig. 5.

Photon trajectories in phantom 1 for (a) and (b) unpolarized and (c) and (d) circularly polarized incident light are drawn with solid lines; in (c) and (d) co- and cross-polarized light are detected, respectively, such that only particles with V-values of the Stokes vector 0.45 (co-polarized) and 0.55 (cross-polarized) are accepted. Trajectories generated using model 1 [in (a), (b), and (d)] and model 2 [in (c)] satisfy ϵl<5% and are drawn as dashed lines. In (a) all trajectories come out of the sample at 19ls<|d|20ls with 0ps<t200ps, while in (b) and (c) 19ls<|d|20ls and 160ps<t180ps. In (d) 4ls<|d|5ls and 80ps<t100ps. The light is incident at point x1,2=0 and the number of simulated particles is 5×105. In (a), (b), and (c) the same number of trajectories is shown (171). Note that different but arbitrary colors were assigned to the individual trajectories in order to better distinguish them among each other.

Fig. 6.
Fig. 6.

Results for phantom 1. (a) Contrast gradient plotted at the intersection of the trajectories generated using Eq. (2) with the x3-axis for three considered cases (see Table 1). (b) Error ϵz of detected particles satisfying ϵl<5%. (c) Average number of scattering events. (d) Average reached depth (ls).

Fig. 7.
Fig. 7.

Results for phantom 2. (a) Contrast gradient plotted at the intersection of the trajectories generated using Eq. (2) with the x3-axis for three considered cases (see Table 1). (b) Error ϵz of detected particles satisfying ϵl<5%. (c) Average number of scattering events. (d) Average reached depth (ls).

Fig. 8.
Fig. 8.

Results for phantom 1. (a) Co-polarized light CO. (b) Cross-polarized light CROSS. (c) Average co-polarized light CO. (d) Average cross-polarized light CROSS.

Fig. 9.
Fig. 9.

Contrast gradient plotted at the intersection of the trajectories generated using Eq. (2) with the x3-axis for three considered cases (see Table 1). Grayscale values for cs1-cross are 0.015.

Tables (1)

Tables Icon

Table 1. Overview of all Considered Test Casesa

Equations (4)

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

C=I0II0,
x1=|d|2+(1+a1·sina2(m))·|d|2·cos(m),x2=0andx3=zit·sina3(m).
C=CO0COCO0,
C=CROSS0CROSSCROSS0,

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