Abstract

A time-resolved Monte Carlo technique was used to simulate the propagation of polarized light in turbid media. Calculated quantities include the reflection Mueller matrices, the transmission Mueller matrices, and the degree of polarization (DOP). The effects of the polarization state of the incident light and of the size of scatterers on the propagation of DOP were studied. Results are shown in animation sequences.

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References

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  1. R. R. Alfano and J. G. Fujimoto, eds., Advances in Optical Imaging and Photon Migration, Vol. 2 of Topics in Optics and Photonics Series (Optical Society of America, Washington, D. C., 1996).
  2. B. Das, K. Yoo, and R. R. Alfano, "Ultrafast time gated imaging," Opt. Lett. 18, 1092-1094(1993).
    [CrossRef] [PubMed]
  3. S. Marengo, C. Pepin, T. Goulet, and D. Houde, "Time-gated transillumination of objects in highly scattering media using a subpicosecond optical amplifier," IEEE J. Sel. Top. Quant. 5, 895-901(1999).
    [CrossRef]
  4. 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]
  5. S. P. Morgan, M. P. Khong, and M. G. Somekh, "Effects of polarization state and scatterer concentration on optical imaging through scattering media," Appl. Opt. 36, 1560-1565(1997).
    [CrossRef] [PubMed]
  6. S. L. Jacques, J. R. Roman, and K. Lee, "Imaging superficial tissues with polarized light," Lasers in Surg. & Med. 26, 119-129(2000).
    [CrossRef]
  7. X. Liang, L. Wang, P. P. Ho, and R. R. Alfano, "Time-resolved polarization shadowgrams in turbid media," Appl. Opt. 36, 2984-2989(1997).
    [CrossRef] [PubMed]
  8. D. Bicout, C. Brosseau, A. S. Martinez, and J. M. Schmitt, "Depolarization of multiply scattered waves by spherical diffusers: influence of the size parameter," Phy. Rev. E 49, 1767-1770(1994).
    [CrossRef]
  9. V. Sankaran, K. Schonenberger, J. T. Walsh, Jr., and D. J. Maitland, "Polarization discrimination of coherently propagation light in turbid media," Appl. Opt. 38, 4252-4261(1999).
    [CrossRef]
  10. M. J. Rakovic, G. W. Kattawar, M. Mehrubeoglu, B. D. Cameron, L. V. Wang, S. Rastegar, and G. L. Cot�, "Light backscattering polarization patterns from turbid media: theory and experiments," Appl. Opt. 38, 3399- 3408(1999).
    [CrossRef]
  11. S. Bartel and A. H. Hielscher, "Monte Carlo simulation of the diffuse backscattering Mueller matrix for highly scattering media," Appl. Opt. 39, 1580-1588(2000).
    [CrossRef]
  12. G. Yao and L. V. Wang, "Two dimensional depth resolved Mueller matrix measurement in biological tissue with optical coherence tomography," Opt. Lett. 24, 537-539(1999).
    [CrossRef]
  13. H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).

Other

R. R. Alfano and J. G. Fujimoto, eds., Advances in Optical Imaging and Photon Migration, Vol. 2 of Topics in Optics and Photonics Series (Optical Society of America, Washington, D. C., 1996).

B. Das, K. Yoo, and R. R. Alfano, "Ultrafast time gated imaging," Opt. Lett. 18, 1092-1094(1993).
[CrossRef] [PubMed]

S. Marengo, C. Pepin, T. Goulet, and D. Houde, "Time-gated transillumination of objects in highly scattering media using a subpicosecond optical amplifier," IEEE J. Sel. Top. Quant. 5, 895-901(1999).
[CrossRef]

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. P. Morgan, M. P. Khong, and M. G. Somekh, "Effects of polarization state and scatterer concentration on optical imaging through scattering media," Appl. Opt. 36, 1560-1565(1997).
[CrossRef] [PubMed]

S. L. Jacques, J. R. Roman, and K. Lee, "Imaging superficial tissues with polarized light," Lasers in Surg. & Med. 26, 119-129(2000).
[CrossRef]

X. Liang, L. Wang, P. P. Ho, and R. R. Alfano, "Time-resolved polarization shadowgrams in turbid media," Appl. Opt. 36, 2984-2989(1997).
[CrossRef] [PubMed]

D. Bicout, C. Brosseau, A. S. Martinez, and J. M. Schmitt, "Depolarization of multiply scattered waves by spherical diffusers: influence of the size parameter," Phy. Rev. E 49, 1767-1770(1994).
[CrossRef]

V. Sankaran, K. Schonenberger, J. T. Walsh, Jr., and D. J. Maitland, "Polarization discrimination of coherently propagation light in turbid media," Appl. Opt. 38, 4252-4261(1999).
[CrossRef]

M. J. Rakovic, G. W. Kattawar, M. Mehrubeoglu, B. D. Cameron, L. V. Wang, S. Rastegar, and G. L. Cot�, "Light backscattering polarization patterns from turbid media: theory and experiments," Appl. Opt. 38, 3399- 3408(1999).
[CrossRef]

S. Bartel and A. H. Hielscher, "Monte Carlo simulation of the diffuse backscattering Mueller matrix for highly scattering media," Appl. Opt. 39, 1580-1588(2000).
[CrossRef]

G. Yao and L. V. Wang, "Two dimensional depth resolved Mueller matrix measurement in biological tissue with optical coherence tomography," Opt. Lett. 24, 537-539(1999).
[CrossRef]

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).

Supplementary Material (5)

» Media 1: MOV (784 KB)     
» Media 2: MOV (948 KB)     
» Media 3: MOV (948 KB)     
» Media 4: MOV (784 KB)     
» Media 5: MOV (948 KB)     

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Figures (9)

Fig. 1.
Fig. 1.

The laboratory coordinate system for the simulation.

Fig. 2.
Fig. 2.

(a) Reflection and (b) transmission Mueller matrices of a slab of turbid medium.

Fig.3.
Fig.3.

(787 KB) Movie of the DOP propagation in the slab. The X axis is along the horizontal direction, and the Z axis is along the vertical direction. R: right-circularly polarized incident light. H: horizontal-linearly polarized incident light.

Fig. 4.
Fig. 4.

(950 KB) Movie of the DOP of the transmitted light with (a) R- and (b) H-polarized incident light. The X axis is along the horizontal direction, and the Y axis is along the vertical direction.

Fig.5.
Fig.5.

(950 KB) Movie of the weighted-averaged numbers of scattering events for (a) R- and (b) H-polarized incident light. The numbers of scattering events are normalized to a maximum value of 7 for the plots. The X axis is along the horizontal direction, and the Y axis is along the vertical direction.

Fig.6.
Fig.6.

(787 KB) Movie of the DOP propagation in the slab. The X axis is along the horizontal direction, and the Z axis is along the vertical direction. R: right-circularly polarized incident light. H: horizontal-linearly polarized incident light.

Fig. 7.
Fig. 7.

(950 KB) Movie of the DOP of the transmitted light with (a) R- and (b) H-polarized incident light. The X axis is along the horizontal direction, and the Y axis is along the vertical direction.

Fig. 8.
Fig. 8.

Probability density function ρ(θ) and |m 12/m 11| at a particle radius of (a) 0.051 µm and (b) 1.02 µm.

Fig. 9.
Fig. 9.

Radial distribution of the DOP of the transmitted light for different scattering coefficients. The particle radius was 1.02 µm. The incident light was H polarized.

Equations (6)

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S = M ( θ ) S ,
M ( θ ) = [ m 11 m 12 0 0 m 12 m 11 0 0 0 0 m 33 m 34 0 0 m 34 m 33 ] .
2 π 0 π m 11 ( θ ) sin ( θ ) d θ = 1 .
ρ ( θ , ϕ ) = m 11 ( θ ) + m 12 ( θ ) [ S 1 cos ( 2 ϕ ) + S 2 sin ( 2 ϕ ) ] S 0 .
ρ θ ( ϕ ) = 1 + m 12 ( θ ) m 11 ( θ ) [ S 1 cos ( 2 ϕ ) + S 2 sin ( 2 ϕ ) ] S 0 .
DOP = S 1 2 + S 2 2 + S 3 2 S 0 .

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