Abstract

A Monte Carlo model was used to analyze the propagation of polarized light in linearly birefringent turbid media, such as fibrous tissues. Linearly and circularly polarized light sources were used to demonstrate the change of polarizations in turbid media with different birefringent parameters. Videos of spatially distributed polarization states of light backscattered from or propagating in birefringent media are presented.

© Optical Society of America

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References

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  1. A. Ambirajan and D. C. Look, "A backward Monte Carlo study of the multiple scattering of a polarized laser beam," J. Quant. Spectrosc. Transfer 58, 171-192(1997).
    [CrossRef]
  2. M. J. Rakovic, G. W. Kattawar, M. Mehrubeoglu, B. D. Cameron, L. V. Wang, S. Rastegar and G. L. Cote, "Light backscattering polarization patterns from turbid media: theory and experiment," Appl. Opt. 38, 3399-3408(1999).
    [CrossRef]
  3. S. Bartel and A. H. Hielscher, "Monte Carlo simulations of the diffuse backscattering Mueller matrix for highly scattering media," Appl. Opt. 39, 1580-1588(2000).
    [CrossRef]
  4. G. Yao and L. V. Wang, "Propagation of polarized light in turbid media: simulated animation sequences," Opt. Express 7, 198-203 (2000). http://www.opticsexpress.org/oearchive/source/23140.htm.
    [CrossRef] [PubMed]
  5. J. F. deBoer, T. E. Milner, M. J. C. van Gemert and J. S. Nelson, "Two-dimensional birefringence imaging in biological tissue by polarization-sensitive optical coherence tomography," Opt. Lett. 22, 934-936(1997).
    [CrossRef] [PubMed]
  6. M. J. Everett, K. Schoenenberger, B. W. Colston, Jr. and L. B. Da Silva, "Birefringence characterization of biological tissue by use of optical coherence tomography," Opt. Lett. 23, 228-230(1998).
    [CrossRef]
  7. G. Yao and L. V. Wang, "Two-dimensional depth-resolved Mueller matrix characterization of biological tissue by optical coherence tomography," Opt. Lett. 24, 537-539 (1999).
    [CrossRef]
  8. S. L. Jiao, G. Yao and L. V. Wang, "Depth-resolved two-dimensional Stokes vectors of backscattered light and Mueller matrices of biological tissue by optical coherence tomography," Appl. Opt. 39, 6318-6324 (2000).
    [CrossRef]
  9. H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).
  10. J. F. de Boer, T. E. Milner, and J. S. Nelson, "Determination of the depth-resolved Stokes parameters of light backscattered from turbid media by use of polarization-sensitive optical coherence tomography," Opt. Lett. 24, 300-302 (1999).
    [CrossRef]

Other (10)

A. Ambirajan and D. C. Look, "A backward Monte Carlo study of the multiple scattering of a polarized laser beam," J. Quant. Spectrosc. Transfer 58, 171-192(1997).
[CrossRef]

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

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

G. Yao and L. V. Wang, "Propagation of polarized light in turbid media: simulated animation sequences," Opt. Express 7, 198-203 (2000). http://www.opticsexpress.org/oearchive/source/23140.htm.
[CrossRef] [PubMed]

J. F. deBoer, T. E. Milner, M. J. C. van Gemert and J. S. Nelson, "Two-dimensional birefringence imaging in biological tissue by polarization-sensitive optical coherence tomography," Opt. Lett. 22, 934-936(1997).
[CrossRef] [PubMed]

M. J. Everett, K. Schoenenberger, B. W. Colston, Jr. and L. B. Da Silva, "Birefringence characterization of biological tissue by use of optical coherence tomography," Opt. Lett. 23, 228-230(1998).
[CrossRef]

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

S. L. Jiao, G. Yao and L. V. Wang, "Depth-resolved two-dimensional Stokes vectors of backscattered light and Mueller matrices of biological tissue by optical coherence tomography," Appl. Opt. 39, 6318-6324 (2000).
[CrossRef]

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

J. F. de Boer, T. E. Milner, and J. S. Nelson, "Determination of the depth-resolved Stokes parameters of light backscattered from turbid media by use of polarization-sensitive optical coherence tomography," Opt. Lett. 24, 300-302 (1999).
[CrossRef]

Supplementary Material (24)

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Figures (11)

Fig. 1.
Fig. 1.

Geometry of a multiple scattering event in a linearly birefringent turbid medium.

Fig. 2.
Fig. 2.

DOLP patterns of backscattered light from (a) an isotropic turbid medium and (b)–(e) birefringent turbid media. The incident light is linearly polarized with the polarization oriented at the x-axis. Orientations of the birefringent slow axes of the turbid media are along the x-axis, y-axis, z-axis, and 45° in the x-y plane for the results in (b) to (e), respectively.

Fig. 3.
Fig. 3.

DOCP patterns of backscattered light from (a) an isotropic turbid medium and (b)–(e) birefringent turbid media. The incident light is right-circularly polarized. Orientations of the birefringent slow axes of the turbid media are along the x-axis, y-axis, z-axis, and 45° in the x-y plane for the results in (b) to (e), respectively.

Fig. 4.
Fig. 4.

DOCP of backscattered light vs. the source-detector distance. Incident light is right-circularly polarized. The blue circles are the results for the birefringent turbid medium with the slow axis oriented along the z-axis in the laboratory coordinate; the red squares are the results for an isotropic turbid medium for comparison.

Fig. 5.
Fig. 5.

(a) Time-resolved DOLP of backscattered light from birefringent turbid media with the slow axes oriented along the 45° in the x-y plane. Incident light is linearly polarized with the polarization oriented at the x-axis. (b) Time-resolved DOCP of backscattered light from birefringent turbid media with the slow axes oriented along the cross section of z-axis. Incident light is right-circularly polarized.

Fig. 6.
Fig. 6.

(880 KB) Videos of the DOLP of the backscattered light from (a) an isotropic turbid medium and (b)–(d) birefringent turbid media with the slow axes oriented along the x-axis, z-axis and 45° angle in the x-y plane, respectively. Incident light is linearly polarized with the polarization oriented at the x-axis. [Media 1] [Media 2] [Media 3] [Media 4]

Fig. 7.
Fig. 7.

(880 KB) Videos of the DOCP of the backscattered light from (a) an isotropic turbid medium and (b)–(d) birefringent turbid media with the slow axes oriented along the x-axis, z-axis and 45° angle in the x-y plane, respectively. Incident light is right-circularly polarized. [Media 5] [Media 6] [Media 7] [Media 8]

Fig. 8.
Fig. 8.

(2,462 KB) Videos of the DOLP propagations in (a) an isotropic turbid medium and (b)–(e) birefringent turbid media with the slow axes oriented along the x-axis, y-axis, z-axis and 45° angle in the x-y plane, respectively. Incident light is linearly polarized with the polarization oriented at the x-axis. [Media 9] [Media 10] [Media 11] [Media 12] [Media 13]

Fig. 9.
Fig. 9.

(2,462 KB) Videos of the DOCP propagations in (a) an isotropic turbid medium and (b)–(e) birefringent turbid media with the slow axes oriented along the x-axis, y-axis, z-axis and 45° angle in the x-y plane, respectively. Incident light is right-circularly polarized. [Media 14] [Media 15] [Media 16] [Media 17] [Media 18]

Fig. 10.
Fig. 10.

(1,935 KB) Videos of the (a) DOP, (b) DOLP and (c) DOCP propagations in a turbid medium with a two-layer structure. The upper layer is a birefringent turbid medium with the slow axis oriented along the y-axis; the thickness is 0.4 mm; the lower layer is a birefringent turbid medium with the slow axis oriented along the x-axis; the thickness is 0.6 mm. Incident light is linearly polarized with the polarization oriented along the x-axis. [Media 19] [Media 20] [Media 21]

Fig. 11.
Fig. 11.

(1,935 KB) Videos of the (a) DOP, (b) DOLP and (c) DOCP propagations in a turbid medium with a two-layer structure. The upper layer is a birefringent turbid medium with the slow axis oriented along the y-axis; the thickness is 0.4 mm; the lower layer is a birefringent turbid medium with the slow axis oriented along the x-axis; the thickness is 0.6 mm. Incident light is right-circularly polarized. [Media 22] [Media 23] [Media 24]

Equations (6)

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S n bs ( x ' , y ' ; μ s , μ a , δ ) = [ μ s ( μ a + μ s ) ] n × R ( ϕ n ) T ( Δ n , β n ) M ( Θ n ) R ( ϕ n 1 n )
× T ( Δ 2 , β 2 ) M ( Θ 2 ) R ( ϕ 12 ) T ( Δ 1 , β 1 ) M ( Θ 1 ) R ( ϕ 1 ) T ( Δ 0 , β 0 ) S 0 ,
T ( Δ , β ) = [ 1 0 0 0 0 C 4 sin 2 ( Δ 2 ) + cos 2 ( Δ 2 ) S 4 sin 2 ( Δ 2 ) S 2 sin ( Δ ) 0 S 4 sin 2 ( Δ 2 ) C 4 sin 2 ( Δ 2 ) + cos 2 ( Δ 2 ) C 2 sin ( Δ ) 0 S 2 sin ( Δ ) C 2 sin ( Δ ) cos ( Δ ) ] ,
C 2 = cos ( 2 β ) , C 4 = cos ( 4 β ) , S 2 = sin ( 2 β ) , S 4 = sin ( 4 β ) .
Δ = ( Δ n ) × 2 π s λ ,
Δ n = n s n f / ( n s cos α ) 2 + ( n f sin α ) 2 n f .

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