Abstract

Recent approaches to the analysis of biological samples with three-dimensional linear birefringence orientation require numerical methods to estimate the best fit parameters from experimental measures. We present a novel analytical method for characterizing the intrinsic retardance and the three-dimensional optic axis orientation of uniform and uniaxial turbid media. It is based on a model that exploits the recently proposed differential generalized Jones calculus, remarkably suppressing the need for numerical procedures. The method is applied to the analysis of samples modeled with polarized sensitive Monte Carlo. The results corroborate its capacity to successfully characterize 3D linear birefringence in a straightforward way.

© 2013 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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2013 (1)

2012 (1)

2011 (5)

2010 (2)

2006 (2)

2005 (1)

2002 (3)

X. Wang and L. V. Wang, “Propagation of polarized light in birefringent turbid media: A Monte Carlo study,” J. Biomed. Opt.7(3), 279–290 (2002).
[CrossRef] [PubMed]

S. Jiao and L. V. Wang, “Jones-matrix imaging of biological tissues with quadruple-channel optical coherence tomography,” J. Biomed. Opt.7(3), 350–358 (2002).
[CrossRef] [PubMed]

S. Jiao and L. V. Wang, “Two-dimensional depth-resolved Mueller matrix of biological tissue measured with double-beam polarization-sensitive optical coherence tomography,” Opt. Lett.27(2), 101–103 (2002).
[CrossRef] [PubMed]

1999 (1)

1996 (1)

1948 (1)

Arce-Diego, J. L.

Azzam, R. M. A.

Barakat, R.

Dainty, C.

Fanjul-Vélez, F.

Gangnus, S. V.

García-Caurel, E.

Ghosh, N.

Haj-Ibrahim, B.

Jacques, S. L.

Jiao, S.

S. Jiao and L. V. Wang, “Two-dimensional depth-resolved Mueller matrix of biological tissue measured with double-beam polarization-sensitive optical coherence tomography,” Opt. Lett.27(2), 101–103 (2002).
[CrossRef] [PubMed]

S. Jiao and L. V. Wang, “Jones-matrix imaging of biological tissues with quadruple-channel optical coherence tomography,” J. Biomed. Opt.7(3), 350–358 (2002).
[CrossRef] [PubMed]

Jones, C. R.

Lara, D.

Matcher, S. J.

Ortega-Quijano, N.

Ossikovski, R.

Prahl, S. A.

Ramella-Roman, J. C.

Ugryumova, N.

Vitkin, I. A.

Wallenburg, M. A.

Wang, L. V.

S. Jiao and L. V. Wang, “Jones-matrix imaging of biological tissues with quadruple-channel optical coherence tomography,” J. Biomed. Opt.7(3), 350–358 (2002).
[CrossRef] [PubMed]

X. Wang and L. V. Wang, “Propagation of polarized light in birefringent turbid media: A Monte Carlo study,” J. Biomed. Opt.7(3), 279–290 (2002).
[CrossRef] [PubMed]

S. Jiao and L. V. Wang, “Two-dimensional depth-resolved Mueller matrix of biological tissue measured with double-beam polarization-sensitive optical coherence tomography,” Opt. Lett.27(2), 101–103 (2002).
[CrossRef] [PubMed]

G. Yao and L. V. Wang, “Two-dimensional depth-resolved Mueller matrix characterization of biological tissue by optical coherence tomography,” Opt. Lett.24(8), 537–539 (1999).
[CrossRef] [PubMed]

Wang, X.

X. Wang and L. V. Wang, “Propagation of polarized light in birefringent turbid media: A Monte Carlo study,” J. Biomed. Opt.7(3), 279–290 (2002).
[CrossRef] [PubMed]

Wood, M. F. G.

Yao, G.

Appl. Opt. (1)

J. Biomed. Opt. (3)

S. Jiao and L. V. Wang, “Jones-matrix imaging of biological tissues with quadruple-channel optical coherence tomography,” J. Biomed. Opt.7(3), 350–358 (2002).
[CrossRef] [PubMed]

N. Ghosh and I. A. Vitkin, “Tissue polarimetry: concepts, challenges, applications, and outlook,” J. Biomed. Opt.16(11), 110801 (2011).
[CrossRef] [PubMed]

X. Wang and L. V. Wang, “Propagation of polarized light in birefringent turbid media: A Monte Carlo study,” J. Biomed. Opt.7(3), 279–290 (2002).
[CrossRef] [PubMed]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (2)

Opt. Express (3)

Opt. Lett. (8)

N. Ortega-Quijano and J. L. Arce-Diego, “Mueller matrix differential decomposition,” Opt. Lett.36(10), 1942–1944 (2011).
[CrossRef] [PubMed]

F. Fanjul-Vélez and J. L. Arce-Diego, “Polarimetry of birefringent biological tissues with arbitrary fibril orientation and variable incidence angle,” Opt. Lett.35(8), 1163–1165 (2010).
[CrossRef] [PubMed]

N. Ugryumova, S. V. Gangnus, and S. J. Matcher, “Three-dimensional optic axis determination using variable-incidence-angle polarization-optical coherence tomography,” Opt. Lett.31(15), 2305–2307 (2006).
[CrossRef] [PubMed]

M. A. Wallenburg, M. F. G. Wood, N. Ghosh, and I. A. Vitkin, “Polarimetry-based method to extract geometry-independent metrics of tissue anisotropy,” Opt. Lett.35(15), 2570–2572 (2010).
[CrossRef] [PubMed]

N. Ortega-Quijano and J. L. Arce-Diego, “Depolarizing differential Mueller matrices,” Opt. Lett.36(13), 2429–2431 (2011).
[CrossRef] [PubMed]

R. Ossikovski, “Differential matrix formalism for depolarizing anisotropic media,” Opt. Lett.36(12), 2330–2332 (2011).
[CrossRef] [PubMed]

S. Jiao and L. V. Wang, “Two-dimensional depth-resolved Mueller matrix of biological tissue measured with double-beam polarization-sensitive optical coherence tomography,” Opt. Lett.27(2), 101–103 (2002).
[CrossRef] [PubMed]

G. Yao and L. V. Wang, “Two-dimensional depth-resolved Mueller matrix characterization of biological tissue by optical coherence tomography,” Opt. Lett.24(8), 537–539 (1999).
[CrossRef] [PubMed]

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Figures (2)

Fig. 1
Fig. 1

a) Measured polar angles of the optic axis for all the samples. b) Measured optic axis azimuthal angles. In both cases, the dotted lines are where the calculated values should fall on.

Fig. 2
Fig. 2

Measured intrinsic (diamonds) and effective (squares) retardance. The dotted lines are where the calculated values should fall on. Results are averaged for the four azimuthal angles.

Equations (17)

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d E / dl =g E ,
g LR z =( 1/ 3 ) η q z O 4 =diag( i η q z /3 , i η q z /3 , i2 η q z /3 ),
O 4 =( 1/ 3 )diag( 1,1,2 ).
g LR =C( θ,ϕ ) g LR z C 1 ( θ,ϕ ),
C( θ,ϕ )=[ sinϕ cosθcosϕ sinθcosϕ cosϕ cosθsinϕ sinθsinϕ 0 sinθ cosθ ],
j=[ g( 1,1 ) g( 1,2 ) g( 2,1 ) g( 2,2 ) ].
j LR =i[ Δη 2 ( cos 2 ϕcos2θ 1 2 cos2ϕ+ 1 6 ) Δηcosϕsinϕ sin 2 θ Δηcosϕsinϕ sin 2 θ Δη 2 ( sin 2 ϕcos2θ+ 1 2 cos2ϕ+ 1 6 ) ].
m ¯ =logm( M ),
m ¯ nd = 1 2 ( m ¯ G m ¯ T G ),
φ= 1 2 atan( δ u δ q ),
δ ef = ( δ q 2 + δ u 2 ) 1/2 .
m nd =A( j j * ) A 1 ,
m ¯ LR =[ 0 0 0 0 0 0 0 δsin2ϕ sin 2 θ 0 0 0 δcos2ϕ sin 2 θ 0 δsin2ϕ sin 2 θ δcos2ϕ sin 2 θ 0 ],
δ ef =δ sin 2 θ.
δ 1 ef =δ sin 2 ( θ χ 1 ) δ 2 ef =δ sin 2 ( θ χ 2 ) .
θ=atan[ Dsin χ 2 sin χ 1 Dcos χ 2 cos χ 1 ],
δ= ( δ 1 ef δ 2 ef ) 1/2 sin( θ χ 1 )sin( θ χ 2 ) .

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