Abstract

The depolarization property of a biomedium with anisotropic biomolecule optical scattering is investigated theoretically. By using a simple ellipsoid model of a single biomolecule, the scattering fields and Mueller matrices are derived from fundamental electromagnetism theory. The biomedium is modeled as a system of uncorrelated anisotropic molecules. On the basis of a statistical model of anisotropic molecular distribution, the scattering depolarization of the biomedium is investigated. Simulated results of the molecular shape and orientation dependent single scattering depolarization D1 and the double scattering depolarization D2 are reported. The D2 contribution is found to be more important for higher-density scattering media. The depolarizations of the forward single and double scattering of a model cell membrane are simulated and discussed. The fitting to a single tetra-methylrhodamine-labeled lipid molecule’s anisotropic imaging experiment has demonstrated that large depolarization arises for the membrane to which the fluorescence emitting molecule is attached. This theory can provide a simulation analysis tool for investigating the scattering polarization/depolarization effect and the photon density wave transport property of a highly scattering biomedium.

© 2009 Optical Society of America

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References

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2008 (1)

2004 (1)

2001 (1)

1999 (1)

G. S. Harms, M. Sonnleitner, G. S. Schutz, H. J. Gruber, and T. Schmidt, “Single-molecule anisotropy imaging,” Biophys. J. 77, 2864-2870 (1999).
[CrossRef] [PubMed]

1993 (1)

1989 (1)

1983 (1)

Andreola, S.

Bertoni, A.

Ferwerda, H. A.

Ghosh, N.

Groenhuis, R. A. J.

Gruber, H. J.

G. S. Harms, M. Sonnleitner, G. S. Schutz, H. J. Gruber, and T. Schmidt, “Single-molecule anisotropy imaging,” Biophys. J. 77, 2864-2870 (1999).
[CrossRef] [PubMed]

Gupta, P. K.

Harms, G. S.

G. S. Harms, M. Sonnleitner, G. S. Schutz, H. J. Gruber, and T. Schmidt, “Single-molecule anisotropy imaging,” Biophys. J. 77, 2864-2870 (1999).
[CrossRef] [PubMed]

Haskell, R. C.

Huang, Y.-S.

Majumder, S. K.

Marchesini, R.

Mohanty, S. K.

Nee, S.-M. F.

Nee, T.-W.

Schmidt, T.

G. S. Harms, M. Sonnleitner, G. S. Schutz, H. J. Gruber, and T. Schmidt, “Single-molecule anisotropy imaging,” Biophys. J. 77, 2864-2870 (1999).
[CrossRef] [PubMed]

Schutz, G. S.

G. S. Harms, M. Sonnleitner, G. S. Schutz, H. J. Gruber, and T. Schmidt, “Single-molecule anisotropy imaging,” Biophys. J. 77, 2864-2870 (1999).
[CrossRef] [PubMed]

Sichirollo, A. E.

Sonnleitner, M.

G. S. Harms, M. Sonnleitner, G. S. Schutz, H. J. Gruber, and T. Schmidt, “Single-molecule anisotropy imaging,” Biophys. J. 77, 2864-2870 (1999).
[CrossRef] [PubMed]

Svaasand, L. O.

Ten Bosch, J. J.

Tromberg, B. J.

Tsai, T. T.

Tuchin, V. V.

V. V. Tuchin, Tissue Optics (SPIE Press, 2007).
[CrossRef]

Yang, D.-M.

Appl. Opt. (4)

Biophys. J. (1)

G. S. Harms, M. Sonnleitner, G. S. Schutz, H. J. Gruber, and T. Schmidt, “Single-molecule anisotropy imaging,” Biophys. J. 77, 2864-2870 (1999).
[CrossRef] [PubMed]

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

Other (2)

S.-M. F. Nee, “Polarization measurement,” in The Measurement, Instrumentation and Sensors Handbook, J.G.Webster, ed (CRC Press and IEEE Press, 1999), pp. 60.1-60.24.

V. V. Tuchin, Tissue Optics (SPIE Press, 2007).
[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

Single scattering by an ensemble of scattering molecules at the scattering center.

Fig. 2
Fig. 2

Double scattering by an ensemble of scattering molecules at the scattering center.

Fig. 3
Fig. 3

For S i = I i ( 1 , 0 , 0 , 1 ) , ( θ i , φ i ) = ( 0 , 0 ) , φ s = 0 , ε = 1.1896 , θ d = 0 ° 180 ° , φ d = 0 ° 360 ° ; upper: D 1 versus u for θ s = 0 ° (solid curve), 60° (dashed-dotted curve); lower: D 1 versus θ s curves for u = 5 , 4 , 3 , 2 , 1 are in order.

Fig. 4
Fig. 4

For S i = I i ( 1 , 0 , 0 , 1 ) , ( θ i , φ i ) = ( θ s , φ s ) = ( 0 ° , 0 ° ) , ε = 1.1896 , θ d = 0 ° 180 ° , φ d = 0 ° 360 ° , φ o = 0 ° 360 ° ; upper: D 2 versus u for θ o = 0 ° 20 ° (dotted–dashed curve) and 0°–2° (solid curve); lower: D 2 versus u curves for θ o = 90 ° , Δ θ o = 2 ° , 20 ° , 60 ° , 180 ° are in order.

Fig. 5
Fig. 5

For S i = I i ( 1 , 0 , 0 , 1 ) , ( θ i , φ i ) = ( θ s , φ s ) = ( 0 ° , 0 ° ) , ε = 1.1896 , θ d = 0 ° 180 ° , φ d = 0 ° 360 ° , φ o = 0 ° 360 ° , u ( b a ) = 5 ; D 2 versus θ o curves for Δ θ o = 2 ° , 60 ° , 120 ° , 180 ° are in order.

Fig. 6
Fig. 6

For ( θ i , φ i ) = ( 0 ° , 0 ° ) , ε = 1.1896 , θ d = 0 ° 180 ° , φ d = 0 ° 360 ° , θ o = 0 ° 180 , φ o = 0 ° 360 ° , φ s = 0 ° , b a = 4 ; total depolarization D versus θ s curves for r a r o = 1 (upper) and r a r o = 10 (lower). Results of S i = I i ( 1 , 1 , 0 , 0 ) , I i ( 1 , 0 , 0 , 1 ) , I i ( 1 , 0 , 1 , 0 ) , I i ( 1 , 1 , 0 , 0 ) are in order.

Fig. 7
Fig. 7

TMR-DPPE membrane–molecule structure shown in Fig. 1 of [5].

Fig. 8
Fig. 8

As the membrane contribution is included, the detailed algorithm is shown for calculating the scattering signal S s for the experiment of [5].

Tables (2)

Tables Icon

Table 1 Scattering Depolarization for Incident Light with Six Polarizations and Five η a Values a

Tables Icon

Table 2 Fitted Membrane Parameters for the Scattering Experiment of [5] a

Equations (34)

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J ( r , θ s , φ s , θ d , φ d , θ i , φ i ) = J o u ( ϵ 1 ) 1 + q x ( ϵ 1 ) [ cos θ s cos φ s cos θ s sin φ s sin θ s sin φ s cos φ s 0 ] × [ 1 + ( β 1 ) sin 2 θ d cos 2 φ d ( β 1 ) sin 2 θ d sin φ d cos φ d ( β 1 ) cos θ d sin θ d cos φ d ( β 1 ) sin 2 θ d sin φ d cos φ d 1 + ( β 1 ) sin 2 θ d sin 2 φ d ( β 1 ) cos θ d sin θ d sin φ d ( β 1 ) cos θ d sin θ d cos φ d ( β 1 ) cos θ d sin θ d sin φ d 1 + ( β 1 ) cos 2 θ d ] × [ cos θ i cos φ i sin φ i cos θ i sin φ i cos φ i sin θ i 0 ] ,
J o = r a r ,
r a = 4 π 2 a 3 3 λ s 2 .
( I s Q s U s V s ) ( r , θ s , φ s , θ d , φ d , θ i , φ i ) = M o ( r , θ s , φ s , θ d , φ d , θ i , φ i ) ( I i Q i U i V i ) .
S s ( r , θ s , φ s , θ i φ i ) = M tot ( r , θ s , φ s , θ i , φ i ) S i ( θ i , φ i ) ,
M tot ( r , θ s , φ s , θ i , φ i ) = M 1 ( r , θ s , φ s , θ i , φ i ) + M 2 ( r , θ s , φ s , θ i , φ i ) + .
P s = Q s 2 + U s 2 + V s 2 I s .
D ( γ , χ ) = 1 P s ( γ , χ ) .
0 4 π f d ( θ d , φ d ) d Ω d = 0 π d θ d sin θ d 0 2 π d φ d f d ( θ d , φ d ) = 1 .
M 1 ( r , θ s , φ s , θ i , φ i ) = 0 π d θ d sin θ d 0 2 π d φ d f d ( θ d , φ d ) M o ( r , θ s , φ s , θ d , φ d , θ i , φ i ) .
M 2 ( r , θ s , φ s , r o , θ o , φ o , θ i , φ i ) = M 1 ( r , θ s , φ s , θ o , φ o ) M 1 ( r o , θ o , φ o , θ i , φ i ) .
M 2 ( r , θ s , φ s , r o , θ i , φ i ) = 0 π d θ o sin θ o 0 2 π d φ o f o ( θ o , φ o ) M 1 ( r , θ s , φ s , θ o , φ o ) M 1 ( r o , θ o , φ o , θ i , φ i ) .
f d ( θ d , φ d ) = { f do for θ d ( a ) < θ d < θ d ( b ) and φ d ( a ) < φ d < φ d ( b ) 0 otherwise } ,
f do 1 = θ d ( a ) θ d ( b ) sin θ d d θ d φ d ( a ) φ d ( b ) d φ d .
f o ( θ o , φ o ) = { f oo for θ o ( a ) < θ o < θ o ( b ) and φ o ( a ) < φ o < φ o ( b ) 0 otherwise } ,
f oo 1 = θ o ( a ) θ o ( b ) sin θ o d θ o φ o ( a ) φ o ( b ) d φ o .
m ( θ s , φ s , θ i , φ i ) = M ( r , θ s , φ s , θ i , φ i ) r 2 r a 2 ,
m 1 ( θ s , φ s , θ i , φ i ) = M 1 ( r , θ s , φ s , θ i , φ i ) r 2 r a 2 ,
m 2 ( θ s , φ s , r o , θ i , φ i ) = r a 2 r o 2 0 π d θ o sin θ o 0 2 π d φ o f o ( θ o , φ o ) m 1 ( θ s , φ s , θ o , φ o ) m 1 ( θ o , φ o , θ i , φ i ) ,
m tot ( θ s , φ s , r o , θ i , φ i ) = m 1 ( θ s , φ s , θ i , φ i ) + m 2 ( θ s , φ s , r o , θ i , φ i ) + .
m 1 ( θ s , φ s , θ i , φ i ) = 0.767 [ 1 m a m b 0 m a 1 m c 0 m b m c 1 0 0 0 0 1 ] ,
m 2 ( θ s , φ s , r o , θ i , φ i ) = 0.353 η a 2 [ 1 0 0 0 0 0.778 0 0 0 0 0.778 0 0 0 0 0.556 ] ,
S s = M tot S i ,
M tot = M mem M mol M mem .
M mem = 232.8 r a 2 r d 2 [ 1 0 0 0 0 0.5877 0 0 0 0 0.5877 0 0 0 0 0.1754 ] ,
M mol = 1.495 r a 2 r d 2 [ 1 0.0776 0 0 0.0776 1 0 0 0 0 0.9970 0 0 0 0 0.9970 ] ,
M mem = 232.8 r a 2 r 2 [ 1 0 0 0 0 0.5877 0 0 0 0 0.5877 0 0 0 0 0.1754 ] ,
M tot = 8.103 × 10 4 r a 6 r 2 r d 4 [ 1 0.0456 0 0 0.0456 0.3454 0 0 0 0 0.3454 0 0 0 0 0.0307 ] ,
I s = r a 2 r 2 I i ( m 11 + m 12 q i + m 13 u i + m 14 v i ) .
d σ s d Ω s = r a 2 ( m 11 + m 12 q i + m 13 u i + m 14 v i ) .
σ s = d Ω s d σ s d Ω s = r a 2 d Ω s ( m 11 + m 12 q i + m 13 u i + m 14 v i ) .
k s = ρ s σ s = ρ s r a 2 d Ω s ( m 11 + m 12 q i + m 13 u i + m 14 v i ) ,
k tot = k s + k a .
N tot = n + i k tot ,

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