Abstract

We present a Monte Carlo simulation program for the propagation of polarized photons in an anisotropic scattering model consisting of poly-dispersed spherical and infinite long cylindrical scatterers. The cylinders are aligned following a Gaussian distribution. Densities and sizes of the spherical and cylindrical scatterers, as well as the orientation of the cylinders are variables for the simulation of different anisotropic media. The good agreement between the simulation and experimental results of polarization imaging confirms the validity of the polarization-dependent Monte Carlo simulation program.

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References

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2008

2007

J. D. Keener, K. J. Chalut, J. W. Pyhtila, and A. Wax, “Application of Mie theory to determine the structure of spheroidal scatterers in biological materials,” Opt. Lett. 32(10), 1326–1328 (2007).
[PubMed]

X. Y. Jiang, N. Zeng, Y. H. He, and H. Ma, “Investigation of Linear Polarization Difference Imaging Based on Rotation of Incident and Backscattered Polarization Angles,” Pro. Biochem. Biophys. 34, 659 (2007).

2006

A. Kienle and R. Hibst, “Light guiding in biological tissue due to scattering,” Phys. Rev. Lett. 97(1), 018104 (2006).
[PubMed]

2005

2004

2003

A. Kienle, F. Forster, R. Diebolder, and R. Hibst, “Light propagation in dentin: influence of microstructure on anisotropy,” Phys. Med. Biol. 48(7–N), 14 (2003).

2000

1999

1998

1995

L. H. Wang, S. L. Jacques, and L.-Q. Zheng, “MCML--Monte Carlo modeling of light transport in multi-layered tissues,” Comput. Methods Programs Biomed. 47(2), 131–146 (1995).
[PubMed]

1993

1968

Andersson-Engels, S.

Bartel, S.

Bruscaglioni, P.

Cameron, B. D.

Chalut, K. J.

Coté, G. L.

Côté, D.

D’Andrea, C.

Diebolder, R.

A. Kienle, F. Forster, R. Diebolder, and R. Hibst, “Light propagation in dentin: influence of microstructure on anisotropy,” Phys. Med. Biol. 48(7–N), 14 (2003).

Forster, F.

A. Kienle, F. Forster, R. Diebolder, and R. Hibst, “Light propagation in dentin: influence of microstructure on anisotropy,” Phys. Med. Biol. 48(7–N), 14 (2003).

Forster, F. K.

Foschum, F.

He, J.

He, Y. H.

X. Y. Jiang, N. Zeng, Y. H. He, and H. Ma, “Investigation of Linear Polarization Difference Imaging Based on Rotation of Incident and Backscattered Polarization Angles,” Pro. Biochem. Biophys. 34, 659 (2007).

Hibst, R.

A. Kienle and R. Hibst, “Light guiding in biological tissue due to scattering,” Phys. Rev. Lett. 97(1), 018104 (2006).
[PubMed]

A. Kienle, F. K. Forster, and R. Hibst, “Anisotropy of light propagation in biological tissue,” Opt. Lett. 29(22), 2617–2619 (2004).
[PubMed]

A. Kienle, F. Forster, R. Diebolder, and R. Hibst, “Light propagation in dentin: influence of microstructure on anisotropy,” Phys. Med. Biol. 48(7–N), 14 (2003).

Hielscher, A. H.

Jacques, S. L.

Jiang, X. Y.

X. Y. Jiang, N. Zeng, Y. H. He, and H. Ma, “Investigation of Linear Polarization Difference Imaging Based on Rotation of Incident and Backscattered Polarization Angles,” Pro. Biochem. Biophys. 34, 659 (2007).

Karlsson, A.

Kattawar, G. W.

Keener, J. D.

Kienle, A.

A. Kienle, C. D’Andrea, F. Foschum, P. Taroni, and A. Pifferi, “Light propagation in dry and wet softwood,” Opt. Express 16(13), 9895–9906 (2008).
[PubMed]

A. Kienle and R. Hibst, “Light guiding in biological tissue due to scattering,” Phys. Rev. Lett. 97(1), 018104 (2006).
[PubMed]

A. Kienle, F. K. Forster, and R. Hibst, “Anisotropy of light propagation in biological tissue,” Opt. Lett. 29(22), 2617–2619 (2004).
[PubMed]

A. Kienle, F. Forster, R. Diebolder, and R. Hibst, “Light propagation in dentin: influence of microstructure on anisotropy,” Phys. Med. Biol. 48(7–N), 14 (2003).

Ma, H.

X. Y. Jiang, N. Zeng, Y. H. He, and H. Ma, “Investigation of Linear Polarization Difference Imaging Based on Rotation of Incident and Backscattered Polarization Angles,” Pro. Biochem. Biophys. 34, 659 (2007).

Mehru Beo Lu, M. B.

Mehrübeoglu, M.

Pifferi, A.

Plass, G. N.

Prahl, S.

Prahl, S. A.

Pyhtila, J. W.

Rakovi, M. J.

Rakovic, M. J.

Ramella-Roman, J.

Ramella-Roman, J. C.

Rastegar, S.

Swartling, J.

Taroni, P.

Vitkin, I.

Wang, L. H.

L. H. Wang, S. L. Jacques, and L.-Q. Zheng, “MCML--Monte Carlo modeling of light transport in multi-layered tissues,” Comput. Methods Programs Biomed. 47(2), 131–146 (1995).
[PubMed]

Wang, L. V.

Wax, A.

Wei, Q.

Zaccanti, G.

Zeng, N.

X. Y. Jiang, N. Zeng, Y. H. He, and H. Ma, “Investigation of Linear Polarization Difference Imaging Based on Rotation of Incident and Backscattered Polarization Angles,” Pro. Biochem. Biophys. 34, 659 (2007).

Zheng, L.-Q.

L. H. Wang, S. L. Jacques, and L.-Q. Zheng, “MCML--Monte Carlo modeling of light transport in multi-layered tissues,” Comput. Methods Programs Biomed. 47(2), 131–146 (1995).
[PubMed]

Appl. Opt.

Comput. Methods Programs Biomed.

L. H. Wang, S. L. Jacques, and L.-Q. Zheng, “MCML--Monte Carlo modeling of light transport in multi-layered tissues,” Comput. Methods Programs Biomed. 47(2), 131–146 (1995).
[PubMed]

J. Opt. Soc. Am. A

Opt. Express

Opt. Lett.

Phys. Med. Biol.

A. Kienle, F. Forster, R. Diebolder, and R. Hibst, “Light propagation in dentin: influence of microstructure on anisotropy,” Phys. Med. Biol. 48(7–N), 14 (2003).

Phys. Rev. Lett.

A. Kienle and R. Hibst, “Light guiding in biological tissue due to scattering,” Phys. Rev. Lett. 97(1), 018104 (2006).
[PubMed]

Pro. Biochem. Biophys.

X. Y. Jiang, N. Zeng, Y. H. He, and H. Ma, “Investigation of Linear Polarization Difference Imaging Based on Rotation of Incident and Backscattered Polarization Angles,” Pro. Biochem. Biophys. 34, 659 (2007).

Other

C. F. Bohren, and D. R. Huffman, Absorption and Scattering of Light by Small Particles (John Wiley and Sons, New York, 1983).

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Figures (7)

Fig. 1
Fig. 1

Scheme of light scattering characteristics by an infinitely long cylinder

Fig. 2
Fig. 2

(a) Phase functions for unpolarized light with different incident angles (b) Phase functions for different polarizations of normally incident light

Fig. 3
Fig. 3

Flow chart of Monte Carlo program of polarized light scattering in medium consisting of spheres and cylinders

Fig. 4
Fig. 4

Infinite cylinder obliquely illuminated by a plane wave

Fig. 5
Fig. 5

R(x, y) pattern obtained from Monte Carlo simulation of a semi-infinite turbid medium containing cylinders along the axis with Δη = 10°

Fig. 6
Fig. 6

Scheme of experimental setup

Fig. 7
Fig. 7

Dependence of Linear Differential Polarization to incident polarization angle

Equations (21)

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(EsEs)=ei3π/42πkrsinζeik(rsinζzcosζ)(T1T3T4T2)(EiEi)
{T1=bnIeinΘ=b0I+2n=1bnIcos(nΘ)T2=anIIeinΘ=a0II+2n=1anIIcos(nΘ)T3=anIeinΘ=2in=1anIsin(nΘ)T4=bnIIeinΘ=2in=1bnIIsin(nΘ)
{anI=CnVnBnDnWnVn+iDn2,anII=AnVniCnDnWnVn+iDn2bnI=WnBn+iDnCnWnVn+iDn2,bnII=iCnWn+AnDnWnVn+iDn2
{An=iξ[ξJn(η)Jn(ξ)ηJn(η)Jn(ξ)]Bn=ξ[m2ξJn(η)Jn(ξ)ηJn(η)Jn(ξ)]Cn=ncosζηJn(η)Jn(ξ)(ξ2η21)Dn=ncosζηJn(η)Hn(1)(ξ)(ξ2η21)Wn=iξ[ηJn(η)Hn(1)(ξ)ξJn(η)Hn(1)(ξ)]Vn=ξ[m2ξJn(η)Hn(1)(ξ)ηJn(η)Hn(1)(ξ)]
{Θ=πθξ=xsinζη=xm2cos2ζx=ka
M(ζ,θ)=2πkrsinζ(m11m12m13m14m21m22m23m24m31m32m33m34m41m42m43m44)
{m11=(|T1|2+|T2|2+|T3|2+|T4|2)/2m12=(|T1|2|T2|2+|T3|2|T4|2)/2m13=Re{T1T4+T2T3}m14=Im{T1T4T2T3}m21=(|T1|2|T2|2|T3|2+|T4|2)/2m22=(|T1|2+|T2|2|T3|2|T4|2)/2m23=Re{T1T4T2T3}m24=Im{T1T4+T2T3}m31=Re{T1T3+T2T4}m32=Re{T1T3T2T4}m33=Re{T1T2+T3T4}m34=Im{T1T2+T3T4}m41=Im{T1*T3+T2T4}m42=Im{T1*T3T2T4}m43=Im{T1*T2T3*T4}m44=Re{T1T2T3T4}
Ss(Is,Qs,Us,Vs)=M(ζ,θ)RS
μs,cyl(ζ)=Qsca(ζ)dCA
Qsca,S(ζ)=Ws,SWs,//Qsca,//(ζ)=θ=02πIs,S(θ)θ=02πIs,//(θ)Qsca,//(ζ)             =θ=02πM(ζ,θ)(I,Q,U,V)T(1)θ=02πM(ζ,θ)(1,1,0,0)T(1)Qsca,//(ζ)
Δs=ln(δ)μt
{x=x+uxΔsy=y+uyΔsz=z+uzΔs
Wafter=Wbefore(μsμs+μa)
R(β)=[10000cos(2β)sin(2β)00sin(2β)cos(2β)00001]
S(θ)=M(ζ,θ)R(β)S
Sout=WS
ε=0 when vz=0 and uz=0ε=tan1(vzwz) in all other cases
φ=tan1(uyux) for backscattered photonφ=tan1(uyux) for transmitted photon
Sfinal=R(φ)R(ε)Sout
LDP(θi,θs)=I(θi,θs)I(θi,θs+π/2)
LDP(θi,θs)=Acos(4θsφ1)+Bcos(2θiφ2(θs))+Ccos(2θsφ3)

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