Abstract

A generalized form of coupled photon transport equations that can handle correlated light beams with distinct frequencies is introduced. The derivation is based on the principle of energy conservation. For a single frequency, the current formulation reduces to a standard photon transport equation, and for fluorescence and phosphorescence, the diffusion models derived from the proposed photon transport model match for homogenous media. The generalized photon transport model is extended to handle wideband inputs in the frequency domain.

© 2012 Optical Society of America

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References

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2008

C. C. Handapangoda, M. Premaratne, L. Yeo, and J. Friend, IEEE J. Sel. Top. Quantum Electron. 14, 105 (2008).
[CrossRef]

2007

2006

2005

1997

A. J. Welch, C. Gardner, R. R. Kortum, E. Chan, G. Criswell, J. Pfefer, and S. Warren, Lasers Surg. Med. 21, 166(1997).
[CrossRef]

1994

1990

P. A. Oberg, Crit. Rev. Biomed. Eng. 18, 125 (1990).

Apreleva, S. V.

Boas, D. A.

Chan, E.

A. J. Welch, C. Gardner, R. R. Kortum, E. Chan, G. Criswell, J. Pfefer, and S. Warren, Lasers Surg. Med. 21, 166(1997).
[CrossRef]

Criswell, G.

A. J. Welch, C. Gardner, R. R. Kortum, E. Chan, G. Criswell, J. Pfefer, and S. Warren, Lasers Surg. Med. 21, 166(1997).
[CrossRef]

Delorme, J. F.

Friend, J.

C. C. Handapangoda, M. Premaratne, L. Yeo, and J. Friend, IEEE J. Sel. Top. Quantum Electron. 14, 105 (2008).
[CrossRef]

Gallant, P.

Gardner, C.

A. J. Welch, C. Gardner, R. R. Kortum, E. Chan, G. Criswell, J. Pfefer, and S. Warren, Lasers Surg. Med. 21, 166(1997).
[CrossRef]

Gemert, M. J. V.

A. J. Welch and M. J. V. Gemert, Optical-Thermal Response of Laser-Irradiated Tissue (Plenum, 1995).

Handapangoda, C. C.

C. C. Handapangoda, M. Premaratne, L. Yeo, and J. Friend, IEEE J. Sel. Top. Quantum Electron. 14, 105 (2008).
[CrossRef]

C. C. Handapangoda, M. Premaratne, and S. Nahavandi, “A fresh look at the validity of the diffusion approximation for modelling fluorescence spectroscopy in biological tissue,” to be presented at the 34th Annual International IEEE EMBS Conference.

C. C. Handapangoda, M. Premaratne, and S. Nahavandi, in Proceedings of ICHIT 2012, LNCS7435, G. Lee and , eds. (Springer, 2012), p. 461.

Kortum, R. R.

A. J. Welch, C. Gardner, R. R. Kortum, E. Chan, G. Criswell, J. Pfefer, and S. Warren, Lasers Surg. Med. 21, 166(1997).
[CrossRef]

Lowery, A. J.

Ma, G.

Nahavandi, S.

C. C. Handapangoda, M. Premaratne, and S. Nahavandi, “A fresh look at the validity of the diffusion approximation for modelling fluorescence spectroscopy in biological tissue,” to be presented at the 34th Annual International IEEE EMBS Conference.

C. C. Handapangoda, M. Premaratne, and S. Nahavandi, in Proceedings of ICHIT 2012, LNCS7435, G. Lee and , eds. (Springer, 2012), p. 461.

Oberg, P. A.

P. A. Oberg, Crit. Rev. Biomed. Eng. 18, 125 (1990).

Patterson, M. S.

Peraiah, A.

A. Peraiah, An Introduction to Radiative Transfer: Methods and Applications in Astrophysics (Cambridge University, 2002).

Pfefer, J.

A. J. Welch, C. Gardner, R. R. Kortum, E. Chan, G. Criswell, J. Pfefer, and S. Warren, Lasers Surg. Med. 21, 166(1997).
[CrossRef]

Pogue, B. W.

Premaratne, E.

Premaratne, M.

C. C. Handapangoda, M. Premaratne, L. Yeo, and J. Friend, IEEE J. Sel. Top. Quantum Electron. 14, 105 (2008).
[CrossRef]

M. Premaratne, E. Premaratne, and A. J. Lowery, Opt. Express 13, 389 (2005).
[CrossRef]

C. C. Handapangoda, M. Premaratne, and S. Nahavandi, “A fresh look at the validity of the diffusion approximation for modelling fluorescence spectroscopy in biological tissue,” to be presented at the 34th Annual International IEEE EMBS Conference.

C. C. Handapangoda, M. Premaratne, and S. Nahavandi, in Proceedings of ICHIT 2012, LNCS7435, G. Lee and , eds. (Springer, 2012), p. 461.

Vinogradov, S. A.

Warren, S.

A. J. Welch, C. Gardner, R. R. Kortum, E. Chan, G. Criswell, J. Pfefer, and S. Warren, Lasers Surg. Med. 21, 166(1997).
[CrossRef]

Welch, A. J.

A. J. Welch, C. Gardner, R. R. Kortum, E. Chan, G. Criswell, J. Pfefer, and S. Warren, Lasers Surg. Med. 21, 166(1997).
[CrossRef]

A. J. Welch and M. J. V. Gemert, Optical-Thermal Response of Laser-Irradiated Tissue (Plenum, 1995).

Wilson, D. F.

Yeo, L.

C. C. Handapangoda, M. Premaratne, L. Yeo, and J. Friend, IEEE J. Sel. Top. Quantum Electron. 14, 105 (2008).
[CrossRef]

Appl. Opt.

Crit. Rev. Biomed. Eng.

P. A. Oberg, Crit. Rev. Biomed. Eng. 18, 125 (1990).

IEEE J. Sel. Top. Quantum Electron.

C. C. Handapangoda, M. Premaratne, L. Yeo, and J. Friend, IEEE J. Sel. Top. Quantum Electron. 14, 105 (2008).
[CrossRef]

Lasers Surg. Med.

A. J. Welch, C. Gardner, R. R. Kortum, E. Chan, G. Criswell, J. Pfefer, and S. Warren, Lasers Surg. Med. 21, 166(1997).
[CrossRef]

Opt. Express

Other

A. J. Welch and M. J. V. Gemert, Optical-Thermal Response of Laser-Irradiated Tissue (Plenum, 1995).

C. C. Handapangoda, M. Premaratne, and S. Nahavandi, “A fresh look at the validity of the diffusion approximation for modelling fluorescence spectroscopy in biological tissue,” to be presented at the 34th Annual International IEEE EMBS Conference.

C. C. Handapangoda, M. Premaratne, and S. Nahavandi, in Proceedings of ICHIT 2012, LNCS7435, G. Lee and , eds. (Springer, 2012), p. 461.

A. Peraiah, An Introduction to Radiative Transfer: Methods and Applications in Astrophysics (Cambridge University, 2002).

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Figures (2)

Fig. 1.
Fig. 1.

Schematic diagram of possible paths traced by photons in a turbid medium having both elastic and inelastic scatterers.

Fig. 2.
Fig. 2.

Schematic diagram of the transfer of radiation energy.

Equations (14)

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G(I2,out)dAdΩ=G(I2,in)dAdΩ+GG,couple(I1,in,I2,out)dAdΩGloss(I2,in)dAdΩ+Ggain(I2,in)dAdΩ,
G(I1,out)dAdΩ=G(I1,in)dAdΩGL,couple(I1,in,I2,out)dAdΩGloss(I1,in)dAdΩ+Ggain(I1,in)dAdΩ.
dν2hν2I2,outdAdΩdt=dν2hν2I2,indAdΩdt+dν2hν2dAdΩdtHG,couple(I1,in)dν2hν2(σa(2)+σs(2))I2,indΩdAdt+dν2hν2σs(2)dΩdAdt4πP2(Ω;Ω)I2,in(Ω)dΩ4π,
dν1hν1I1,outdAdΩdt=dν1hν1I1,indAdΩdtdν1hν1dAdΩdtHL,couple(I1,in)dν1hν1(σa(1)+σs(1))I1,indΩdAdt+dν1hν1σs(1)dΩdAdt4πP1(Ω;Ω)I1,in(Ω)dΩ4π,
Im(r+Δr,Ω,t+Δt)Im(r,Ω,t)=(1ct+Ω·)Im(r,Ω,t)ds+O(ds),
(1ct+Ω·)I2(r,Ω,t)=HG,couple(I1(r,Ω,t))σt(2)I2(r,Ω,t)+σs(2)4πP2(Ω;Ω)I2(r,Ω,t)dΩ4π,
(1ct+Ω·)I1(r,Ω,t)=HL,couple(I1(r,Ω,t))σt(1)I1(r,Ω,t)+σs(1)4πP1(Ω;Ω)I1(r,Ω,t)dΩ4π,
HG,couple=σs,mov(1)4πPcouple(Ω;Ω)I1(r,Ω,t)dΩ4π,
HL,couple=σs,mov(1)4πPcouple(Ω;Ω)I1(r,Ω,t)dΩ4π=σs,mov(1)I1(r,Ω,t).
G(Im,out)dAdΩ=G(Im,in)dAdΩGL,couple(Im,in,I1,out)dAdΩGL,couple(Im,in,In,out)dAdΩGL,couple(Im,in,IN,out)dAdΩ+GG,couple(I1,in,Im,out)dAdΩ++GG,couple(In,in,Im,out)dAdΩ++GG,couple(IN,in,Im,out)dAdΩGloss(I1,in)dAdΩ+Ggain(I1,in)dAdΩ,
F(ω)=f(t)ejωtdt,
(jωmc+Ω·)I(r,Ω,ωm)=LωLm1I(r,Ω,ωm)LωLmnI(r,Ω,ωm)LωLmNI(r,Ω,ωm)+LωG1mI(r,Ω,ω1)++LωGnmI(r,Ω,ωn)++LωGNmI(r,Ω,ωN)σt(m)I(r,Ω,ωm)+σs(m)4πPm(Ω;Ω)I(r,Ω,ωm)dΩ4π,
Ω·I(r,Ω,ω)+WI(r,Ω,ω)=LI(r,Ω,ω)+ΓI(r,Ω,ω)+14π4πPI(r,Ω,ω)dΩ,
Lmn={k=1NLωLmkm=n;mkLωGnmmn.

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