Abstract

Diffuse photon-density waves generated by an instantaneous line source that is parallel to the interface between two semi-infinite turbid media are studied by use of the diffusion approximation. For two nonabsorbing media the Green functions for diffuse light are obtained based on the Green functions for temperature fields that were derived with the Cagniard-de Hoop method. The boundary conditions for diffuse light take into account the discontinuity in the specific intensity at the interface between two media with different refractive indices. The results of the calculations of the specific intensities and the gradient lines for different sets of parameters are presented.

© 2004 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. S. Chandrasekhar, Radiative Transfer (Dover, New York, 1960).
  2. M. L. Shendeleva, “Reflection and refraction of a transient temperature field at a plane interface using Cagniard-de Hoop approach,” Phys. Rev. E 64, 036612-1–036612-7 (2001).
    [CrossRef]
  3. M. S. Patterson, B. Chance, B. C. Wilson, “Time resolved reflectance and transmittance for the noninvasive measurement of tissue optical properties,” Appl. Opt. 28, 2331–2336 (1989).
    [CrossRef] [PubMed]
  4. R. C. Haskell, L. O. Svaasand, T.-T. Tsay, T.-C. Feng, M. S. McAdams, B. J. Tromberg, “Boundary conditions for the diffusion equation in radiative transfer,” J. Opt. Soc. Am. A 11, 2727–2741 (1994).
    [CrossRef]
  5. J.-M. Tualle, E. Tinet, J. Prat, S. Avrillier, “Light propagation near turbid-turbid planar interface,” Opt. Commun. 183, 337–346 (2000).
    [CrossRef]
  6. J.-M. Tualle, J. Prat, E. Tinet, S. Avrillier, “Real-space Green function calculation for the solution of the diffusion equation in stratified turbid media,” J. Opt. Soc. Am. A 17, 2046–2055 (2000).
    [CrossRef]
  7. A. Kienle, M. S. Patterson, N. Dögnitz, R. Bays, G. Wagnières, H. van den Bergh, “Noninvasive determination of the optical properties of two-layered turbid media,” Appl. Opt. 37, 779–791 (1998).
    [CrossRef]
  8. G. Alexandrakis, T. J. Farrell, M. S. Patterson, “Accuracy of the diffusion approximation in determining the optical properties of a two-layer turbid medium,” Appl. Opt. 37, 7401–7409 (1998).
    [CrossRef]
  9. D. Contini, F. Martelli, G. Zaccanti, “Photon migration through a turbid slab described by a model based on diffusion approximation. I. Theory,” Appl. Opt. 36, 4587–4599 (1997).
    [CrossRef] [PubMed]
  10. F. Martelli, A. Sassaroli, Y. Yamada, G. Zaccanti, “Analytical approximate solutions of the time-domain diffusion equation in layered slabs,” J. Opt. Soc. Am. A 19, 71–80 (2002).
    [CrossRef]
  11. L. Wang, S. L. Jacques, L. Zheng, “MCML-Monte Carlo modeling of light transport in multi-layered tissues,” Comput. Methods Programs Biomed. 47, 131–146 (1995).
    [CrossRef] [PubMed]
  12. A. H. Hielscher, H. Liu, B. Chance, F. K. Tittel, S. L. Jacques, “Time-resolved photon emission from layered turbid media,” Appl. Opt. 35, 719–728 (1996).
    [CrossRef] [PubMed]
  13. D. Boas, J. P. Culver, J. J. Stott, A. K. Dunn, “Three dimensional Monte Carlo code for photon migration through complex heterogeneous media including the adult human head,” Opt. Express 10, 159–170 (2002), http://www.opticsexpress.org .
    [CrossRef] [PubMed]
  14. M. A. O’Leary, D. A. Boas, B. Chance, A. G. Yodh, “Refraction of diffuse photon density waves,” Phys. Rev. Lett. 69, 2658–2661 (1992).
    [CrossRef] [PubMed]
  15. M. L. Shendeleva, J. A. Molloy, N. N. Ljepojevic, “Modeling of interfacial temperature effects due to an impulsive line heat source,” Appl. Phys. Lett. 80, 1486–1488 (2002).
    [CrossRef]
  16. M. L. Shendeleva, J. A. Molloy, N. N. Ljepojevic, “Periodic line hear source at the interface,” Rev. Sci. Instrum. 74, 427–429 (2003).
    [CrossRef]

2003 (1)

M. L. Shendeleva, J. A. Molloy, N. N. Ljepojevic, “Periodic line hear source at the interface,” Rev. Sci. Instrum. 74, 427–429 (2003).
[CrossRef]

2002 (3)

2001 (1)

M. L. Shendeleva, “Reflection and refraction of a transient temperature field at a plane interface using Cagniard-de Hoop approach,” Phys. Rev. E 64, 036612-1–036612-7 (2001).
[CrossRef]

2000 (2)

1998 (2)

1997 (1)

1996 (1)

1995 (1)

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

1994 (1)

1992 (1)

M. A. O’Leary, D. A. Boas, B. Chance, A. G. Yodh, “Refraction of diffuse photon density waves,” Phys. Rev. Lett. 69, 2658–2661 (1992).
[CrossRef] [PubMed]

1989 (1)

Alexandrakis, G.

Avrillier, S.

Bays, R.

Boas, D.

Boas, D. A.

M. A. O’Leary, D. A. Boas, B. Chance, A. G. Yodh, “Refraction of diffuse photon density waves,” Phys. Rev. Lett. 69, 2658–2661 (1992).
[CrossRef] [PubMed]

Chance, B.

Chandrasekhar, S.

S. Chandrasekhar, Radiative Transfer (Dover, New York, 1960).

Contini, D.

Culver, J. P.

Dögnitz, N.

Dunn, A. K.

Farrell, T. J.

Feng, T.-C.

Haskell, R. C.

Hielscher, A. H.

Jacques, S. L.

A. H. Hielscher, H. Liu, B. Chance, F. K. Tittel, S. L. Jacques, “Time-resolved photon emission from layered turbid media,” Appl. Opt. 35, 719–728 (1996).
[CrossRef] [PubMed]

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

Kienle, A.

Liu, H.

Ljepojevic, N. N.

M. L. Shendeleva, J. A. Molloy, N. N. Ljepojevic, “Periodic line hear source at the interface,” Rev. Sci. Instrum. 74, 427–429 (2003).
[CrossRef]

M. L. Shendeleva, J. A. Molloy, N. N. Ljepojevic, “Modeling of interfacial temperature effects due to an impulsive line heat source,” Appl. Phys. Lett. 80, 1486–1488 (2002).
[CrossRef]

Martelli, F.

McAdams, M. S.

Molloy, J. A.

M. L. Shendeleva, J. A. Molloy, N. N. Ljepojevic, “Periodic line hear source at the interface,” Rev. Sci. Instrum. 74, 427–429 (2003).
[CrossRef]

M. L. Shendeleva, J. A. Molloy, N. N. Ljepojevic, “Modeling of interfacial temperature effects due to an impulsive line heat source,” Appl. Phys. Lett. 80, 1486–1488 (2002).
[CrossRef]

O’Leary, M. A.

M. A. O’Leary, D. A. Boas, B. Chance, A. G. Yodh, “Refraction of diffuse photon density waves,” Phys. Rev. Lett. 69, 2658–2661 (1992).
[CrossRef] [PubMed]

Patterson, M. S.

Prat, J.

Sassaroli, A.

Shendeleva, M. L.

M. L. Shendeleva, J. A. Molloy, N. N. Ljepojevic, “Periodic line hear source at the interface,” Rev. Sci. Instrum. 74, 427–429 (2003).
[CrossRef]

M. L. Shendeleva, J. A. Molloy, N. N. Ljepojevic, “Modeling of interfacial temperature effects due to an impulsive line heat source,” Appl. Phys. Lett. 80, 1486–1488 (2002).
[CrossRef]

M. L. Shendeleva, “Reflection and refraction of a transient temperature field at a plane interface using Cagniard-de Hoop approach,” Phys. Rev. E 64, 036612-1–036612-7 (2001).
[CrossRef]

Stott, J. J.

Svaasand, L. O.

Tinet, E.

Tittel, F. K.

Tromberg, B. J.

Tsay, T.-T.

Tualle, J.-M.

van den Bergh, H.

Wagnières, G.

Wang, L.

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

Wilson, B. C.

Yamada, Y.

Yodh, A. G.

M. A. O’Leary, D. A. Boas, B. Chance, A. G. Yodh, “Refraction of diffuse photon density waves,” Phys. Rev. Lett. 69, 2658–2661 (1992).
[CrossRef] [PubMed]

Zaccanti, G.

Zheng, L.

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

Appl. Opt. (5)

Appl. Phys. Lett. (1)

M. L. Shendeleva, J. A. Molloy, N. N. Ljepojevic, “Modeling of interfacial temperature effects due to an impulsive line heat source,” Appl. Phys. Lett. 80, 1486–1488 (2002).
[CrossRef]

Comput. Methods Programs Biomed. (1)

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

J. Opt. Soc. Am. A (3)

Opt. Commun. (1)

J.-M. Tualle, E. Tinet, J. Prat, S. Avrillier, “Light propagation near turbid-turbid planar interface,” Opt. Commun. 183, 337–346 (2000).
[CrossRef]

Opt. Express (1)

Phys. Rev. E (1)

M. L. Shendeleva, “Reflection and refraction of a transient temperature field at a plane interface using Cagniard-de Hoop approach,” Phys. Rev. E 64, 036612-1–036612-7 (2001).
[CrossRef]

Phys. Rev. Lett. (1)

M. A. O’Leary, D. A. Boas, B. Chance, A. G. Yodh, “Refraction of diffuse photon density waves,” Phys. Rev. Lett. 69, 2658–2661 (1992).
[CrossRef] [PubMed]

Rev. Sci. Instrum. (1)

M. L. Shendeleva, J. A. Molloy, N. N. Ljepojevic, “Periodic line hear source at the interface,” Rev. Sci. Instrum. 74, 427–429 (2003).
[CrossRef]

Other (1)

S. Chandrasekhar, Radiative Transfer (Dover, New York, 1960).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (3)

Fig. 1
Fig. 1

Contour lines of the specific intensity and the gradient lines of the diffuse flux (arrows) at t = 0.5 s in a two-medium model with parameters D 1 v 1 = 1 cm2/s, N = 1, and γ = 0.5. An instantaneous line source is located at (0, 1).

Fig. 2
Fig. 2

Contour lines of the specific intensity and the gradient lines of the diffuse flux (arrows) at t = 0.5 s in a two-medium model with parameters D 1 v 1 = 1 cm2/s, N = 2, and γ = 0.707. An instantaneous line source is located at (0, 1).

Fig. 3
Fig. 3

Contour lines of the specific intensity and the gradient lines of the diffuse flux (arrows) at t = 0.5 s for a two-medium model with parameters D 1 v 1 = 1 cm2/s, N = 0.707, and γ = 1.41. An instantaneous line source is located at (0, 1).

Equations (28)

Equations on this page are rendered with MathJax. Learn more.

1vϕt-DΔϕ+βϕ=Q0,
J=-Dϕ.
2ϕ1x2+2ϕ1z2-1D1v1ϕ1t=-1D1v1 δtδxδz-z0,
2ϕ2x2+2ϕ2z2-1D2v2ϕ2t=0,
N2ϕ1=ϕ2,
γ2ϕ1z=ϕ2z,
v1v2=n2n1=N, D1D2=γ.
ϕ˜j=ϕjnj2,
ϕ˜1=ϕ˜2, ϕ˜1z=N2γ2ϕ˜2z,
DjHDjvj,
kjHDjvj2,
ϕ1=ϕS+ϕR,
ϕS=14πD1v1texp-r124D1v1t,
ϕR=r24πD1v1t3/20exp-β2+1r224D1v1t×Reξ2+11/2-μξ2+ν21/2ξ2+11/2+μξ2+ν21/2dβ+H1-νHφ-arcsinν×arcsinνφexp-r22cos2φ-ε4D1v1t×2μ cos ε cosφ-εsin2 ε-ν21/2cos2 ε+μ2sin2 ε-ν2dε.
ξ=iβ2+1sin φ+β cos φ,
μ=N2γ2=D2v12D1v22,
ν=γN=D1v1D2v2.
χH=k2Hk1H, nH=D1HD2H.
αcr=arcsinν.
ϕ2=N2R1+νR22πD1v1t3/20exp-β2+1R1+νR224D1v1t×Reβ2+11/2ξ2+11/2+μξ2+ν21/2ξβdβ,
R1=xb2+z02,
R2=x-xb2+z2,
xbR2=νx-xbR1.
sin φsin θ=ν,
-iξx-zξ2+ν2+z0ξ2+1=R1+νR2β2+1,
β1v1=β2v2.
ϕ1=14πD1v1texp-r124D1v1t+1-N31+N3exp-r224D1v1t.
ϕ2=N21+N312πD1v1texp-r124D1v1t,

Metrics