Abstract

An isotropic scaling formulation is evaluated for transient radiative transfer in a one-dimensional planar slab subject to collimated and/or diffuse irradiation. The Monte Carlo method is used to implement the equivalent scattering and exact simulations of the transient short-pulse radiation transport through forward and backward anisotropic scattering planar media. The scaled equivalent isotropic scattering results are compared with predictions of anisotropic scattering in various problems. It is found that the equivalent isotropic scaling law is not appropriate for backward-scattering media in transient radiative transfer. Even for an optically diffuse medium, the differences in temporal transmittance and reflectance profiles between predictions of backward anisotropic scattering and equivalent isotropic scattering are large. Additionally, for both forward and backward anisotropic scattering media, the transient equivalent isotropic results are strongly affected by the change of photon flight time, owing to the change of flight direction associated with the isotropic scaling technique.

© 2000 Optical Society of America

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  1. J. H. Joseph, W. J. Wiscombe, J. A. Weinman, “The Delta–Eddington approximation for radiative flux transfer,” J. Atmos. Sci. 33, 2452–2459 (1976).
    [CrossRef]
  2. W. J. Wiscombe, “The Delta-M method: rapid yet accurate radiative flux calculations for strongly asymmetric phase functions,” J. Atmos. Sci. 34, 1408–1442 (1977).
    [CrossRef]
  3. H. Lee, R. O. Buckius, “Scaling anisotropic scattering in radiation heat transfer for a planar medium,” ASME J. Heat Transfer 104, 68–75 (1982).
    [CrossRef]
  4. T.-K. Kim, H. S. Lee, “Scaled isotropic results for two-dimensional anisotropic scattering media,” ASME J. Heat Transfer 112, 721–727 (1990).
    [CrossRef]
  5. B. H. J. McKellar, M. A. Box, “The scaling group of the radiative transfer for a planar medium,” J. Atmos. Sci. 38, 1063–1068 (1981).
    [CrossRef]
  6. Z. Guo, S. Maruyama, “Scaling anisotropic scattering in radiative transfer in three-dimensional nonhomogeneous media,” Int. Commun. Heat Mass Transfer 26, 997–1007 (1999).
    [CrossRef]
  7. Z. Guo, S. Maruyama, “Radiative heat transfer in inhomogeneous, nongray, and anisotropically scattering Media,” Int. J. Heat Mass Transfer 43, 2325–2336 (2000).
    [CrossRef]
  8. 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]
  9. Y. Yamada, “Light–tissue interaction and optical imaging in biomedicine,” in Annual Review of Heat Transfer, C. L. Tien, ed. (Begell House, New York, 1995), Vol. 6, pp. 1–59.
  10. M. Q. Brewster, Y. Yamada, “Optical properties of thick, turbid media from picosecond time-resolved light scattering measurements,” Int. J. Heat Mass Transfer 38, 2569–2581 (1995).
    [CrossRef]
  11. D. T. Deply, M. Cope, P. van der Zee, S. Arridge, S. Wray, J. Wyatt, “Estimation of optical pathlength through tissue from direct time of flight measurement,” Phys. Med. Biol. 33, 1433–1442 (1988).
    [CrossRef]
  12. S. J. Madsen, B. C. Wilson, M. S. Patterson, Y. D. Park, S. J. Jacques, Y. Hefetz, “Experimental tests of a simple diffusion model for the estimation of scattering and absorption coefficients of turbid media from time-resolved diffusion reflectance measurements,” Appl. Opt. 31, 3509–3517 (1992).
    [CrossRef] [PubMed]
  13. B. C. Wilson, G. Adam, “A Monte Carlo model for the absorption and flux distributions of light tissue,” Med. Phys. 10, 824–830 (1983).
    [CrossRef] [PubMed]
  14. S. T. Flock, M. S. Patterson, B. C. Wilson, D. R. Wyman, “Monte Carlo modelling of light propagation in highly scattering tissues. I. Model predictions and comparison with diffusion theory,” IEEE Trans. Biomed. Eng. 36, 1162–1167 (1989).
    [CrossRef] [PubMed]
  15. Y. Hasegawa, Y. Yamada, M. Tamura, Y. Nomura, “Monte Carlo simulation of light transmission through living tissues,” Appl. Opt. 30, 4515–4520 (1991).
    [CrossRef] [PubMed]
  16. S. Kumar, K. Mitra, “Microscale aspects of thermal radiation transport and laser applications,” Adv. Heat Transfer 33, 187–294 (1998).
    [CrossRef]
  17. S. Kumar, K. Mitra, Y. Yamada, “Hyperbolic damped-wave models for transient light-pulse propagation in scattering media,” Appl. Opt. 35, 3372–3378 (1996).
    [CrossRef] [PubMed]
  18. K. Mitra, M.-S. Lai, S. Kumar, “Transient radiation transport in participating media within a rectangular enclosure,” J. Thermophys. Heat Transfer 11, 409–414 (1997).
    [CrossRef]
  19. K. Mitra, S. Kumar, “Development and comparison of models for light-pulse transport through scattering–absorbing media,” Appl. Opt. 38, 188–196 (1999).
    [CrossRef]
  20. J. H. Churnside, J. J. Wilson, V. V. Tatarskii, “Lidar profiles of fish schools,” Appl. Opt. 36, 6011–6020 (1997).
    [CrossRef] [PubMed]
  21. M. M. Krekova, G. M. Krekov, I. V. Samokhvalov, V. S. Shamanaev, “Numerical evaluation of the possibilities of remote laser sensing of fish schools,” Appl. Opt. 33, 5715–5720 (1994).
    [CrossRef] [PubMed]
  22. K. Mitra, J. H. Churnside, “Transient radiative transfer equation applied to oceanographic lidar,” Appl. Opt. 38, 889–895 (1999).
    [CrossRef]
  23. H. C. von de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).
  24. R. Siegel, J. R. Howell, Thermal Radiation Heat Transfer, 3rd ed. (Hemisphere, Washington, D.C., 1992).
  25. Z. Guo, S. Kumar, K.-C. San, “Multi-dimensional Monte Carlo simulation of short pulse laser radiation transport in scattering media,” J. Thermophys. Heat Transfer (to be published).
  26. L. Wang, P. P. Ho, C. Liu, G. Zhang, R. R. Alfano, “Ballistic 2-D image through scattering walls using an ultrafast optical Kerr gate,” Science 253, 769–771 (1991).
    [CrossRef] [PubMed]

2000

Z. Guo, S. Maruyama, “Radiative heat transfer in inhomogeneous, nongray, and anisotropically scattering Media,” Int. J. Heat Mass Transfer 43, 2325–2336 (2000).
[CrossRef]

1999

1998

S. Kumar, K. Mitra, “Microscale aspects of thermal radiation transport and laser applications,” Adv. Heat Transfer 33, 187–294 (1998).
[CrossRef]

1997

J. H. Churnside, J. J. Wilson, V. V. Tatarskii, “Lidar profiles of fish schools,” Appl. Opt. 36, 6011–6020 (1997).
[CrossRef] [PubMed]

K. Mitra, M.-S. Lai, S. Kumar, “Transient radiation transport in participating media within a rectangular enclosure,” J. Thermophys. Heat Transfer 11, 409–414 (1997).
[CrossRef]

1996

1995

M. Q. Brewster, Y. Yamada, “Optical properties of thick, turbid media from picosecond time-resolved light scattering measurements,” Int. J. Heat Mass Transfer 38, 2569–2581 (1995).
[CrossRef]

1994

1992

1991

Y. Hasegawa, Y. Yamada, M. Tamura, Y. Nomura, “Monte Carlo simulation of light transmission through living tissues,” Appl. Opt. 30, 4515–4520 (1991).
[CrossRef] [PubMed]

L. Wang, P. P. Ho, C. Liu, G. Zhang, R. R. Alfano, “Ballistic 2-D image through scattering walls using an ultrafast optical Kerr gate,” Science 253, 769–771 (1991).
[CrossRef] [PubMed]

1990

T.-K. Kim, H. S. Lee, “Scaled isotropic results for two-dimensional anisotropic scattering media,” ASME J. Heat Transfer 112, 721–727 (1990).
[CrossRef]

1989

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]

S. T. Flock, M. S. Patterson, B. C. Wilson, D. R. Wyman, “Monte Carlo modelling of light propagation in highly scattering tissues. I. Model predictions and comparison with diffusion theory,” IEEE Trans. Biomed. Eng. 36, 1162–1167 (1989).
[CrossRef] [PubMed]

1988

D. T. Deply, M. Cope, P. van der Zee, S. Arridge, S. Wray, J. Wyatt, “Estimation of optical pathlength through tissue from direct time of flight measurement,” Phys. Med. Biol. 33, 1433–1442 (1988).
[CrossRef]

1983

B. C. Wilson, G. Adam, “A Monte Carlo model for the absorption and flux distributions of light tissue,” Med. Phys. 10, 824–830 (1983).
[CrossRef] [PubMed]

1982

H. Lee, R. O. Buckius, “Scaling anisotropic scattering in radiation heat transfer for a planar medium,” ASME J. Heat Transfer 104, 68–75 (1982).
[CrossRef]

1981

B. H. J. McKellar, M. A. Box, “The scaling group of the radiative transfer for a planar medium,” J. Atmos. Sci. 38, 1063–1068 (1981).
[CrossRef]

1977

W. J. Wiscombe, “The Delta-M method: rapid yet accurate radiative flux calculations for strongly asymmetric phase functions,” J. Atmos. Sci. 34, 1408–1442 (1977).
[CrossRef]

1976

J. H. Joseph, W. J. Wiscombe, J. A. Weinman, “The Delta–Eddington approximation for radiative flux transfer,” J. Atmos. Sci. 33, 2452–2459 (1976).
[CrossRef]

Adam, G.

B. C. Wilson, G. Adam, “A Monte Carlo model for the absorption and flux distributions of light tissue,” Med. Phys. 10, 824–830 (1983).
[CrossRef] [PubMed]

Alfano, R. R.

L. Wang, P. P. Ho, C. Liu, G. Zhang, R. R. Alfano, “Ballistic 2-D image through scattering walls using an ultrafast optical Kerr gate,” Science 253, 769–771 (1991).
[CrossRef] [PubMed]

Arridge, S.

D. T. Deply, M. Cope, P. van der Zee, S. Arridge, S. Wray, J. Wyatt, “Estimation of optical pathlength through tissue from direct time of flight measurement,” Phys. Med. Biol. 33, 1433–1442 (1988).
[CrossRef]

Box, M. A.

B. H. J. McKellar, M. A. Box, “The scaling group of the radiative transfer for a planar medium,” J. Atmos. Sci. 38, 1063–1068 (1981).
[CrossRef]

Brewster, M. Q.

M. Q. Brewster, Y. Yamada, “Optical properties of thick, turbid media from picosecond time-resolved light scattering measurements,” Int. J. Heat Mass Transfer 38, 2569–2581 (1995).
[CrossRef]

Buckius, R. O.

H. Lee, R. O. Buckius, “Scaling anisotropic scattering in radiation heat transfer for a planar medium,” ASME J. Heat Transfer 104, 68–75 (1982).
[CrossRef]

Chance, B.

Churnside, J. H.

Cope, M.

D. T. Deply, M. Cope, P. van der Zee, S. Arridge, S. Wray, J. Wyatt, “Estimation of optical pathlength through tissue from direct time of flight measurement,” Phys. Med. Biol. 33, 1433–1442 (1988).
[CrossRef]

Deply, D. T.

D. T. Deply, M. Cope, P. van der Zee, S. Arridge, S. Wray, J. Wyatt, “Estimation of optical pathlength through tissue from direct time of flight measurement,” Phys. Med. Biol. 33, 1433–1442 (1988).
[CrossRef]

Flock, S. T.

S. T. Flock, M. S. Patterson, B. C. Wilson, D. R. Wyman, “Monte Carlo modelling of light propagation in highly scattering tissues. I. Model predictions and comparison with diffusion theory,” IEEE Trans. Biomed. Eng. 36, 1162–1167 (1989).
[CrossRef] [PubMed]

Guo, Z.

Z. Guo, S. Maruyama, “Radiative heat transfer in inhomogeneous, nongray, and anisotropically scattering Media,” Int. J. Heat Mass Transfer 43, 2325–2336 (2000).
[CrossRef]

Z. Guo, S. Maruyama, “Scaling anisotropic scattering in radiative transfer in three-dimensional nonhomogeneous media,” Int. Commun. Heat Mass Transfer 26, 997–1007 (1999).
[CrossRef]

Z. Guo, S. Kumar, K.-C. San, “Multi-dimensional Monte Carlo simulation of short pulse laser radiation transport in scattering media,” J. Thermophys. Heat Transfer (to be published).

Hasegawa, Y.

Hefetz, Y.

Ho, P. P.

L. Wang, P. P. Ho, C. Liu, G. Zhang, R. R. Alfano, “Ballistic 2-D image through scattering walls using an ultrafast optical Kerr gate,” Science 253, 769–771 (1991).
[CrossRef] [PubMed]

Howell, J. R.

R. Siegel, J. R. Howell, Thermal Radiation Heat Transfer, 3rd ed. (Hemisphere, Washington, D.C., 1992).

Jacques, S. J.

Joseph, J. H.

J. H. Joseph, W. J. Wiscombe, J. A. Weinman, “The Delta–Eddington approximation for radiative flux transfer,” J. Atmos. Sci. 33, 2452–2459 (1976).
[CrossRef]

Kim, T.-K.

T.-K. Kim, H. S. Lee, “Scaled isotropic results for two-dimensional anisotropic scattering media,” ASME J. Heat Transfer 112, 721–727 (1990).
[CrossRef]

Krekov, G. M.

Krekova, M. M.

Kumar, S.

K. Mitra, S. Kumar, “Development and comparison of models for light-pulse transport through scattering–absorbing media,” Appl. Opt. 38, 188–196 (1999).
[CrossRef]

S. Kumar, K. Mitra, “Microscale aspects of thermal radiation transport and laser applications,” Adv. Heat Transfer 33, 187–294 (1998).
[CrossRef]

K. Mitra, M.-S. Lai, S. Kumar, “Transient radiation transport in participating media within a rectangular enclosure,” J. Thermophys. Heat Transfer 11, 409–414 (1997).
[CrossRef]

S. Kumar, K. Mitra, Y. Yamada, “Hyperbolic damped-wave models for transient light-pulse propagation in scattering media,” Appl. Opt. 35, 3372–3378 (1996).
[CrossRef] [PubMed]

Z. Guo, S. Kumar, K.-C. San, “Multi-dimensional Monte Carlo simulation of short pulse laser radiation transport in scattering media,” J. Thermophys. Heat Transfer (to be published).

Lai, M.-S.

K. Mitra, M.-S. Lai, S. Kumar, “Transient radiation transport in participating media within a rectangular enclosure,” J. Thermophys. Heat Transfer 11, 409–414 (1997).
[CrossRef]

Lee, H.

H. Lee, R. O. Buckius, “Scaling anisotropic scattering in radiation heat transfer for a planar medium,” ASME J. Heat Transfer 104, 68–75 (1982).
[CrossRef]

Lee, H. S.

T.-K. Kim, H. S. Lee, “Scaled isotropic results for two-dimensional anisotropic scattering media,” ASME J. Heat Transfer 112, 721–727 (1990).
[CrossRef]

Liu, C.

L. Wang, P. P. Ho, C. Liu, G. Zhang, R. R. Alfano, “Ballistic 2-D image through scattering walls using an ultrafast optical Kerr gate,” Science 253, 769–771 (1991).
[CrossRef] [PubMed]

Madsen, S. J.

Maruyama, S.

Z. Guo, S. Maruyama, “Radiative heat transfer in inhomogeneous, nongray, and anisotropically scattering Media,” Int. J. Heat Mass Transfer 43, 2325–2336 (2000).
[CrossRef]

Z. Guo, S. Maruyama, “Scaling anisotropic scattering in radiative transfer in three-dimensional nonhomogeneous media,” Int. Commun. Heat Mass Transfer 26, 997–1007 (1999).
[CrossRef]

McKellar, B. H. J.

B. H. J. McKellar, M. A. Box, “The scaling group of the radiative transfer for a planar medium,” J. Atmos. Sci. 38, 1063–1068 (1981).
[CrossRef]

Mitra, K.

Nomura, Y.

Park, Y. D.

Patterson, M. S.

Samokhvalov, I. V.

San, K.-C.

Z. Guo, S. Kumar, K.-C. San, “Multi-dimensional Monte Carlo simulation of short pulse laser radiation transport in scattering media,” J. Thermophys. Heat Transfer (to be published).

Shamanaev, V. S.

Siegel, R.

R. Siegel, J. R. Howell, Thermal Radiation Heat Transfer, 3rd ed. (Hemisphere, Washington, D.C., 1992).

Tamura, M.

Tatarskii, V. V.

van der Zee, P.

D. T. Deply, M. Cope, P. van der Zee, S. Arridge, S. Wray, J. Wyatt, “Estimation of optical pathlength through tissue from direct time of flight measurement,” Phys. Med. Biol. 33, 1433–1442 (1988).
[CrossRef]

von de Hulst, H. C.

H. C. von de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).

Wang, L.

L. Wang, P. P. Ho, C. Liu, G. Zhang, R. R. Alfano, “Ballistic 2-D image through scattering walls using an ultrafast optical Kerr gate,” Science 253, 769–771 (1991).
[CrossRef] [PubMed]

Weinman, J. A.

J. H. Joseph, W. J. Wiscombe, J. A. Weinman, “The Delta–Eddington approximation for radiative flux transfer,” J. Atmos. Sci. 33, 2452–2459 (1976).
[CrossRef]

Wilson, B. C.

S. J. Madsen, B. C. Wilson, M. S. Patterson, Y. D. Park, S. J. Jacques, Y. Hefetz, “Experimental tests of a simple diffusion model for the estimation of scattering and absorption coefficients of turbid media from time-resolved diffusion reflectance measurements,” Appl. Opt. 31, 3509–3517 (1992).
[CrossRef] [PubMed]

S. T. Flock, M. S. Patterson, B. C. Wilson, D. R. Wyman, “Monte Carlo modelling of light propagation in highly scattering tissues. I. Model predictions and comparison with diffusion theory,” IEEE Trans. Biomed. Eng. 36, 1162–1167 (1989).
[CrossRef] [PubMed]

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]

B. C. Wilson, G. Adam, “A Monte Carlo model for the absorption and flux distributions of light tissue,” Med. Phys. 10, 824–830 (1983).
[CrossRef] [PubMed]

Wilson, J. J.

Wiscombe, W. J.

W. J. Wiscombe, “The Delta-M method: rapid yet accurate radiative flux calculations for strongly asymmetric phase functions,” J. Atmos. Sci. 34, 1408–1442 (1977).
[CrossRef]

J. H. Joseph, W. J. Wiscombe, J. A. Weinman, “The Delta–Eddington approximation for radiative flux transfer,” J. Atmos. Sci. 33, 2452–2459 (1976).
[CrossRef]

Wray, S.

D. T. Deply, M. Cope, P. van der Zee, S. Arridge, S. Wray, J. Wyatt, “Estimation of optical pathlength through tissue from direct time of flight measurement,” Phys. Med. Biol. 33, 1433–1442 (1988).
[CrossRef]

Wyatt, J.

D. T. Deply, M. Cope, P. van der Zee, S. Arridge, S. Wray, J. Wyatt, “Estimation of optical pathlength through tissue from direct time of flight measurement,” Phys. Med. Biol. 33, 1433–1442 (1988).
[CrossRef]

Wyman, D. R.

S. T. Flock, M. S. Patterson, B. C. Wilson, D. R. Wyman, “Monte Carlo modelling of light propagation in highly scattering tissues. I. Model predictions and comparison with diffusion theory,” IEEE Trans. Biomed. Eng. 36, 1162–1167 (1989).
[CrossRef] [PubMed]

Yamada, Y.

S. Kumar, K. Mitra, Y. Yamada, “Hyperbolic damped-wave models for transient light-pulse propagation in scattering media,” Appl. Opt. 35, 3372–3378 (1996).
[CrossRef] [PubMed]

M. Q. Brewster, Y. Yamada, “Optical properties of thick, turbid media from picosecond time-resolved light scattering measurements,” Int. J. Heat Mass Transfer 38, 2569–2581 (1995).
[CrossRef]

Y. Hasegawa, Y. Yamada, M. Tamura, Y. Nomura, “Monte Carlo simulation of light transmission through living tissues,” Appl. Opt. 30, 4515–4520 (1991).
[CrossRef] [PubMed]

Y. Yamada, “Light–tissue interaction and optical imaging in biomedicine,” in Annual Review of Heat Transfer, C. L. Tien, ed. (Begell House, New York, 1995), Vol. 6, pp. 1–59.

Zhang, G.

L. Wang, P. P. Ho, C. Liu, G. Zhang, R. R. Alfano, “Ballistic 2-D image through scattering walls using an ultrafast optical Kerr gate,” Science 253, 769–771 (1991).
[CrossRef] [PubMed]

Adv. Heat Transfer

S. Kumar, K. Mitra, “Microscale aspects of thermal radiation transport and laser applications,” Adv. Heat Transfer 33, 187–294 (1998).
[CrossRef]

Appl. Opt.

S. Kumar, K. Mitra, Y. Yamada, “Hyperbolic damped-wave models for transient light-pulse propagation in scattering media,” Appl. Opt. 35, 3372–3378 (1996).
[CrossRef] [PubMed]

Y. Hasegawa, Y. Yamada, M. Tamura, Y. Nomura, “Monte Carlo simulation of light transmission through living tissues,” Appl. Opt. 30, 4515–4520 (1991).
[CrossRef] [PubMed]

S. J. Madsen, B. C. Wilson, M. S. Patterson, Y. D. Park, S. J. Jacques, Y. Hefetz, “Experimental tests of a simple diffusion model for the estimation of scattering and absorption coefficients of turbid media from time-resolved diffusion reflectance measurements,” Appl. Opt. 31, 3509–3517 (1992).
[CrossRef] [PubMed]

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]

K. Mitra, S. Kumar, “Development and comparison of models for light-pulse transport through scattering–absorbing media,” Appl. Opt. 38, 188–196 (1999).
[CrossRef]

J. H. Churnside, J. J. Wilson, V. V. Tatarskii, “Lidar profiles of fish schools,” Appl. Opt. 36, 6011–6020 (1997).
[CrossRef] [PubMed]

M. M. Krekova, G. M. Krekov, I. V. Samokhvalov, V. S. Shamanaev, “Numerical evaluation of the possibilities of remote laser sensing of fish schools,” Appl. Opt. 33, 5715–5720 (1994).
[CrossRef] [PubMed]

K. Mitra, J. H. Churnside, “Transient radiative transfer equation applied to oceanographic lidar,” Appl. Opt. 38, 889–895 (1999).
[CrossRef]

ASME J. Heat Transfer

H. Lee, R. O. Buckius, “Scaling anisotropic scattering in radiation heat transfer for a planar medium,” ASME J. Heat Transfer 104, 68–75 (1982).
[CrossRef]

T.-K. Kim, H. S. Lee, “Scaled isotropic results for two-dimensional anisotropic scattering media,” ASME J. Heat Transfer 112, 721–727 (1990).
[CrossRef]

IEEE Trans. Biomed. Eng.

S. T. Flock, M. S. Patterson, B. C. Wilson, D. R. Wyman, “Monte Carlo modelling of light propagation in highly scattering tissues. I. Model predictions and comparison with diffusion theory,” IEEE Trans. Biomed. Eng. 36, 1162–1167 (1989).
[CrossRef] [PubMed]

Int. Commun. Heat Mass Transfer

Z. Guo, S. Maruyama, “Scaling anisotropic scattering in radiative transfer in three-dimensional nonhomogeneous media,” Int. Commun. Heat Mass Transfer 26, 997–1007 (1999).
[CrossRef]

Int. J. Heat Mass Transfer

Z. Guo, S. Maruyama, “Radiative heat transfer in inhomogeneous, nongray, and anisotropically scattering Media,” Int. J. Heat Mass Transfer 43, 2325–2336 (2000).
[CrossRef]

M. Q. Brewster, Y. Yamada, “Optical properties of thick, turbid media from picosecond time-resolved light scattering measurements,” Int. J. Heat Mass Transfer 38, 2569–2581 (1995).
[CrossRef]

J. Atmos. Sci.

B. H. J. McKellar, M. A. Box, “The scaling group of the radiative transfer for a planar medium,” J. Atmos. Sci. 38, 1063–1068 (1981).
[CrossRef]

J. H. Joseph, W. J. Wiscombe, J. A. Weinman, “The Delta–Eddington approximation for radiative flux transfer,” J. Atmos. Sci. 33, 2452–2459 (1976).
[CrossRef]

W. J. Wiscombe, “The Delta-M method: rapid yet accurate radiative flux calculations for strongly asymmetric phase functions,” J. Atmos. Sci. 34, 1408–1442 (1977).
[CrossRef]

J. Thermophys. Heat Transfer

K. Mitra, M.-S. Lai, S. Kumar, “Transient radiation transport in participating media within a rectangular enclosure,” J. Thermophys. Heat Transfer 11, 409–414 (1997).
[CrossRef]

Med. Phys.

B. C. Wilson, G. Adam, “A Monte Carlo model for the absorption and flux distributions of light tissue,” Med. Phys. 10, 824–830 (1983).
[CrossRef] [PubMed]

Phys. Med. Biol.

D. T. Deply, M. Cope, P. van der Zee, S. Arridge, S. Wray, J. Wyatt, “Estimation of optical pathlength through tissue from direct time of flight measurement,” Phys. Med. Biol. 33, 1433–1442 (1988).
[CrossRef]

Science

L. Wang, P. P. Ho, C. Liu, G. Zhang, R. R. Alfano, “Ballistic 2-D image through scattering walls using an ultrafast optical Kerr gate,” Science 253, 769–771 (1991).
[CrossRef] [PubMed]

Other

H. C. von de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).

R. Siegel, J. R. Howell, Thermal Radiation Heat Transfer, 3rd ed. (Hemisphere, Washington, D.C., 1992).

Z. Guo, S. Kumar, K.-C. San, “Multi-dimensional Monte Carlo simulation of short pulse laser radiation transport in scattering media,” J. Thermophys. Heat Transfer (to be published).

Y. Yamada, “Light–tissue interaction and optical imaging in biomedicine,” in Annual Review of Heat Transfer, C. L. Tien, ed. (Begell House, New York, 1995), Vol. 6, pp. 1–59.

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Figures (6)

Fig. 1
Fig. 1

Comparison of temporal distributions of transient transmittance for various scattering media in 10-mm-thick slab subject to collimated irradiation.

Fig. 2
Fig. 2

Comparison of temporal distributions of transient transmittance for various scattering media in 30-mm-thick slab subject to collimated irradiation.

Fig. 3
Fig. 3

Comparison of temporal distributions of transient reflectance for various scattering media in 10-mm-thick slab subject to collimated irradiation.

Fig. 4
Fig. 4

Plots of logarithmic reflectance versus time for various scattering media subject to collimated irradiation with slab thickness (a) L = 10 mm and (b) L = 30 mm.

Fig. 5
Fig. 5

Temporal distributions of transient transmittance for various scattering media in 10-mm-thick slab subject to diffuse irradiation.

Fig. 6
Fig. 6

Temporal distributions of transient reflectance for various scattering media in 10-mm-thick slab subject to diffuse irradiation.

Tables (3)

Tables Icon

Table 1 Properties of Five Selected Media

Tables Icon

Table 2 Optical Thickness of the Selected Media for Various Values of Slab Thickness

Tables Icon

Table 3 Values of Total Transmittance and the Largest Relative Errors between Anisotropic Scattering and Equivalent Isotropic Scattering Results for Several Calculation Examples

Equations (7)

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

Φμ=n=0 anPnμ,
Φμ=1-g21+g2-2gμ3/2,
σsI=1-gσs.
σeI=σsI+σa=1-gωσe,
ωI=σsIσeI=1-gω1-gω.
g=12-11 Φμμdμ.
ϕ=2πR, θ=cos-11+g2-1-g2/1+g-2gR22g,

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