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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Editor: Stephen A. Burns
  • Vol. 23, Iss. 7 — Jul. 1, 2006
  • pp: 1639–1644

Radiative transfer equations with varying refractive index: a mathematical perspective

Guillaume Bal  »View Author Affiliations


JOSA A, Vol. 23, Issue 7, pp. 1639-1644 (2006)
http://dx.doi.org/10.1364/JOSAA.23.001639


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Abstract

Established mathematical techniques to model the energy density of high-frequency waves in random media by radiative transfer equations and to model the small mean-free-path limit of radiative transfer solutions by diffusion equations are reviewed. These techniques are then applied to the derivation of radiative transfer and diffusion equations for the radiance, also known as specific intensity, of electromagnetic waves in situations where the refractive index of the underlying structure varies smoothly in space.

© 2006 Optical Society of America

OCIS Codes
(030.5620) Coherence and statistical optics : Radiative transfer
(080.2710) Geometric optics : Inhomogeneous optical media
(170.5280) Medical optics and biotechnology : Photon migration
(290.1990) Scattering : Diffusion

ToC Category:
Coherence and Statistical Optics

History
Original Manuscript: November 22, 2005
Manuscript Accepted: January 20, 2006

Virtual Issues
Vol. 1, Iss. 8 Virtual Journal for Biomedical Optics

Citation
Guillaume Bal, "Radiative transfer equations with varying refractive index: a mathematical perspective," J. Opt. Soc. Am. A 23, 1639-1644 (2006)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-23-7-1639


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References

  1. S. Chandrasekhar, Radiative Transfer (Dover, 1960).
  2. A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, 1978).
  3. L. Erdös and H. T. Yau, 'Linear Boltzmann equation as the weak coupling limit of a random Schrödinger equation,' Commun. Pure Appl. Math. 53, 667-735 (2000). [CrossRef]
  4. H. Spohn, 'Derivation of the transport equation for electrons moving through random impurities,' J. Stat. Phys. 17, 385-412 (1977). [CrossRef]
  5. G. Bal, 'Kinetic models for scalar wave fields in random media,' Wave Motion 43, 132-157 (2005).
  6. L. Ryzhik, G. Papanicolaou, and J. B. Keller, 'Transport equations for elastic and other waves in random media,' Wave Motion 24, 327-370 (1996). [CrossRef]
  7. A. Bensoussan, J.-L. Lions, and G. C. Papanicolaou, 'Boundary layers and homogenization of transport processes,' Res. Inst. Math. Sci. Kyoto Univ. 15, 53-157 (1979). [CrossRef]
  8. R. Dautray and J.-L. Lions, Mathematical Analysis and Numerical Methods for Science and Technology (Springer-Verlag, 1993), Vol. 6. [CrossRef]
  9. E. W. Larsen and J. B. Keller, 'Asymptotic solution of neutron transport problems for small mean free paths,' J. Math. Phys. 15, 75-81 (1974). [CrossRef]
  10. H. A. Ferwerda, 'The radiative transfer equation for scattering media with a spatially varying refractive index,' J. Opt. A, Pure Appl. Opt. 1, L1-L2 (1999). [CrossRef]
  11. T. Khan and H. Jiang, 'A new diffusion approximation to the radiative transfer equation for scattering media with spatially varying refractive indices,' J. Opt. A, Pure Appl. Opt. 5, 137-141 (2003). [CrossRef]
  12. T. Khan and A. Thomas, 'Comparison of PN or spherical harmonics approximation for scattering media with spatially varying and spatially constant refractive indices,' Opt. Commun. 255, 130-166 (2005). [CrossRef]
  13. L. Martí-López, J. Bouza-Domínguez, J. C. Hebden, A. S. R. Arridge, and R. A. Martinéz-Celerio, 'Validity conditions for the radiative transfer equation,' J. Opt. Soc. Am. A 20, 2046-2056 (2003). [CrossRef]
  14. M. Premaratne, E. Premaratne, and A. J. Lowery, 'The photon transport equation for turbid biological media with spatially varying isotropic refractive index,' Opt. Express 13, 389-399 (2005). [CrossRef] [PubMed]
  15. J. Tualle and E. Tenet, 'Derivation of the radiative transfer equation for scattering media with spatially varying refractive index,' Opt. Commun. 228, 33-38 (2003). [CrossRef]
  16. M. L. Shendeleva, 'Radiative transfer in a turbid medium with a varying refractive index: comment,' J. Opt. Soc. Am. A 21, 2464-2467 (2004). [CrossRef]
  17. K. Kline and W. I. Kay, Electromagnetic Theory and Geometrical Optics (Wiley-Interscience, 1965).
  18. G. B. Whitham, Linear and Nonlinear Waves (Wiley-Interscience, 1974).
  19. P. Gérard, P. A. Markowich, N. J. Mauser, and F. Poupaud, 'Homogenization limits and Wigner transforms,' Commun. Pure Appl. Math. 50, 323-380 (1997). [CrossRef]
  20. P.-L. Lions and T. Paul, 'Sur les mesures de Wigner,' Rev. Mat. Iberoam. 9, 553-618 (1993). [CrossRef]
  21. G. Bal, J. B. Keller, G. Papanicolaou, and L. Ryzhik, 'Transport theory for waves with reflection and transmission at interfaces,' Wave Motion 30, 303-327 (1999). [CrossRef]
  22. G. Bal, G. Papanicolaou, and L. Ryzhik, 'Probabilistic theory of transport processes with polarization,' SIAM J. Appl. Math. 60, 1639-1666 (2000). [CrossRef]
  23. J. Spanier and E. M. Gelbard, Monte Carlo Principles and Neutron Transport Problems (Addison-Wesley, 1969).
  24. G. Bal and M. Moscoso, 'Polarization effects of seismic waves on the basis of radiative transport theory,' Geophys. J. Int. 142, 571-585 (2000). [CrossRef]

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