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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Stephen A. Burns
  • Vol. 23, Iss. 1 — Jan. 1, 2006
  • pp: 91–98

Modified two-flux approximation for identification of radiative properties of absorbing and scattering media from directional-hemispherical measurements

Leonid Dombrovsky, Jaona Randrianalisoa, and Dominique Baillis  »View Author Affiliations

JOSA A, Vol. 23, Issue 1, pp. 91-98 (2006)

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A modified two-flux approximation is suggested for calculating the hemispherical transmittance and reflectance of a refracting, absorbing, and scattering medium in the case of collimated irradiation of the sample along the normal to the interface. The Fresnel reflection is taken into account in this approach. It is shown that the new approximation is rather accurate for the model transport scattering function. For an arbitrary scattering medium, the error of the modified two-flux approximation is estimated by comparison with the exact numerical calculations for the Henyey–Greenstein scattering function in a wide range of albedos and optical thicknesses. Possible applications of the derived analytical solution to identification problems are discussed.

© 2006 Optical Society of America

OCIS Codes
(120.5700) Instrumentation, measurement, and metrology : Reflection
(120.5710) Instrumentation, measurement, and metrology : Refraction
(120.7000) Instrumentation, measurement, and metrology : Transmission
(290.4210) Scattering : Multiple scattering

ToC Category:

Virtual Issues
Vol. 1, Iss. 2 Virtual Journal for Biomedical Optics

Leonid Dombrovsky, Jaona Randrianalisoa, and Dominique Baillis, "Modified two-flux approximation for identification of radiative properties of absorbing and scattering media from directional-hemispherical measurements," J. Opt. Soc. Am. A 23, 91-98 (2006)

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  1. D. Baillis and J.-F. Sacadura, "Thermal radiation properties of dispersed media: theoretical prediction and experimental characterization," J. Quant. Spectrosc. Radiat. Transf. 67, 327-363 (2000). [CrossRef]
  2. J.-F. Sacadura and D. Baillis, "Experimental characterization of thermal radiation properties of disperse media," Int. J. Therm. Sci. 41, 699-707 (2002). [CrossRef]
  3. M. F. Modest, Radiative Heat Transfer, 2nd ed. (Academic, 2003).
  4. K. S. Adzerikho, E. F. Nogotov, and V. P. Trofimov, Radiative Heat Transfer in Two-Phase Media (CRC Press, 1992).
  5. L. A. Dombrovsky, Radiation Heat Transfer in Disperse Systems (Begell House, 1996).
  6. B. Davison, Neutron Transport Theory (Oxford U. Press, 1957).
  7. B. H. J. McKellar and M. A. Box, "The scaling group of the radiative transfer equation," J. Atmos. Sci. 38, 1063-1068 (1981). [CrossRef]
  8. H. Lee and R. O. Buckius, "Scaling anisotropic scattering in radiation heat transfer for a planar medium," ASME J. Heat Transfer 104, 68-75 (1982). [CrossRef]
  9. L. A. Dombrovsky, "Approximate methods for calculating radiation heat transfer in dispersed systems," Therm. Eng. 43, 235-243 (1996).
  10. H. T. K. Tagne and D. Baillis, "Isotropic scaling limits for one-dimensional radiative heat transfer with collimated incidence," J. Quant. Spectrosc. Radiat. Transf. 93, 103-113 (2005). [CrossRef]
  11. V. V. Sobolev, Light Scattering in Planetary Atmospheres (Pergamon, 1975).
  12. M. Caldas and V. Semião, "A new approximate phase function for isolated particles and polydispersions," J. Quant. Spectrosc. Radiat. Transf. 68, 521-542 (2001). [CrossRef]
  13. P. J. Coelho, "Bounded skew high order resolution schemes for the discrete ordinates method," J. Comput. Phys. 175, 412-437 (2002). [CrossRef]
  14. B.-T. Liou and C.-Y. Wu, "Radiative transfer in a multi-layer medium with Fresnel interfaces," Heat Mass Transfer 32, 103-107 (1996). [CrossRef]
  15. C. Muresan, R. Vaillon, C. Menezo, and R. Morlot, "Discrete ordinates solution of coupled conductive radiative heat transfer in a two-layer slab with Fresnel interfaces subject to diffuse and obliquely collimated irradiation," J. Quant. Spectrosc. Radiat. Transf. 84, 551-562 (2004). [CrossRef]
  16. L. A. Dombrovsky, "Thermal radiation from nonisothermal spherical particle," Int. J. Heat Mass Transfer 43, 1661-1672 (2000). [CrossRef]
  17. L. A. Dombrovsky, "A modified differential approximation for thermal radiation of semitransparent nonisothermal particles: application to optical diagnostics of plasma spraying," J. Quant. Spectrosc. Radiat. Transf. 73, 433-441 (2002). [CrossRef]
  18. L. Pilon and R. Viskanta, "Radiation characteristics of glass containing bubbles," J. Am. Ceram. Soc. 86, 1313-1320 (2003). [CrossRef]
  19. D. Baillis, L. Pilon, H. Randrianalisoa, R. Gomez, and R. Viskanta, "Measurements of radiation characteristics of fused quartz containing bubbles," J. Opt. Soc. Am. A 21, 149-159 (2004). [CrossRef]
  20. L. Dombrovsky, J. Randrianalisoa, D. Baillis, and L. Pilon, "Use of Mie theory to analyze experimental data to identify infrared properties of fused quartz containing bubbles," Appl. Opt. (to be published).
  21. A. J. Martin and J. Pidorenko, "Insulation microspheres and method of manufacture," U.S. patent 5,713,974 (February 3, 1998).
  22. M. S. Allen, R. G. Baumgartner, J. E. Fesnire, and S. D. Augustynowicz, "Advances in microsphere insulation systems," AIP Conf. Proc. 710, 619-626 (2004). [CrossRef]
  23. M. L. German and P. S. Grinchuk, "Mathematical model for calculating the heat-protection properties of the composite coating 'ceramic microspheres-binder'," J. Eng. Phys. Thermophys. 75, 1301-1313 (2002). [CrossRef]
  24. L. A. Dombrovsky, "Modeling of thermal radiation of a polymer coating containing hollow microspheres," High Temp. 43, 247-258 (2005). [CrossRef]

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