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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 15, Iss. 13 — Jun. 25, 2007
  • pp: 8479–8485

The far-field modified uncorrelated single-scattering approximation in light scattering by a small volume element

Peng-Wang Zhai, George W. Kattawar, and Ping Yang  »View Author Affiliations


Optics Express, Vol. 15, Issue 13, pp. 8479-8485 (2007)
http://dx.doi.org/10.1364/OE.15.008479


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Abstract

Consider light scattering by a small volume element filled with randomly positioned particles, the far-field modified uncorrelated single-scattering approximation (MUSSA) leads to the incoherent summation of the phase matrices of particles in the volume. The validity of the MUSSA is revisited in this paper to include the variation of the particles’ positions. Analytical results show that the MUSSA does not require the distance between any pair of particles in the volume to be larger than what is required in the single-scattering approximation (SSA). Instead, it requires the dimension of the volume to be large compared to the incident wavelength. The new results also make the requirements of MUSSA easier to be met. We also analyze energy conservation for the MUSSA.

© 2007 Optical Society of America

OCIS Codes
(020.1670) Atomic and molecular physics : Coherent optical effects
(030.5620) Coherence and statistical optics : Radiative transfer
(290.4210) Scattering : Multiple scattering
(290.5850) Scattering : Scattering, particles

ToC Category:
Scattering

History
Original Manuscript: June 5, 2007
Revised Manuscript: June 18, 2007
Manuscript Accepted: June 19, 2007
Published: June 22, 2007

Virtual Issues
Vol. 2, Iss. 7 Virtual Journal for Biomedical Optics

Citation
Peng-Wang Zhai, George W. Kattawar, and Ping Yang, "The far-field modified uncorrelated single-scattering approximation in light scattering by a small volume element," Opt. Express 15, 8479-8485 (2007)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-13-8479


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References

  1. V. Kourganoff, Basic Methods in Transfer Problems, (Clarendon Press, London, 1952).
  2. S. Chandrasekhar, Radiative Transfer (Dover, New York, 1960).
  3. R. W. Preisendorfer, Radiative Transfer on Discrete Spaces (Pergamon Press, Oxford, 1965).
  4. G. N. Plass and G. W. Kattawar, "Monte Carlo calculations of light scattering from clouds," Appl. Opt.  7, 415- 419 (1968). [CrossRef] [PubMed]
  5. C. N. Adams and G. W. Kattawar, "Solutions of the equation of radiative transfer by an invariant imbedding approach," J. Quant. Spectrosc. Radiat. Transf. 10, 341-366 (1970). [CrossRef]
  6. H. C. van de Hulst, Multiple Light Scattering: Tables, Formulas, and Applications, 1 and 2. (Academic Press, New York, 1980).
  7. G. I. Marchuk, G. A. Mikhailov, M. A. Nazaraliev, R. A. Darbinjan, B. A. Kargin, and B. S. Elepov, the Monte Carlo Methods in Atmospheric Optics (Springer-Verlag, Berlin, 1980).
  8. K. Stamnes, S.-C. Tsay, W. Wiscombe, and K. Jayaweera, "Numerically stable algorithm for discrete-ordinate method radiative trasfer in multiple scattering and emitting layered media," Appl. Opt.,  27, 2502-2509 (1988). [CrossRef]
  9. F. Weng, "A multi-layer discrete-ordinate method for vector radiative transfer in a vertically-inhomogeneous, emitting and scattering atmosphere-I. theory," J. Quant. Spectrosc. Radiat. Transf. 47, 19-33 (1992). [CrossRef]
  10. F. Weng, "A multi-layer discrete-ordinate method for vector radiative transfer in a vertically-inhomogeneous, emitting and scattering atmosphere-II. Application," J. Quant. Spectrosc. Radiat. Transf. 47, 35-42 (1992). [CrossRef]
  11. R. D. M. Garcia and C. E. Siewert, "A generalized spherical harmonics solution for radiative transfer models that include polarization effects," J. Quant. Spectrosc. Radiat. Transf. 36, 401-423 (1986). [CrossRef]
  12. D. M. O’Brien, "Accelerated quasi Monte Carlo integration of the radiative transfer equation," J. Quant. Spectrosc. Radiat. Transf.  48, 41-59 (1992). [CrossRef]
  13. E. P. Zege, I. L. Katsev, and I. N. Polonsky, "Multicomponent approach to light propagation in clouds and mists," Appl. Opt.,  32, 2803-2812 (1993). [CrossRef] [PubMed]
  14. K. F. Evans, "The spherical harmonic discrete ordinate method for three-dimensional atmospheric radiative transfer," J. Atmos. Sci.  55, 429-446 (1998). [CrossRef]
  15. K. N. Liou, An Introduction to Atmospheric Radiation, Second Edition, (Academic Press, New York, 2002).
  16. M. I. Mishchenko, "Vector radiative transfer equation for arbitrarily shaped and arbitrarily oriented particles: a microphysical derivation from statistical electromagnetics," Appl. Opt. 41, 7114-7134 (2002). [CrossRef] [PubMed]
  17. M. I. Mishchenko, L. D. Travis and A. A. Lacis, Multiple Scattering of Light by Particles, (Cambridge University Press, Cambridge, UK, 2006).
  18. M. I. Mishchenko, J. W. Hovenier, and D. W. Mackowski, "Single scattering by a small volume element," J. Opt. Soc. Am. A 21, 71-87 (2004) [CrossRef]
  19. J. W. Hovenier, "Measuring scattering matrices of small particles at optical wavelengths," in Light Scattering by Nonspherical Particles, M. I. Mishchenko, J. W. Hovenier, and L. D. Travis, eds. (Academic, San Diego, Calif., 2000), pp. 355-365.
  20. H. Volten, O. Munoz, E. Rol, J. F. de Haan, W. Vassen, J. W. Hovenier, K. Muinonen, and T. Nousiainen, "Scattering matrices of mineral aerosol particles at 441.6 nm and 632.8 nm," J. Geophys. Res. 106, 17375-17402 (2001). [CrossRef]
  21. O. Munoz, H. Volten, J. F. de Haan, W. Vassen, J. W. Hovenier, "Experimental determination of scattering matrices of randomly oriented flay ash and clay particles at 442 and 633 nm," J. Geophys. Res. 106, 22833- 22844 (2001). [CrossRef]
  22. J. W. Hovenier, H. Volten, O. Munoz, W. J. van der Zande, and L. B. F. M. Waters, "Laboratory studies of scattering matrices for randomly oriented particles: potentials, problems, and perspectives," J. Quant. Spectrosc. Radiat. Transf. 79/80, 741-755 (2003). [CrossRef]

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