Skip to main content
Log in

Approximations of the scattering phase functions of particles

  • Published:
Advances in Atmospheric Sciences Aims and scope Submit manuscript

Abstract

Based on anomalous diffraction theory and the modified Rayleigh-Debye approximation, a physically realistic model in bridging form is described to approximate the scattering phase function of particles. When compared with the exact method, the bridging technique reported here provides a reasonable approximation to the Mie results over a broader range of angles and size parameters, and it demonstrates the advantage of being computationally economic. In addition, the new phase function model can be essentially extended to other shapes and conveniently used in more complicated scattering and emission problems related to the solutions of the radiative transfer equations.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Acquista, C., 1976: Light scattering by tenuous particles: A generalization of the Rayleigh-Gans-Rocard approach. Applied Optics, 15, 2932–2936.

    Google Scholar 

  • Bourrly, C., P. Chiappetta, and T. Lemaire, 1989: Electromagnetic scattering by large rotating particles in the eikonal formalism. Optics Communications, 70, 173–176.

    Article  Google Scholar 

  • Caldas, M., and V. Semião, 2001: A new approximate phase function for isolated particles and polydispersions. Journal of Quantitative Spectroscopy & Radiative Transfer, 68, 521–542.

    Article  Google Scholar 

  • Chen, T. W., 1984: Generalized eikonal approximation. Physical Review (C), 30, 585–592.

    Google Scholar 

  • Chu, C. M., and S. W. Churchill, 1955: Representation of the angular distribution of radiation scattered by a spherical particle. Journal of the Optical Society of America, 45, 958–962.

    Google Scholar 

  • Chylek, P., and J. D. Klett, 1991a: Absorption and scattering of electromagnetic radiation by prismatic columns: Anomalous diffraction approximation. Journal of the Optical Society of America, A8, 1713–1720.

    Google Scholar 

  • Chylek, P., and J. D. Klett, 1991b: Extinction cross section of nonspherical particles in the anomalous diffraction approximation. Journal of the Optical Society of America, A8, 274–281.

    Google Scholar 

  • Cornette, W. M., and J. G. Shanks, 1992: Physically reasonable analytic expression for the single-scattering phase function. Applied Optics, 31, 3152–3160.

    Google Scholar 

  • Draine, B. T., 2003: Scattering by interstellar dust grains. I. Optical and ultraviolet. Astrophysical Journal, 598, 1017–1035.

    Article  Google Scholar 

  • Fournier, G. R, and B. T. N. Evans, 1991: Approximation to extinction efficiency for randomly oriented spheroids. Applied Optics, 30, 2042–2048.

    Google Scholar 

  • Fournier, G. R., and J. L. Forand, 1994: Analytic phase function for ocean water. Proceedings of the International Society for Optical Engineering (SPIE), Vol. 2258, Ocean Optics XII, J. S. Jaffe, Ed., 194–201pp.

  • Fournier, G. R., and B. T. N. Evans, 1996: Approximation to extinction efficiency from randomly oriented circular and elliptical cylinders. Applied Optics, 35, 4271–4282.

    Google Scholar 

  • Greeberg, J. M., and A. S. Meltzer, 1960: Scattering by nonspherical particles. Journal of Applied Physics, 31, 82–84.

    Article  Google Scholar 

  • Gordon, J. E., 1985: Simple method for approximating Mie scattering. Journal of the Optical Society of America, A2, 156–159.

    Google Scholar 

  • Gross, D. A., and P. Latimer, 1970: General solutions for the extinction and absorption efficiency of arbitrary oriented cylinders by anomalous diffraction approximation methods. Journal of the Optical Society of America, 60, 904–907.

    Google Scholar 

  • Henyey, L. C., and J. L. Greenstein, 1941: Diffuse radiation in the galaxy. Astrophysical Journal, 93, 70–83.

    Article  Google Scholar 

  • Irvine, W. M., 1965: Multiple scattering by large particles. Astrophysical Journal, 142, 1563–1575.

    Article  Google Scholar 

  • Kahnert, F. M., 2003: Numerical methods in electromagnetic scattering theory. Journal of Quantitative Spectroscopy & Radiative Transfer, 79–80, 775–824.

    Article  Google Scholar 

  • Kattawar, G. W., 1975: A three-parameter analytic phase function for multiple scattering calculations. Journal of Quantitative Spectroscopy & Radiative Transfer, 15, 839–849.

    Article  Google Scholar 

  • Khlebtsov, N. G., 1984: Integral equation for problems of light scattering matrix for soft spheroids comparable in size with the wavelength of light. Optics & Spectroscopy, 46, 292–295.

    Google Scholar 

  • Khlebtsov, N. G., and A. G. Melnikov, 1991: Integral equation for light scattering problems: Application to the orientationally induced birefringence of colloidal dispersions. Journal of Colloid and Interface Science, 142, 396–408.

    Article  Google Scholar 

  • Khlebtsov, N. G., A. G. Melnikov, and V. A. Bogatyrev, 1991: The linear dichroism and birefringence of colloidal dispersions: Approximate and exact approaches. Journal of Colloid and Interface Science, 146, 463–478.

    Article  Google Scholar 

  • Klett, J. D., and R. A. Sutherland, 1992: Approximate methods for modeling the scattering properties of non-spherical particles: Evaluation of the Wentzel-Kramers-Brillouin method. Applied Optics, 31, 373–386.

    Google Scholar 

  • Liou, K. N., 2002: An Introduction to Atmospheric Radiation. 2nd ed. Academic, San Diego, 169–252.

    Google Scholar 

  • Liu, P., 1994: A new phase function approximating to Mie scattering for radiative transport equations. Physics in Medicine and Biology, 39, 1025–1036.

    Article  Google Scholar 

  • Liu, Y., W. P. Arnott, and J. Hallet, 1998: Anomalous diffraction theory for arbitrarily oriented finite circular cylinders and comparison with exact T-matrix results. Applied Optics, 37, 5019–5030.

    Article  Google Scholar 

  • Maslowska, A., P. J. Flatau, and G. L. Stephen, 1994: On the validity of the anomalous diffraction theory to light scattering by cubes. Optics Communications, 107, 35–40.

    Article  Google Scholar 

  • McKellar, B. H. J., and M. A. Box, 1981: The scaling group of the radiative transfer equation. J. Atmos. Sci., 38, 1063–1068.

    Article  Google Scholar 

  • Meeten, G. H., 1982: An anomalous diffraction theory of linear birefringence and dichroism in colloidal dispersions. Journal of Colloid and Interface Science, 87, 407–415.

    Article  Google Scholar 

  • Mishchenko, M. I., W. J. Wiscombe, J. W. Hovenier, and L. D. Travis, 2000: Overview of scattering by nonspherical particles. Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications. M. I. Mishchenko et al., Eds., Academic, San Diego, 29–60.

    Google Scholar 

  • Modest, M. F., 2003: Radiative Heat Transfer. 2nd ed. Academic, New York, 362–368.

    Google Scholar 

  • Muinouen, K., 1996: Light scattering by Gaussian random particles: Rayleigh and Rayleigh—Gans approximations. Journal of Quantitative Spectroscopy & Radiative Transfer, 55, 603–613.

    Article  Google Scholar 

  • Napper, D. H., 1967: A diffraction theory approach to the total scattering by cubes. Colloid & Polymer Science, 218, 41–46.

    Google Scholar 

  • Perrin, J. M., and P. Chiappetta, 1985: Light scattering by large particles, I: A new theoretical description in the eikonal picture. Optica Acta, 32, 907–921.

    Google Scholar 

  • Perrin, J. M., and P. Chiappetta, 1986: Light scattering by large particles, II: A vectorical description in the eikonal picture. Optica Acta, 33, 1001–1022.

    Google Scholar 

  • Reynolds, L. O., and N. J. McCormick, 1980: Approximate two-parameter phase function for light scattering. Journal of the Optical Society of America, 70, 1206–1212.

    Google Scholar 

  • Saxon, D. S., 1955: Lectures on the scattering of light. Scientific Report No.9 Contract AF19 (122)–239, Meteorology Department, Univ. California, Los Angeles, 51–62.

    Google Scholar 

  • Sharma, S. K., and A. K. Roy, 2000: New approximate phase functions: Test for nonspherical particles. Journal of Quantitative Spectroscopy & Radiative Transfer, 64, 327–337.

    Article  Google Scholar 

  • Sharma, S. K., A. K. Roy, and D. J. Somerford, 1998: New approximate phase functions for scattering of unpolarized light by dielectric particles. Journal of Quantitative Spectroscopy & Radiative Transfer, 60, 1001–1010.

    Article  Google Scholar 

  • Shimizu, K., 1983: Modification of the Rayleigh-Debye approximation. Journal of the Optical Society of America, 73, 504–507.

    Article  Google Scholar 

  • Streekstra, G. J., A. G. Hooekstra, and R. M. Heethaar, 1994: Anomalous diffraction by arbitrarily oriented ellipsoids: Application in ektacytometry. Applied Optics, 33, 7288–7296.

    Article  Google Scholar 

  • Sun, W., and Q. Fu, 2001: Anomalous diffraction theory for arbitrarily oriented hexagonal crystals. Journal of Quantitative Spectroscopy & Radiative Transfer, 63, 727–737.

    Article  Google Scholar 

  • Van de Hulst, H. C., 1957: Light Scattering by Small Particles. John Wiley & Sons, New York, 172–195pp.

    Google Scholar 

  • Wriedt, T., 1998: A review of elastic light scattering theories. Particle & Particle Systems Characterization, 15, 67–74.

    Article  Google Scholar 

  • Xu, M., and R. R. Alfano, 2003: Anomalous diffraction of light with geometrical path statistics of rays and a Gaussian ray approximation. Optics Letters, 28(3), 179–181.

    Google Scholar 

  • Zhao, J.-Q., 2003: Light scattering by arbitrary shaped particles. Ph. D. dissertation, Cold and Arid Regions Environmental and Engineering Research Institute, Chinese Academy of Sciences, 49–50.

    Google Scholar 

  • Zhao, J.-Q., and Y.-Q. Hu, 2003: Bridging technique for calculating the extinction efficiency of arbitrary shaped particles. Applied Optics, 42, 4937–45.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zhao, JQ., Shi, G., Che, H. et al. Approximations of the scattering phase functions of particles. Adv. Atmos. Sci. 23, 802–808 (2006). https://doi.org/10.1007/s00376-006-0802-y

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00376-006-0802-y

Key words

Navigation