Abstract

The extinction efficiencies of atmospheric particles are essential to determining radiation attenuation and thus are fundamentally related to atmospheric radiative transfer. The extinction efficiencies can also be used to retrieve particle sizes or refractive indices through particle characterization techniques. This study first uses the Debye series to improve the accuracy of high-frequency extinction formulae for spheroids in the context of Complex angular momentum theory by determining an optimal number of edge-effect terms. We show that the optimal edge-effect terms can be accurately obtained by comparing the results from the approximate formula with their counterparts computed from the invariant imbedding Debye series and T-matrix methods. An invariant imbedding T-matrix method is employed for particles with strong absorption, in which case the extinction efficiency is equivalent to two plus the edge-effect efficiency. For weakly absorptive or non-absorptive particles, the T-matrix results contain the interference between the diffraction and higher-order transmitted rays. Therefore, the Debye series was used to compute the edge-effect efficiency by separating the interference from the transmission on the extinction efficiency. We found that the optimal number strongly depends on the refractive index and is relatively insensitive to the particle geometry and size parameter. By building a table of optimal numbers of edge-effect terms, we developed an efficient and accurate extinction simulator that has been fully tested for randomly oriented spheroids with various aspect ratios and a wide range of refractive indices.

© 2017 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Bridging the gap between the Rayleigh and Thomson limits for spheres and spheroids

G. R. Fournier and B. T. N. Evans
Appl. Opt. 32(30) 6159-6166 (1993)

Light scattering by polydispersions of randomly oriented spheroids with sizes comparable to wavelengths of observation

Michael I. Mishchenko and Larry D. Travis
Appl. Opt. 33(30) 7206-7225 (1994)

References

  • View by:
  • |
  • |
  • |

  1. K. N. Liou, An Introduction to Atmospheric Radiation (Academic Press, 2002).
  2. G. Crawley, M. Cournil, and D. D. Benedetto, “Size analysis of fine particle suspensions by spectral turbidimetry: Potential and limits,” Powder Technol. 91(3), 197–208 (1997).
    [Crossref]
  3. M. Z. Li, A. Thor Frette, and D. Wilkinson, “Particle size distribution determination from spectral extinction using neural networks,” Ind. Eng. Chem. Res. 40(21), 4615–4622 (2001).
    [Crossref]
  4. L. Wang, X. Sun, and J. Xing, “Retrieval of spheroidal particle size distribution using the approximate method in spectral extinction technique,” Opt. Commun. 285(7), 1646–1653 (2012).
    [Crossref]
  5. M. I. Cotterell, R. E. Willoughby, B. R. Bzdek, A. I. Orr-Ewing, and J. P. Reid, “A complete parameterization of the relative humidity and wavelength dependence of the refractive index of hygroscopic inorganic aerosol particles,” Atmos. Chem. Phys. Discuss. (in review).
  6. H. M. Nussenzveig, Diffraction Effects in Semiclassical Scattering (Cambridge University, 1992).
  7. M. Berg, C. Sorensen, and A. Chakrabarti, “A new explanation of the extinction paradox,” J. Quant. Spectrosc. Radiat. Transf. 112(7), 1170–1181 (2011).
    [Crossref]
  8. O. Dubovik, A. Sinyuk, T. Lapyonok, B. N. Holben, M. Mishchenko, P. Yang, T. F. Eck, H. Volten, O. Muñoz, B. Veihelmann, W. J. van der Zande, J.-F. Leon, M. Sorokin, and I. Slutsker, “Application of spheroid models to account for aerosol particle nonsphericity in remote sensing of desert dust,” J. Geophys. Res. 111(D11), D11208 (2006).
    [Crossref]
  9. G. R. Fournier and B. T. Evans, “Approximation to extinction efficiency for randomly oriented spheroids,” Appl. Opt. 30(15), 2042–2048 (1991).
    [Crossref] [PubMed]
  10. B. T. Evans and G. R. Fournier, “Analytic approximation to randomly oriented spheroid extinction,” Appl. Opt. 33(24), 5796–5804 (1994).
    [Crossref] [PubMed]
  11. J. Q. Zhao and Y. Q. Hu, “Bridging technique for calculating the extinction efficiency of arbitrary shaped particles,” Appl. Opt. 42(24), 4937–4945 (2003).
    [Crossref] [PubMed]
  12. A. A. Kokhanovsky and E. P. Zege, “Optical properties of aerosol particles: A review of approximate analytical solutions,” J. Aerosol Sci. 28(1), 1–21 (1997).
    [Crossref]
  13. A. J. Baran and S. Havemann, “Rapid computation of the optical properties of hexagonal columns using complex angular momentum theory,” J. Quant. Spectrosc. Radiat. Transf. 63(2-6), 499–519 (1999).
    [Crossref]
  14. P. Yang, Q. Feng, G. Hong, G. W. Kattawar, W. J. Wiscombe, M. I. Mishchenko, O. Dubovik, I. Laszlo, and I. N. Sokolik, “Modeling of the scattering and radiative properties of non-spherical dust-like aerosols,” J. Aerosol Sci. 38(10), 995–1014 (2007).
    [Crossref]
  15. L. Bi, P. Yang, G. W. Kattawar, and R. Kahn, “Single-scattering properties of triaxial ellipsoidal particles for a size parameter range from the Rayleigh to geometric-optics regimes,” Appl. Opt. 48(1), 114–126 (2009).
    [Crossref] [PubMed]
  16. K. N. Liou, Y. Takano, and P. Yang, “On geometric optics and surface waves for light scattering by spheres,” J. Quant. Spectrosc. Radiat. Transf. 111(12–13), 1980–1989 (2010).
    [Crossref]
  17. H. M. Nussenzveig and W. J. Wiscombe, “Efficiency factors in Mie scattering,” Phys. Rev. Lett. 45(18), 1490–1494 (1980).
    [Crossref]
  18. L. Bi and P. Yang, “High-frequency extinction efficiencies of spheroids: Rigorous T-matrix solutions and semi-empirical approximations,” Opt. Express 22(9), 10270–10293 (2014).
    [Crossref] [PubMed]
  19. V. A. Fock, Electromagnetic Diffraction and Propagation Problems (Pergamon, 1965).
  20. D. S. Jones, “High-frequency scattering of electromagnetic waves,” Proc. R. Soc. Lond. A Math. Phys. Sci. 240(1221), 206–213 (1957).
    [Crossref]
  21. L. Bi, P. Yang, G. W. Kattawar, and M. I. Mishchenko, “Optical tunneling by arbitrary macroscopic three-dimensional objects,” Phys. Rev. A 92(1), 013814 (2015).
    [Crossref]
  22. F. Xu, J. A. Lock, and G. Gouesbet, “Debye series for light scattering by a nonspherical particle,” Phys. Rev. A 81(4), 043824 (2010).
    [Crossref]
  23. E. A. Hovenac and J. A. Lock, “Assessing the contribution of surface waves and complex rays to far-field Mie scattering by use of the Debye series,” JOSAA 9(5), 781–795 (1992).
    [Crossref]
  24. B. R. Johnson, “Invariant imbedding T matrix approach to electromagnetic scattering,” Appl. Opt. 27(23), 4861–4873 (1988).
    [Crossref] [PubMed]
  25. L. Bi, P. Yang, G. W. Kattawar, and M. I. Mishchenko, “Efficient implementation of the invariant imbedding T-matrix method and the separation of variables method applied to large non-spherical inhomogeneous particles,” J. Quant. Spectrosc. Radiat. Transf. 116(2), 169–183 (2013).
    [Crossref]
  26. H. C. van de Hulst, Light Scattering by Small Particles (Dover, 1981).

2015 (1)

L. Bi, P. Yang, G. W. Kattawar, and M. I. Mishchenko, “Optical tunneling by arbitrary macroscopic three-dimensional objects,” Phys. Rev. A 92(1), 013814 (2015).
[Crossref]

2014 (1)

2013 (1)

L. Bi, P. Yang, G. W. Kattawar, and M. I. Mishchenko, “Efficient implementation of the invariant imbedding T-matrix method and the separation of variables method applied to large non-spherical inhomogeneous particles,” J. Quant. Spectrosc. Radiat. Transf. 116(2), 169–183 (2013).
[Crossref]

2012 (1)

L. Wang, X. Sun, and J. Xing, “Retrieval of spheroidal particle size distribution using the approximate method in spectral extinction technique,” Opt. Commun. 285(7), 1646–1653 (2012).
[Crossref]

2011 (1)

M. Berg, C. Sorensen, and A. Chakrabarti, “A new explanation of the extinction paradox,” J. Quant. Spectrosc. Radiat. Transf. 112(7), 1170–1181 (2011).
[Crossref]

2010 (2)

F. Xu, J. A. Lock, and G. Gouesbet, “Debye series for light scattering by a nonspherical particle,” Phys. Rev. A 81(4), 043824 (2010).
[Crossref]

K. N. Liou, Y. Takano, and P. Yang, “On geometric optics and surface waves for light scattering by spheres,” J. Quant. Spectrosc. Radiat. Transf. 111(12–13), 1980–1989 (2010).
[Crossref]

2009 (1)

2007 (1)

P. Yang, Q. Feng, G. Hong, G. W. Kattawar, W. J. Wiscombe, M. I. Mishchenko, O. Dubovik, I. Laszlo, and I. N. Sokolik, “Modeling of the scattering and radiative properties of non-spherical dust-like aerosols,” J. Aerosol Sci. 38(10), 995–1014 (2007).
[Crossref]

2006 (1)

O. Dubovik, A. Sinyuk, T. Lapyonok, B. N. Holben, M. Mishchenko, P. Yang, T. F. Eck, H. Volten, O. Muñoz, B. Veihelmann, W. J. van der Zande, J.-F. Leon, M. Sorokin, and I. Slutsker, “Application of spheroid models to account for aerosol particle nonsphericity in remote sensing of desert dust,” J. Geophys. Res. 111(D11), D11208 (2006).
[Crossref]

2003 (1)

2001 (1)

M. Z. Li, A. Thor Frette, and D. Wilkinson, “Particle size distribution determination from spectral extinction using neural networks,” Ind. Eng. Chem. Res. 40(21), 4615–4622 (2001).
[Crossref]

1999 (1)

A. J. Baran and S. Havemann, “Rapid computation of the optical properties of hexagonal columns using complex angular momentum theory,” J. Quant. Spectrosc. Radiat. Transf. 63(2-6), 499–519 (1999).
[Crossref]

1997 (2)

G. Crawley, M. Cournil, and D. D. Benedetto, “Size analysis of fine particle suspensions by spectral turbidimetry: Potential and limits,” Powder Technol. 91(3), 197–208 (1997).
[Crossref]

A. A. Kokhanovsky and E. P. Zege, “Optical properties of aerosol particles: A review of approximate analytical solutions,” J. Aerosol Sci. 28(1), 1–21 (1997).
[Crossref]

1994 (1)

1992 (1)

E. A. Hovenac and J. A. Lock, “Assessing the contribution of surface waves and complex rays to far-field Mie scattering by use of the Debye series,” JOSAA 9(5), 781–795 (1992).
[Crossref]

1991 (1)

1988 (1)

1980 (1)

H. M. Nussenzveig and W. J. Wiscombe, “Efficiency factors in Mie scattering,” Phys. Rev. Lett. 45(18), 1490–1494 (1980).
[Crossref]

1957 (1)

D. S. Jones, “High-frequency scattering of electromagnetic waves,” Proc. R. Soc. Lond. A Math. Phys. Sci. 240(1221), 206–213 (1957).
[Crossref]

Baran, A. J.

A. J. Baran and S. Havemann, “Rapid computation of the optical properties of hexagonal columns using complex angular momentum theory,” J. Quant. Spectrosc. Radiat. Transf. 63(2-6), 499–519 (1999).
[Crossref]

Benedetto, D. D.

G. Crawley, M. Cournil, and D. D. Benedetto, “Size analysis of fine particle suspensions by spectral turbidimetry: Potential and limits,” Powder Technol. 91(3), 197–208 (1997).
[Crossref]

Berg, M.

M. Berg, C. Sorensen, and A. Chakrabarti, “A new explanation of the extinction paradox,” J. Quant. Spectrosc. Radiat. Transf. 112(7), 1170–1181 (2011).
[Crossref]

Bi, L.

L. Bi, P. Yang, G. W. Kattawar, and M. I. Mishchenko, “Optical tunneling by arbitrary macroscopic three-dimensional objects,” Phys. Rev. A 92(1), 013814 (2015).
[Crossref]

L. Bi and P. Yang, “High-frequency extinction efficiencies of spheroids: Rigorous T-matrix solutions and semi-empirical approximations,” Opt. Express 22(9), 10270–10293 (2014).
[Crossref] [PubMed]

L. Bi, P. Yang, G. W. Kattawar, and M. I. Mishchenko, “Efficient implementation of the invariant imbedding T-matrix method and the separation of variables method applied to large non-spherical inhomogeneous particles,” J. Quant. Spectrosc. Radiat. Transf. 116(2), 169–183 (2013).
[Crossref]

L. Bi, P. Yang, G. W. Kattawar, and R. Kahn, “Single-scattering properties of triaxial ellipsoidal particles for a size parameter range from the Rayleigh to geometric-optics regimes,” Appl. Opt. 48(1), 114–126 (2009).
[Crossref] [PubMed]

Bzdek, B. R.

M. I. Cotterell, R. E. Willoughby, B. R. Bzdek, A. I. Orr-Ewing, and J. P. Reid, “A complete parameterization of the relative humidity and wavelength dependence of the refractive index of hygroscopic inorganic aerosol particles,” Atmos. Chem. Phys. Discuss. (in review).

Chakrabarti, A.

M. Berg, C. Sorensen, and A. Chakrabarti, “A new explanation of the extinction paradox,” J. Quant. Spectrosc. Radiat. Transf. 112(7), 1170–1181 (2011).
[Crossref]

Cotterell, M. I.

M. I. Cotterell, R. E. Willoughby, B. R. Bzdek, A. I. Orr-Ewing, and J. P. Reid, “A complete parameterization of the relative humidity and wavelength dependence of the refractive index of hygroscopic inorganic aerosol particles,” Atmos. Chem. Phys. Discuss. (in review).

Cournil, M.

G. Crawley, M. Cournil, and D. D. Benedetto, “Size analysis of fine particle suspensions by spectral turbidimetry: Potential and limits,” Powder Technol. 91(3), 197–208 (1997).
[Crossref]

Crawley, G.

G. Crawley, M. Cournil, and D. D. Benedetto, “Size analysis of fine particle suspensions by spectral turbidimetry: Potential and limits,” Powder Technol. 91(3), 197–208 (1997).
[Crossref]

Dubovik, O.

P. Yang, Q. Feng, G. Hong, G. W. Kattawar, W. J. Wiscombe, M. I. Mishchenko, O. Dubovik, I. Laszlo, and I. N. Sokolik, “Modeling of the scattering and radiative properties of non-spherical dust-like aerosols,” J. Aerosol Sci. 38(10), 995–1014 (2007).
[Crossref]

O. Dubovik, A. Sinyuk, T. Lapyonok, B. N. Holben, M. Mishchenko, P. Yang, T. F. Eck, H. Volten, O. Muñoz, B. Veihelmann, W. J. van der Zande, J.-F. Leon, M. Sorokin, and I. Slutsker, “Application of spheroid models to account for aerosol particle nonsphericity in remote sensing of desert dust,” J. Geophys. Res. 111(D11), D11208 (2006).
[Crossref]

Eck, T. F.

O. Dubovik, A. Sinyuk, T. Lapyonok, B. N. Holben, M. Mishchenko, P. Yang, T. F. Eck, H. Volten, O. Muñoz, B. Veihelmann, W. J. van der Zande, J.-F. Leon, M. Sorokin, and I. Slutsker, “Application of spheroid models to account for aerosol particle nonsphericity in remote sensing of desert dust,” J. Geophys. Res. 111(D11), D11208 (2006).
[Crossref]

Evans, B. T.

Feng, Q.

P. Yang, Q. Feng, G. Hong, G. W. Kattawar, W. J. Wiscombe, M. I. Mishchenko, O. Dubovik, I. Laszlo, and I. N. Sokolik, “Modeling of the scattering and radiative properties of non-spherical dust-like aerosols,” J. Aerosol Sci. 38(10), 995–1014 (2007).
[Crossref]

Fournier, G. R.

Gouesbet, G.

F. Xu, J. A. Lock, and G. Gouesbet, “Debye series for light scattering by a nonspherical particle,” Phys. Rev. A 81(4), 043824 (2010).
[Crossref]

Havemann, S.

A. J. Baran and S. Havemann, “Rapid computation of the optical properties of hexagonal columns using complex angular momentum theory,” J. Quant. Spectrosc. Radiat. Transf. 63(2-6), 499–519 (1999).
[Crossref]

Holben, B. N.

O. Dubovik, A. Sinyuk, T. Lapyonok, B. N. Holben, M. Mishchenko, P. Yang, T. F. Eck, H. Volten, O. Muñoz, B. Veihelmann, W. J. van der Zande, J.-F. Leon, M. Sorokin, and I. Slutsker, “Application of spheroid models to account for aerosol particle nonsphericity in remote sensing of desert dust,” J. Geophys. Res. 111(D11), D11208 (2006).
[Crossref]

Hong, G.

P. Yang, Q. Feng, G. Hong, G. W. Kattawar, W. J. Wiscombe, M. I. Mishchenko, O. Dubovik, I. Laszlo, and I. N. Sokolik, “Modeling of the scattering and radiative properties of non-spherical dust-like aerosols,” J. Aerosol Sci. 38(10), 995–1014 (2007).
[Crossref]

Hovenac, E. A.

E. A. Hovenac and J. A. Lock, “Assessing the contribution of surface waves and complex rays to far-field Mie scattering by use of the Debye series,” JOSAA 9(5), 781–795 (1992).
[Crossref]

Hu, Y. Q.

Johnson, B. R.

Jones, D. S.

D. S. Jones, “High-frequency scattering of electromagnetic waves,” Proc. R. Soc. Lond. A Math. Phys. Sci. 240(1221), 206–213 (1957).
[Crossref]

Kahn, R.

Kattawar, G. W.

L. Bi, P. Yang, G. W. Kattawar, and M. I. Mishchenko, “Optical tunneling by arbitrary macroscopic three-dimensional objects,” Phys. Rev. A 92(1), 013814 (2015).
[Crossref]

L. Bi, P. Yang, G. W. Kattawar, and M. I. Mishchenko, “Efficient implementation of the invariant imbedding T-matrix method and the separation of variables method applied to large non-spherical inhomogeneous particles,” J. Quant. Spectrosc. Radiat. Transf. 116(2), 169–183 (2013).
[Crossref]

L. Bi, P. Yang, G. W. Kattawar, and R. Kahn, “Single-scattering properties of triaxial ellipsoidal particles for a size parameter range from the Rayleigh to geometric-optics regimes,” Appl. Opt. 48(1), 114–126 (2009).
[Crossref] [PubMed]

P. Yang, Q. Feng, G. Hong, G. W. Kattawar, W. J. Wiscombe, M. I. Mishchenko, O. Dubovik, I. Laszlo, and I. N. Sokolik, “Modeling of the scattering and radiative properties of non-spherical dust-like aerosols,” J. Aerosol Sci. 38(10), 995–1014 (2007).
[Crossref]

Kokhanovsky, A. A.

A. A. Kokhanovsky and E. P. Zege, “Optical properties of aerosol particles: A review of approximate analytical solutions,” J. Aerosol Sci. 28(1), 1–21 (1997).
[Crossref]

Lapyonok, T.

O. Dubovik, A. Sinyuk, T. Lapyonok, B. N. Holben, M. Mishchenko, P. Yang, T. F. Eck, H. Volten, O. Muñoz, B. Veihelmann, W. J. van der Zande, J.-F. Leon, M. Sorokin, and I. Slutsker, “Application of spheroid models to account for aerosol particle nonsphericity in remote sensing of desert dust,” J. Geophys. Res. 111(D11), D11208 (2006).
[Crossref]

Laszlo, I.

P. Yang, Q. Feng, G. Hong, G. W. Kattawar, W. J. Wiscombe, M. I. Mishchenko, O. Dubovik, I. Laszlo, and I. N. Sokolik, “Modeling of the scattering and radiative properties of non-spherical dust-like aerosols,” J. Aerosol Sci. 38(10), 995–1014 (2007).
[Crossref]

Leon, J.-F.

O. Dubovik, A. Sinyuk, T. Lapyonok, B. N. Holben, M. Mishchenko, P. Yang, T. F. Eck, H. Volten, O. Muñoz, B. Veihelmann, W. J. van der Zande, J.-F. Leon, M. Sorokin, and I. Slutsker, “Application of spheroid models to account for aerosol particle nonsphericity in remote sensing of desert dust,” J. Geophys. Res. 111(D11), D11208 (2006).
[Crossref]

Li, M. Z.

M. Z. Li, A. Thor Frette, and D. Wilkinson, “Particle size distribution determination from spectral extinction using neural networks,” Ind. Eng. Chem. Res. 40(21), 4615–4622 (2001).
[Crossref]

Liou, K. N.

K. N. Liou, Y. Takano, and P. Yang, “On geometric optics and surface waves for light scattering by spheres,” J. Quant. Spectrosc. Radiat. Transf. 111(12–13), 1980–1989 (2010).
[Crossref]

Lock, J. A.

F. Xu, J. A. Lock, and G. Gouesbet, “Debye series for light scattering by a nonspherical particle,” Phys. Rev. A 81(4), 043824 (2010).
[Crossref]

E. A. Hovenac and J. A. Lock, “Assessing the contribution of surface waves and complex rays to far-field Mie scattering by use of the Debye series,” JOSAA 9(5), 781–795 (1992).
[Crossref]

Mishchenko, M.

O. Dubovik, A. Sinyuk, T. Lapyonok, B. N. Holben, M. Mishchenko, P. Yang, T. F. Eck, H. Volten, O. Muñoz, B. Veihelmann, W. J. van der Zande, J.-F. Leon, M. Sorokin, and I. Slutsker, “Application of spheroid models to account for aerosol particle nonsphericity in remote sensing of desert dust,” J. Geophys. Res. 111(D11), D11208 (2006).
[Crossref]

Mishchenko, M. I.

L. Bi, P. Yang, G. W. Kattawar, and M. I. Mishchenko, “Optical tunneling by arbitrary macroscopic three-dimensional objects,” Phys. Rev. A 92(1), 013814 (2015).
[Crossref]

L. Bi, P. Yang, G. W. Kattawar, and M. I. Mishchenko, “Efficient implementation of the invariant imbedding T-matrix method and the separation of variables method applied to large non-spherical inhomogeneous particles,” J. Quant. Spectrosc. Radiat. Transf. 116(2), 169–183 (2013).
[Crossref]

P. Yang, Q. Feng, G. Hong, G. W. Kattawar, W. J. Wiscombe, M. I. Mishchenko, O. Dubovik, I. Laszlo, and I. N. Sokolik, “Modeling of the scattering and radiative properties of non-spherical dust-like aerosols,” J. Aerosol Sci. 38(10), 995–1014 (2007).
[Crossref]

Muñoz, O.

O. Dubovik, A. Sinyuk, T. Lapyonok, B. N. Holben, M. Mishchenko, P. Yang, T. F. Eck, H. Volten, O. Muñoz, B. Veihelmann, W. J. van der Zande, J.-F. Leon, M. Sorokin, and I. Slutsker, “Application of spheroid models to account for aerosol particle nonsphericity in remote sensing of desert dust,” J. Geophys. Res. 111(D11), D11208 (2006).
[Crossref]

Nussenzveig, H. M.

H. M. Nussenzveig and W. J. Wiscombe, “Efficiency factors in Mie scattering,” Phys. Rev. Lett. 45(18), 1490–1494 (1980).
[Crossref]

Orr-Ewing, A. I.

M. I. Cotterell, R. E. Willoughby, B. R. Bzdek, A. I. Orr-Ewing, and J. P. Reid, “A complete parameterization of the relative humidity and wavelength dependence of the refractive index of hygroscopic inorganic aerosol particles,” Atmos. Chem. Phys. Discuss. (in review).

Reid, J. P.

M. I. Cotterell, R. E. Willoughby, B. R. Bzdek, A. I. Orr-Ewing, and J. P. Reid, “A complete parameterization of the relative humidity and wavelength dependence of the refractive index of hygroscopic inorganic aerosol particles,” Atmos. Chem. Phys. Discuss. (in review).

Sinyuk, A.

O. Dubovik, A. Sinyuk, T. Lapyonok, B. N. Holben, M. Mishchenko, P. Yang, T. F. Eck, H. Volten, O. Muñoz, B. Veihelmann, W. J. van der Zande, J.-F. Leon, M. Sorokin, and I. Slutsker, “Application of spheroid models to account for aerosol particle nonsphericity in remote sensing of desert dust,” J. Geophys. Res. 111(D11), D11208 (2006).
[Crossref]

Slutsker, I.

O. Dubovik, A. Sinyuk, T. Lapyonok, B. N. Holben, M. Mishchenko, P. Yang, T. F. Eck, H. Volten, O. Muñoz, B. Veihelmann, W. J. van der Zande, J.-F. Leon, M. Sorokin, and I. Slutsker, “Application of spheroid models to account for aerosol particle nonsphericity in remote sensing of desert dust,” J. Geophys. Res. 111(D11), D11208 (2006).
[Crossref]

Sokolik, I. N.

P. Yang, Q. Feng, G. Hong, G. W. Kattawar, W. J. Wiscombe, M. I. Mishchenko, O. Dubovik, I. Laszlo, and I. N. Sokolik, “Modeling of the scattering and radiative properties of non-spherical dust-like aerosols,” J. Aerosol Sci. 38(10), 995–1014 (2007).
[Crossref]

Sorensen, C.

M. Berg, C. Sorensen, and A. Chakrabarti, “A new explanation of the extinction paradox,” J. Quant. Spectrosc. Radiat. Transf. 112(7), 1170–1181 (2011).
[Crossref]

Sorokin, M.

O. Dubovik, A. Sinyuk, T. Lapyonok, B. N. Holben, M. Mishchenko, P. Yang, T. F. Eck, H. Volten, O. Muñoz, B. Veihelmann, W. J. van der Zande, J.-F. Leon, M. Sorokin, and I. Slutsker, “Application of spheroid models to account for aerosol particle nonsphericity in remote sensing of desert dust,” J. Geophys. Res. 111(D11), D11208 (2006).
[Crossref]

Sun, X.

L. Wang, X. Sun, and J. Xing, “Retrieval of spheroidal particle size distribution using the approximate method in spectral extinction technique,” Opt. Commun. 285(7), 1646–1653 (2012).
[Crossref]

Takano, Y.

K. N. Liou, Y. Takano, and P. Yang, “On geometric optics and surface waves for light scattering by spheres,” J. Quant. Spectrosc. Radiat. Transf. 111(12–13), 1980–1989 (2010).
[Crossref]

Thor Frette, A.

M. Z. Li, A. Thor Frette, and D. Wilkinson, “Particle size distribution determination from spectral extinction using neural networks,” Ind. Eng. Chem. Res. 40(21), 4615–4622 (2001).
[Crossref]

van der Zande, W. J.

O. Dubovik, A. Sinyuk, T. Lapyonok, B. N. Holben, M. Mishchenko, P. Yang, T. F. Eck, H. Volten, O. Muñoz, B. Veihelmann, W. J. van der Zande, J.-F. Leon, M. Sorokin, and I. Slutsker, “Application of spheroid models to account for aerosol particle nonsphericity in remote sensing of desert dust,” J. Geophys. Res. 111(D11), D11208 (2006).
[Crossref]

Veihelmann, B.

O. Dubovik, A. Sinyuk, T. Lapyonok, B. N. Holben, M. Mishchenko, P. Yang, T. F. Eck, H. Volten, O. Muñoz, B. Veihelmann, W. J. van der Zande, J.-F. Leon, M. Sorokin, and I. Slutsker, “Application of spheroid models to account for aerosol particle nonsphericity in remote sensing of desert dust,” J. Geophys. Res. 111(D11), D11208 (2006).
[Crossref]

Volten, H.

O. Dubovik, A. Sinyuk, T. Lapyonok, B. N. Holben, M. Mishchenko, P. Yang, T. F. Eck, H. Volten, O. Muñoz, B. Veihelmann, W. J. van der Zande, J.-F. Leon, M. Sorokin, and I. Slutsker, “Application of spheroid models to account for aerosol particle nonsphericity in remote sensing of desert dust,” J. Geophys. Res. 111(D11), D11208 (2006).
[Crossref]

Wang, L.

L. Wang, X. Sun, and J. Xing, “Retrieval of spheroidal particle size distribution using the approximate method in spectral extinction technique,” Opt. Commun. 285(7), 1646–1653 (2012).
[Crossref]

Wilkinson, D.

M. Z. Li, A. Thor Frette, and D. Wilkinson, “Particle size distribution determination from spectral extinction using neural networks,” Ind. Eng. Chem. Res. 40(21), 4615–4622 (2001).
[Crossref]

Willoughby, R. E.

M. I. Cotterell, R. E. Willoughby, B. R. Bzdek, A. I. Orr-Ewing, and J. P. Reid, “A complete parameterization of the relative humidity and wavelength dependence of the refractive index of hygroscopic inorganic aerosol particles,” Atmos. Chem. Phys. Discuss. (in review).

Wiscombe, W. J.

P. Yang, Q. Feng, G. Hong, G. W. Kattawar, W. J. Wiscombe, M. I. Mishchenko, O. Dubovik, I. Laszlo, and I. N. Sokolik, “Modeling of the scattering and radiative properties of non-spherical dust-like aerosols,” J. Aerosol Sci. 38(10), 995–1014 (2007).
[Crossref]

H. M. Nussenzveig and W. J. Wiscombe, “Efficiency factors in Mie scattering,” Phys. Rev. Lett. 45(18), 1490–1494 (1980).
[Crossref]

Xing, J.

L. Wang, X. Sun, and J. Xing, “Retrieval of spheroidal particle size distribution using the approximate method in spectral extinction technique,” Opt. Commun. 285(7), 1646–1653 (2012).
[Crossref]

Xu, F.

F. Xu, J. A. Lock, and G. Gouesbet, “Debye series for light scattering by a nonspherical particle,” Phys. Rev. A 81(4), 043824 (2010).
[Crossref]

Yang, P.

L. Bi, P. Yang, G. W. Kattawar, and M. I. Mishchenko, “Optical tunneling by arbitrary macroscopic three-dimensional objects,” Phys. Rev. A 92(1), 013814 (2015).
[Crossref]

L. Bi and P. Yang, “High-frequency extinction efficiencies of spheroids: Rigorous T-matrix solutions and semi-empirical approximations,” Opt. Express 22(9), 10270–10293 (2014).
[Crossref] [PubMed]

L. Bi, P. Yang, G. W. Kattawar, and M. I. Mishchenko, “Efficient implementation of the invariant imbedding T-matrix method and the separation of variables method applied to large non-spherical inhomogeneous particles,” J. Quant. Spectrosc. Radiat. Transf. 116(2), 169–183 (2013).
[Crossref]

K. N. Liou, Y. Takano, and P. Yang, “On geometric optics and surface waves for light scattering by spheres,” J. Quant. Spectrosc. Radiat. Transf. 111(12–13), 1980–1989 (2010).
[Crossref]

L. Bi, P. Yang, G. W. Kattawar, and R. Kahn, “Single-scattering properties of triaxial ellipsoidal particles for a size parameter range from the Rayleigh to geometric-optics regimes,” Appl. Opt. 48(1), 114–126 (2009).
[Crossref] [PubMed]

P. Yang, Q. Feng, G. Hong, G. W. Kattawar, W. J. Wiscombe, M. I. Mishchenko, O. Dubovik, I. Laszlo, and I. N. Sokolik, “Modeling of the scattering and radiative properties of non-spherical dust-like aerosols,” J. Aerosol Sci. 38(10), 995–1014 (2007).
[Crossref]

O. Dubovik, A. Sinyuk, T. Lapyonok, B. N. Holben, M. Mishchenko, P. Yang, T. F. Eck, H. Volten, O. Muñoz, B. Veihelmann, W. J. van der Zande, J.-F. Leon, M. Sorokin, and I. Slutsker, “Application of spheroid models to account for aerosol particle nonsphericity in remote sensing of desert dust,” J. Geophys. Res. 111(D11), D11208 (2006).
[Crossref]

Zege, E. P.

A. A. Kokhanovsky and E. P. Zege, “Optical properties of aerosol particles: A review of approximate analytical solutions,” J. Aerosol Sci. 28(1), 1–21 (1997).
[Crossref]

Zhao, J. Q.

Appl. Opt. (5)

Ind. Eng. Chem. Res. (1)

M. Z. Li, A. Thor Frette, and D. Wilkinson, “Particle size distribution determination from spectral extinction using neural networks,” Ind. Eng. Chem. Res. 40(21), 4615–4622 (2001).
[Crossref]

J. Aerosol Sci. (2)

A. A. Kokhanovsky and E. P. Zege, “Optical properties of aerosol particles: A review of approximate analytical solutions,” J. Aerosol Sci. 28(1), 1–21 (1997).
[Crossref]

P. Yang, Q. Feng, G. Hong, G. W. Kattawar, W. J. Wiscombe, M. I. Mishchenko, O. Dubovik, I. Laszlo, and I. N. Sokolik, “Modeling of the scattering and radiative properties of non-spherical dust-like aerosols,” J. Aerosol Sci. 38(10), 995–1014 (2007).
[Crossref]

J. Geophys. Res. (1)

O. Dubovik, A. Sinyuk, T. Lapyonok, B. N. Holben, M. Mishchenko, P. Yang, T. F. Eck, H. Volten, O. Muñoz, B. Veihelmann, W. J. van der Zande, J.-F. Leon, M. Sorokin, and I. Slutsker, “Application of spheroid models to account for aerosol particle nonsphericity in remote sensing of desert dust,” J. Geophys. Res. 111(D11), D11208 (2006).
[Crossref]

J. Quant. Spectrosc. Radiat. Transf. (4)

M. Berg, C. Sorensen, and A. Chakrabarti, “A new explanation of the extinction paradox,” J. Quant. Spectrosc. Radiat. Transf. 112(7), 1170–1181 (2011).
[Crossref]

A. J. Baran and S. Havemann, “Rapid computation of the optical properties of hexagonal columns using complex angular momentum theory,” J. Quant. Spectrosc. Radiat. Transf. 63(2-6), 499–519 (1999).
[Crossref]

K. N. Liou, Y. Takano, and P. Yang, “On geometric optics and surface waves for light scattering by spheres,” J. Quant. Spectrosc. Radiat. Transf. 111(12–13), 1980–1989 (2010).
[Crossref]

L. Bi, P. Yang, G. W. Kattawar, and M. I. Mishchenko, “Efficient implementation of the invariant imbedding T-matrix method and the separation of variables method applied to large non-spherical inhomogeneous particles,” J. Quant. Spectrosc. Radiat. Transf. 116(2), 169–183 (2013).
[Crossref]

JOSAA (1)

E. A. Hovenac and J. A. Lock, “Assessing the contribution of surface waves and complex rays to far-field Mie scattering by use of the Debye series,” JOSAA 9(5), 781–795 (1992).
[Crossref]

Opt. Commun. (1)

L. Wang, X. Sun, and J. Xing, “Retrieval of spheroidal particle size distribution using the approximate method in spectral extinction technique,” Opt. Commun. 285(7), 1646–1653 (2012).
[Crossref]

Opt. Express (1)

Phys. Rev. A (2)

L. Bi, P. Yang, G. W. Kattawar, and M. I. Mishchenko, “Optical tunneling by arbitrary macroscopic three-dimensional objects,” Phys. Rev. A 92(1), 013814 (2015).
[Crossref]

F. Xu, J. A. Lock, and G. Gouesbet, “Debye series for light scattering by a nonspherical particle,” Phys. Rev. A 81(4), 043824 (2010).
[Crossref]

Phys. Rev. Lett. (1)

H. M. Nussenzveig and W. J. Wiscombe, “Efficiency factors in Mie scattering,” Phys. Rev. Lett. 45(18), 1490–1494 (1980).
[Crossref]

Powder Technol. (1)

G. Crawley, M. Cournil, and D. D. Benedetto, “Size analysis of fine particle suspensions by spectral turbidimetry: Potential and limits,” Powder Technol. 91(3), 197–208 (1997).
[Crossref]

Proc. R. Soc. Lond. A Math. Phys. Sci. (1)

D. S. Jones, “High-frequency scattering of electromagnetic waves,” Proc. R. Soc. Lond. A Math. Phys. Sci. 240(1221), 206–213 (1957).
[Crossref]

Other (5)

V. A. Fock, Electromagnetic Diffraction and Propagation Problems (Pergamon, 1965).

K. N. Liou, An Introduction to Atmospheric Radiation (Academic Press, 2002).

M. I. Cotterell, R. E. Willoughby, B. R. Bzdek, A. I. Orr-Ewing, and J. P. Reid, “A complete parameterization of the relative humidity and wavelength dependence of the refractive index of hygroscopic inorganic aerosol particles,” Atmos. Chem. Phys. Discuss. (in review).

H. M. Nussenzveig, Diffraction Effects in Semiclassical Scattering (Cambridge University, 1992).

H. C. van de Hulst, Light Scattering by Small Particles (Dover, 1981).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (10)

Fig. 1
Fig. 1

Prolate spheroid (a) and oblate spheroid (b).

Fig. 2
Fig. 2

The values of c 2 , c 4 , c 2 β 1 + c 3 β 4/3 and c 2 β 1 + c 3 β 4/3 + c 4 β 5/3 in the complex refractive index domain. The size parameter β is equal to 10. The black curves represent a value of zero.

Fig. 3
Fig. 3

Comparison of the results of a sphere computed from the rigorous solutions and the formulae.

Fig. 4
Fig. 4

The optimal number of edge-effect terms (a); the errors of the approximate results with optimal edge-effect terms (b); similar to (b), (c) is for four edge-effect terms;the accuracy improved by truncating the edge-effect terms (d). The lower parts of the figures show the results of non-absorptive particles ( m i = 0) and weakly absorptive particles ( m i = 10−7, 10−6, 10−5, 10−4, and 10−3). The size parameter is 10.

Fig. 5
Fig. 5

The optimal numbers of edge-effect terms for four spheres with size parameters of 5, 15, 20, and 25 (subplot (a), (b), (c), and (d), respectively).

Fig. 6
Fig. 6

The edge-effect efficiencies with respect to size parameter: a comparison of the results with four edge-effect terms and their counterparts with an optimal number of edge-effect terms.

Fig. 7
Fig. 7

Comparison of the extinction efficiencies of spheroids computed from the T-matrix solution and the extinction formula.

Fig. 8
Fig. 8

The optimal numbers of edge-effect terms for spheroids. The aspect ratios are 0.5 (a), 0.6 (b), 0.7 (c), 0.8 (d), 0.9 (e), 1.2 (f), 1.4 (g), 1.6 (h) and 1.8 (i). The size parameter is 10.

Fig. 9
Fig. 9

Similar to Fig. 4 (d), this shows the percentage improvement in accuracy by truncating edge-effect terms of spheroids. The aspect ratios are 0.5 (a), 0.6 (b), 0.7 (c), 0.8 (d), 0.9 (e), 1.2 (f), 1.4 (g), 1.6 (h) and 1.8 (i). The size parameter is 10.

Fig. 10
Fig. 10

The errors of the extinction efficiency computed with different numbers of edge-effect terms.

Equations (22)

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

Q ext,edge = c 1 β 2/3 + c 2 β 1 + c 3 β 4/3 + c 4 β 5/3 ,
c 1 =1.9924,
c 2 =2Im[ ( m 2 +1 )/ m 2 1 ],
c 3 =0.7154,
c 4 =0.6641Im[ e iπ/3 ( m 2 +1 )( 2 m 4 6 m 2 +3 )/ ( m 2 1 ) 3/2 ].
Q ext,edge = q 1 c 1 β 2/3 ( c a ) 4/3 + q 2 c 2 β ( c a )+ q 3 c 3 β 4/3 ( c a ) 2/3 + q 4 c 4 β 5/3 ( c a ) 1/3 ,
q 1 = p 2/3 F 2 1 [ 2/ 3,1/ 2,1,1 p 2 ],
q 2 = F 2 1 [ 1/ 2,1/ 2,1,1 p 2 ],
q 3 = p 2/3 F 2 1 [ 1/ 3,1/ 2,1,1 p 2 ],
q 4 = p 4/3 F 2 1 [ 1/ 6,1/ 2,1,1 p 2 ].
q 1 = p 2 F 2 1 [ 2/ 3,1/ 2,1,1 p 2 ],
q 2 = p 1 F 2 1 [ 1/2 ,1/2 ,1,1 p 2 ],
q 3 = F 2 1 [ 1/3 ,1/2 ,1,1 p 2 ],
q 4 =p F 2 1 [ 1/6 ,1/2 ,1,1 p 2 ].
p= ( cos 2 θ+ a 2 c 2 sin 2 θ ) 1/2 .
Q ext,edge =2+ 1 k 2 r 2 Re l=1 ( 2 a l b l ) ,
a l = ς n (2) ' (x) ς n (2) (mx)m ς n (2) ' (x) ς n (2) ' (mx) ς n (1) ' (x) ς n (2) ' (mx)+m ς n (1) ' (x) ς n (2) ' (mx) ,
b l = m ς n (2) ' (x) ς n (2) (mx) ς n (2) ' (x) ς n (2) ' (mx) m ς n (1) ' (x) ς n (2) ' (mx)+ ς n (1) ' (x) ς n (2) ' (x) .
| Q edge,4terms Q edge,debye || Q edge,optimal Q edge,debye | Q edge,debye ×100%.
| Q ext,4terms Q ext,IITM || Q ext,optimal Q ext,IITM | Q ext,IITM ×100%,
| Q ext,optimal Q ext,IITM | Q ext,IITM ×100%,
| Q ext,4terms Q ext,IITM | Q ext,IITM ×100%.

Metrics