Abstract

A general bridging technique is developed to calculate the extinction efficiency of particles by combining the extended Rayleigh-Debye approximation and the modified anomalous diffraction theory. Comparisons with the exact methods are performed for spheres, spheroids, infinite cylinders, and finite cylinders. The overall features of the extinction efficiencies calculated from the new, to our knowledge, bridging method are in agreement with those calculated from the exact methods. Also discussed are accuracy of the new method and its domain of applicability. The new technique can be potentially applied to particles of virtually any shapes and sizes.

© 2003 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef]
  8. B. T. Draine, P. J. Flatau, “Discrete-dipole approximation for calculations,” J. Opt. Soc. Am. A 11, 1491–1499 (1994).
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  9. H. Y. Chen, M. F. Lskander, “Light scattering and absorption by fractal agglomerate and coagulations of smoke aerosols,” J. Mod. Opt. 37, 171–181 (1990).
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  28. J. D. Klett, “Anomalous diffraction model for inversion of multispectral extinction data including absorption effects,” Appl. Opt. 23, 4499–4508 (1984).
    [CrossRef] [PubMed]
  29. S. A. Ackerman, G. L. Stephens, “The absorption of solar radiation by cloud droplets: an application of anomalous diffraction theory,” J. Atmos. Sci. 44, 1574–1588 (1987).
    [CrossRef]
  30. D. L. Mitchell, “Parameterization of the Mie extinction and absorption coefficients for water clouds,” J. Atmos. Sci. 57, 1311–1326 (2000).
    [CrossRef]
  31. P. Latimer, “Light scattering by ellipsoids,” J. Colloid Interface Sci. 53, 102–109 (1975).
    [CrossRef]
  32. P. Latimer, P. Barber, “Scattering by ellipsoids of revolution,” J. Colloid Interface Sci. 63, 310–316 (1978).
    [CrossRef]
  33. P. Yang, K. N. Liou, K. Wyser, D. Mitchell, “Parameterization of scattering and absorption properties of individual ice crystals,” J. Geophys. Res. D 105, 4699–4718 (2000).
    [CrossRef]
  34. B. T. N. Evans, G. R. Fournier, “A simple approximation to extinction efficiency valid over all size parameters,” Appl. Opt. 29, 4666–4670 (1990).
    [CrossRef] [PubMed]
  35. G. R. Fournier, B. T. N. Evans, “Approximation to extinction efficiency for randomly oriented spheroids,” Appl. Opt. 30, 2042–2048 (1991).
    [CrossRef] [PubMed]
  36. B. T. N. Evans, G. R. Fournier, “Analytic approximation to randomly oriented spheroid extinction,” Appl. Opt. 33, 5796–5804 (1994).
    [CrossRef] [PubMed]
  37. R. Penndorf, “Scattering and extinction coefficients for small spherical aerosols,” J. Atmos. Sci. 19, 193 (1961).
    [CrossRef]
  38. W. A. Farone, M. J. Robinson, “The range of validity of the anomalous diffraction approximation to electromagnetic scattering by spheres,” Appl. Opt. 7, 643–645 (1968).
    [CrossRef] [PubMed]
  39. G. L. Stephens, “Scattering of plane waves by soft obstacles: anomalous diffraction theory for circular cylinders,” Appl. Opt. 23, 954–959 (1984).
    [CrossRef] [PubMed]
  40. S. Asano, M. Sato, “Light scattering by randomly oriented spheroidal particles,” Appl. Opt. 19, 962–974 (1980).
    [CrossRef] [PubMed]
  41. A. Maslowska, P. J. Flatau, G. L. Stephens, “On the validity of the anomalous diffraction theory to light scattering by cubes,” Opt. Commun. 107, 35–40 (1994).
    [CrossRef]
  42. D. S. Jones, “High frequency scattering of electromagnetic wave,” Proc. R. Soc. London Ser. A 240, 206–213 (1957).
    [CrossRef]
  43. H. M. Nussenzveig, W. J. Wiscombe, “Efficiency factors in Mie scattering,” Phys. Rev. Lett. 45, 1490–1494 (1980).
    [CrossRef]
  44. A. Mugnai, W. J. Wiscombe, “Scattering of radiation by moderately nonspherical particles,” J. Atmos. Sci. 37, 1291–1307 (1980).
    [CrossRef]
  45. P. Latimer, “Predicted scattering by spheroids: comparison of approximate and exact methods,” Appl. Opt. 19, 3039–3041 (1980).
    [CrossRef] [PubMed]
  46. L. E. Paramonov, V. N. Lopatin, F. Y. Sidko, “Light scattering of soft spheroidal particles,” Opt. Spectrosc. (USSR) 61, 358–361 (1986).
  47. Y. Takano, K. N. Liou, P. Minnis, “The effects of small ice crystals on cirrus infrared radiative properties,” J. Atmos. Sci. 49, 1487–1493 (1992).
    [CrossRef]
  48. M. I. Mishchenko, L. D. Travis, “Light scattering by polydispersions of randomly oriented spheroids with sizes comparable to wavelengths of observation,” Appl. Opt. 33, 7206–7225 (1994).
    [CrossRef] [PubMed]
  49. T. W. Chen, “Effective sphere for spheroid in light scattering,” Opt. Commun. 114, 199–202 (1995).
    [CrossRef]
  50. V. Vouk, “Projected area of convex bodies,” Nature (London) 162, 330–331 (1948).
    [CrossRef]
  51. F. D. Bryant, P. Latimer, “Optical efficiencies of large particles of arbitrary shape and orientation,” J. Colloid Interface Sci. 30, 291–304 (1969).
    [CrossRef]

2000 (2)

D. L. Mitchell, “Parameterization of the Mie extinction and absorption coefficients for water clouds,” J. Atmos. Sci. 57, 1311–1326 (2000).
[CrossRef]

P. Yang, K. N. Liou, K. Wyser, D. Mitchell, “Parameterization of scattering and absorption properties of individual ice crystals,” J. Geophys. Res. D 105, 4699–4718 (2000).
[CrossRef]

1998 (1)

1996 (3)

1995 (1)

T. W. Chen, “Effective sphere for spheroid in light scattering,” Opt. Commun. 114, 199–202 (1995).
[CrossRef]

1994 (4)

1992 (1)

Y. Takano, K. N. Liou, P. Minnis, “The effects of small ice crystals on cirrus infrared radiative properties,” J. Atmos. Sci. 49, 1487–1493 (1992).
[CrossRef]

1991 (4)

1990 (3)

1987 (2)

S. A. Ackerman, G. L. Stephens, “The absorption of solar radiation by cloud droplets: an application of anomalous diffraction theory,” J. Atmos. Sci. 44, 1574–1588 (1987).
[CrossRef]

T. W. Chen, “Scattering of a stratified sphere in high energy approximation,” Appl. Opt. 26, 4155–4158 (1987).
[CrossRef] [PubMed]

1986 (2)

J. M. Perrin, P. Chiappetta, “Light scattering by large particles, II: a vectorical description in the eikonal picture,” Opt. Acta. 33, 1001–1022 (1986).
[CrossRef]

L. E. Paramonov, V. N. Lopatin, F. Y. Sidko, “Light scattering of soft spheroidal particles,” Opt. Spectrosc. (USSR) 61, 358–361 (1986).

1985 (1)

J. M. Perrin, P. Chiappetta, “Light scattering by large particles, I: a new theoretical description in the eikonal picture,” Opt. Acta. 32, 907–921 (1985).
[CrossRef]

1984 (3)

1980 (5)

S. Asano, M. Sato, “Light scattering by randomly oriented spheroidal particles,” Appl. Opt. 19, 962–974 (1980).
[CrossRef] [PubMed]

P. Latimer, “Predicted scattering by spheroids: comparison of approximate and exact methods,” Appl. Opt. 19, 3039–3041 (1980).
[CrossRef] [PubMed]

P. Chiappetta, “Multiple scattering approach to light scattering by arbitrarily shaped particles,” J. Phys. A 13, 2101–2108 (1980).
[CrossRef]

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

A. Mugnai, W. J. Wiscombe, “Scattering of radiation by moderately nonspherical particles,” J. Atmos. Sci. 37, 1291–1307 (1980).
[CrossRef]

1978 (1)

P. Latimer, P. Barber, “Scattering by ellipsoids of revolution,” J. Colloid Interface Sci. 63, 310–316 (1978).
[CrossRef]

1977 (1)

T. Wu, L. L. Tsai, “Scattering from arbitrarily-shaped lossy dielectric bodies of revolution,” Radio. Sci. 2, 709–718 (1977).
[CrossRef]

1975 (2)

1973 (1)

E. M. Purcell, C. P. Pennypacker, “Scattering and absorption of light by nonspherical dielectric grains,” Astrophys. J. 196, 705–714 (1973).
[CrossRef]

1971 (1)

P. C. Waterman, “Symmetry, unitarity, and geometry in electromagnetic scattering,” Phys. Rev. D 3, 825–839 (1971).
[CrossRef]

1970 (1)

1969 (1)

F. D. Bryant, P. Latimer, “Optical efficiencies of large particles of arbitrary shape and orientation,” J. Colloid Interface Sci. 30, 291–304 (1969).
[CrossRef]

1968 (1)

1967 (1)

D. H. Napper, “A diffraction theory approach to the total scattering by cubes,” Kolloid Z. Z. Polym. 218, 41–45 (1967).
[CrossRef]

1966 (1)

S. K. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equation in isotropic media,” IEEE Trans. Antennas. Propag. AP-14, 302–307 (1966).

1965 (1)

P. C. Waterman, “Matrix formulation of electromagnetic scattering,” Proc. IEEE 53, 805–812 (1965).
[CrossRef]

1961 (1)

R. Penndorf, “Scattering and extinction coefficients for small spherical aerosols,” J. Atmos. Sci. 19, 193 (1961).
[CrossRef]

1960 (2)

D. Deirmendjian, “Atmospheric extinction of infra-red radiation,” Q. J. R. Meteorol. Soc. 86, 371–381 (1960).
[CrossRef]

J. M. Greeberg, A. S. Meltzer, “Scattering by nonspherical particles,” J. Appl. Phys. 31, 82–84 (1960).
[CrossRef]

1957 (1)

D. S. Jones, “High frequency scattering of electromagnetic wave,” Proc. R. Soc. London Ser. A 240, 206–213 (1957).
[CrossRef]

1948 (1)

V. Vouk, “Projected area of convex bodies,” Nature (London) 162, 330–331 (1948).
[CrossRef]

Ackerman, S. A.

S. A. Ackerman, G. L. Stephens, “The absorption of solar radiation by cloud droplets: an application of anomalous diffraction theory,” J. Atmos. Sci. 44, 1574–1588 (1987).
[CrossRef]

Arnott, W. P.

Asano, S.

Barber, P.

P. Latimer, P. Barber, “Scattering by ellipsoids of revolution,” J. Colloid Interface Sci. 63, 310–316 (1978).
[CrossRef]

P. Barber, C. Yeh, “Scattering of electromagnetic waves by arbitrarily shaped dielectric bodies,” Appl. Opt. 14, 2864–2872 (1975).
[CrossRef] [PubMed]

Barber, P. W.

P. W. Barber, S. C. Hill, Light Scattering by Particles: Computational Methods (World Scientific, Singapore, 1990).

Bryant, F. D.

F. D. Bryant, P. Latimer, “Optical efficiencies of large particles of arbitrary shape and orientation,” J. Colloid Interface Sci. 30, 291–304 (1969).
[CrossRef]

Chen, H. Y.

H. Y. Chen, M. F. Lskander, “Light scattering and absorption by fractal agglomerate and coagulations of smoke aerosols,” J. Mod. Opt. 37, 171–181 (1990).
[CrossRef]

Chen, T. W.

T. W. Chen, “Effective sphere for spheroid in light scattering,” Opt. Commun. 114, 199–202 (1995).
[CrossRef]

T. W. Chen, “Scattering of a stratified sphere in high energy approximation,” Appl. Opt. 26, 4155–4158 (1987).
[CrossRef] [PubMed]

T. W. Chen, “Generalized eikonal approximation,” Phys. Rev. C 30, 585–592 (1984).
[CrossRef]

Chiappetta, P.

J. M. Perrin, P. Chiappetta, “Light scattering by large particles, II: a vectorical description in the eikonal picture,” Opt. Acta. 33, 1001–1022 (1986).
[CrossRef]

J. M. Perrin, P. Chiappetta, “Light scattering by large particles, I: a new theoretical description in the eikonal picture,” Opt. Acta. 32, 907–921 (1985).
[CrossRef]

P. Chiappetta, “Multiple scattering approach to light scattering by arbitrarily shaped particles,” J. Phys. A 13, 2101–2108 (1980).
[CrossRef]

Chýlek, P.

Deirmendjian, D.

D. Deirmendjian, “Atmospheric extinction of infra-red radiation,” Q. J. R. Meteorol. Soc. 86, 371–381 (1960).
[CrossRef]

Draine, B. T.

Evans, B. T. N.

Farone, W. A.

Flatau, P. J.

Fournier, G. R.

Greeberg, J. M.

J. M. Greeberg, A. S. Meltzer, “Scattering by nonspherical particles,” J. Appl. Phys. 31, 82–84 (1960).
[CrossRef]

Gross, D. A.

Hallet, J.

Hill, S. C.

P. W. Barber, S. C. Hill, Light Scattering by Particles: Computational Methods (World Scientific, Singapore, 1990).

Jones, D. S.

D. S. Jones, “High frequency scattering of electromagnetic wave,” Proc. R. Soc. London Ser. A 240, 206–213 (1957).
[CrossRef]

Klett, J. D.

Latimer, P.

P. Latimer, “Predicted scattering by spheroids: comparison of approximate and exact methods,” Appl. Opt. 19, 3039–3041 (1980).
[CrossRef] [PubMed]

P. Latimer, P. Barber, “Scattering by ellipsoids of revolution,” J. Colloid Interface Sci. 63, 310–316 (1978).
[CrossRef]

P. Latimer, “Light scattering by ellipsoids,” J. Colloid Interface Sci. 53, 102–109 (1975).
[CrossRef]

D. A. Gross, P. Latimer, “General solutions for the extinction and absorption efficiencies of arbitrarily oriented cylinders by anomalous-diffraction approximation methods,” J. Opt. Soc. Am. 60, 904–907 (1970).
[CrossRef]

F. D. Bryant, P. Latimer, “Optical efficiencies of large particles of arbitrary shape and orientation,” J. Colloid Interface Sci. 30, 291–304 (1969).
[CrossRef]

Liou, K. N.

P. Yang, K. N. Liou, K. Wyser, D. Mitchell, “Parameterization of scattering and absorption properties of individual ice crystals,” J. Geophys. Res. D 105, 4699–4718 (2000).
[CrossRef]

P. Yang, K. N. Liou, “Finite-difference time domain method for light scattering by small ice crystals in three-dimensional space,” J. Opt. Soc. Am. A 13, 2072–2085 (1996).
[CrossRef]

Y. Takano, K. N. Liou, P. Minnis, “The effects of small ice crystals on cirrus infrared radiative properties,” J. Atmos. Sci. 49, 1487–1493 (1992).
[CrossRef]

Liu, Y.

Lopatin, V. N.

L. E. Paramonov, V. N. Lopatin, F. Y. Sidko, “Light scattering of soft spheroidal particles,” Opt. Spectrosc. (USSR) 61, 358–361 (1986).

Lskander, M. F.

H. Y. Chen, M. F. Lskander, “Light scattering and absorption by fractal agglomerate and coagulations of smoke aerosols,” J. Mod. Opt. 37, 171–181 (1990).
[CrossRef]

Mackowski, D. W.

M. I. Mishchenko, L. D. Travis, D. W. Mackowski, “T-matrix computations of light scattering by nonspherical particles: a review,” J. Quant. Spectrosc. Radiat. Transfer 55, 535–575 (1996).
[CrossRef]

Maslowska, A.

A. Maslowska, P. J. Flatau, G. L. Stephens, “On the validity of the anomalous diffraction theory to light scattering by cubes,” Opt. Commun. 107, 35–40 (1994).
[CrossRef]

Meltzer, A. S.

J. M. Greeberg, A. S. Meltzer, “Scattering by nonspherical particles,” J. Appl. Phys. 31, 82–84 (1960).
[CrossRef]

Minnis, P.

Y. Takano, K. N. Liou, P. Minnis, “The effects of small ice crystals on cirrus infrared radiative properties,” J. Atmos. Sci. 49, 1487–1493 (1992).
[CrossRef]

Mishchenko, M. I.

Mitchell, D.

P. Yang, K. N. Liou, K. Wyser, D. Mitchell, “Parameterization of scattering and absorption properties of individual ice crystals,” J. Geophys. Res. D 105, 4699–4718 (2000).
[CrossRef]

Mitchell, D. L.

D. L. Mitchell, “Parameterization of the Mie extinction and absorption coefficients for water clouds,” J. Atmos. Sci. 57, 1311–1326 (2000).
[CrossRef]

Mugnai, A.

A. Mugnai, W. J. Wiscombe, “Scattering of radiation by moderately nonspherical particles,” J. Atmos. Sci. 37, 1291–1307 (1980).
[CrossRef]

Napper, D. H.

D. H. Napper, “A diffraction theory approach to the total scattering by cubes,” Kolloid Z. Z. Polym. 218, 41–45 (1967).
[CrossRef]

Nussenzveig, H. M.

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

Paramonov, L. E.

L. E. Paramonov, V. N. Lopatin, F. Y. Sidko, “Light scattering of soft spheroidal particles,” Opt. Spectrosc. (USSR) 61, 358–361 (1986).

Penndorf, R.

R. Penndorf, “Scattering and extinction coefficients for small spherical aerosols,” J. Atmos. Sci. 19, 193 (1961).
[CrossRef]

Pennypacker, C. P.

E. M. Purcell, C. P. Pennypacker, “Scattering and absorption of light by nonspherical dielectric grains,” Astrophys. J. 196, 705–714 (1973).
[CrossRef]

Perrin, J. M.

J. M. Perrin, P. Chiappetta, “Light scattering by large particles, II: a vectorical description in the eikonal picture,” Opt. Acta. 33, 1001–1022 (1986).
[CrossRef]

J. M. Perrin, P. Chiappetta, “Light scattering by large particles, I: a new theoretical description in the eikonal picture,” Opt. Acta. 32, 907–921 (1985).
[CrossRef]

Purcell, E. M.

E. M. Purcell, C. P. Pennypacker, “Scattering and absorption of light by nonspherical dielectric grains,” Astrophys. J. 196, 705–714 (1973).
[CrossRef]

Robinson, M. J.

Sato, M.

Sidko, F. Y.

L. E. Paramonov, V. N. Lopatin, F. Y. Sidko, “Light scattering of soft spheroidal particles,” Opt. Spectrosc. (USSR) 61, 358–361 (1986).

Stephens, G. L.

A. Maslowska, P. J. Flatau, G. L. Stephens, “On the validity of the anomalous diffraction theory to light scattering by cubes,” Opt. Commun. 107, 35–40 (1994).
[CrossRef]

P. J. Flatau, G. L. Stephens, B. T. Draine, “Light scattering by rectangular solids in the discrete-dipole approximation: a new algorithm exploiting the Block-Toeplitz structure,” J. Opt. Soc. Am. A 7, 593–600 (1990).
[CrossRef]

S. A. Ackerman, G. L. Stephens, “The absorption of solar radiation by cloud droplets: an application of anomalous diffraction theory,” J. Atmos. Sci. 44, 1574–1588 (1987).
[CrossRef]

G. L. Stephens, “Scattering of plane waves by soft obstacles: anomalous diffraction theory for circular cylinders,” Appl. Opt. 23, 954–959 (1984).
[CrossRef] [PubMed]

Takano, Y.

Y. Takano, K. N. Liou, P. Minnis, “The effects of small ice crystals on cirrus infrared radiative properties,” J. Atmos. Sci. 49, 1487–1493 (1992).
[CrossRef]

Travis, L. D.

M. I. Mishchenko, L. D. Travis, D. W. Mackowski, “T-matrix computations of light scattering by nonspherical particles: a review,” J. Quant. Spectrosc. Radiat. Transfer 55, 535–575 (1996).
[CrossRef]

M. I. Mishchenko, L. D. Travis, “Light scattering by polydispersions of randomly oriented spheroids with sizes comparable to wavelengths of observation,” Appl. Opt. 33, 7206–7225 (1994).
[CrossRef] [PubMed]

Tsai, L. L.

T. Wu, L. L. Tsai, “Scattering from arbitrarily-shaped lossy dielectric bodies of revolution,” Radio. Sci. 2, 709–718 (1977).
[CrossRef]

Van de Hulst, H. C.

H. C. Van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).

Vouk, V.

V. Vouk, “Projected area of convex bodies,” Nature (London) 162, 330–331 (1948).
[CrossRef]

Waterman, P. C.

P. C. Waterman, “Symmetry, unitarity, and geometry in electromagnetic scattering,” Phys. Rev. D 3, 825–839 (1971).
[CrossRef]

P. C. Waterman, “Matrix formulation of electromagnetic scattering,” Proc. IEEE 53, 805–812 (1965).
[CrossRef]

Wiscombe, W. J.

A. Mugnai, W. J. Wiscombe, “Scattering of radiation by moderately nonspherical particles,” J. Atmos. Sci. 37, 1291–1307 (1980).
[CrossRef]

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

Wu, T.

T. Wu, L. L. Tsai, “Scattering from arbitrarily-shaped lossy dielectric bodies of revolution,” Radio. Sci. 2, 709–718 (1977).
[CrossRef]

Wyser, K.

P. Yang, K. N. Liou, K. Wyser, D. Mitchell, “Parameterization of scattering and absorption properties of individual ice crystals,” J. Geophys. Res. D 105, 4699–4718 (2000).
[CrossRef]

Yang, P.

P. Yang, K. N. Liou, K. Wyser, D. Mitchell, “Parameterization of scattering and absorption properties of individual ice crystals,” J. Geophys. Res. D 105, 4699–4718 (2000).
[CrossRef]

P. Yang, K. N. Liou, “Finite-difference time domain method for light scattering by small ice crystals in three-dimensional space,” J. Opt. Soc. Am. A 13, 2072–2085 (1996).
[CrossRef]

Yee, S. K.

S. K. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equation in isotropic media,” IEEE Trans. Antennas. Propag. AP-14, 302–307 (1966).

Yeh, C.

Appl. Opt. (13)

P. Barber, C. Yeh, “Scattering of electromagnetic waves by arbitrarily shaped dielectric bodies,” Appl. Opt. 14, 2864–2872 (1975).
[CrossRef] [PubMed]

T. W. Chen, “Scattering of a stratified sphere in high energy approximation,” Appl. Opt. 26, 4155–4158 (1987).
[CrossRef] [PubMed]

J. D. Klett, “Anomalous diffraction model for inversion of multispectral extinction data including absorption effects,” Appl. Opt. 23, 4499–4508 (1984).
[CrossRef] [PubMed]

B. T. N. Evans, G. R. Fournier, “A simple approximation to extinction efficiency valid over all size parameters,” Appl. Opt. 29, 4666–4670 (1990).
[CrossRef] [PubMed]

G. R. Fournier, B. T. N. Evans, “Approximation to extinction efficiency for randomly oriented spheroids,” Appl. Opt. 30, 2042–2048 (1991).
[CrossRef] [PubMed]

B. T. N. Evans, G. R. Fournier, “Analytic approximation to randomly oriented spheroid extinction,” Appl. Opt. 33, 5796–5804 (1994).
[CrossRef] [PubMed]

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Figures (10)

Fig. 1
Fig. 1

Extinction efficiencies as a function of phase parameter 2x(mr - 1) predicted by the Mie theory and the approximate formula for spheres with refractive index m = 1.33 - 0.0i and 1.33 - 1.0i.

Fig. 2
Fig. 2

Same as Fig. 1 but with refractive index m = 2.0 - 0.0i and 2.0 - 1.0i.

Fig. 3
Fig. 3

Contour diagram of the maximum relative percent error between the Mie theory and the approximation.

Fig. 4
Fig. 4

Size-averaged (with Δx = 1) extinction efficiency of Mie calculations and the proposed approximation versus the phase parameter. Refractive index m equals 3.0 - 0.0i.

Fig. 5
Fig. 5

Comparison between the approximation and the exact result of the T-matrix calculation for randomly oriented oblate spheroids with refractive index m = 1.33 - 0.0i and aspect ratio u = 0.2, 0.5.

Fig. 6
Fig. 6

Comparison between the approximation and the exact result of the T-matrix calculation for randomly oriented prolate spheroids with refractive index m = 1.33 - 0.0i and aspect ratio u = 2.0, 5.0.

Fig. 7
Fig. 7

Comparison of extinction efficiencies of an infinitely long cylinder for normal incidence computed from the exact solution and the approximate method with refractive index m = 1.33 - 0.0i and 1.33 - 1.0i.

Fig. 8
Fig. 8

Same as Fig. 7 but with refractive index m = 2.0 - 0.0i and 2.0 - 1.0i.

Fig. 9
Fig. 9

Comparison between the approximation and the T-matrix method for randomly oriented cylinders. The a/L ratio is 0.5, and the wavelength is 2 µm.

Fig. 10
Fig. 10

Comparison between the approximation and the T-matrix method for randomly oriented cylinders when the refractive index is 1.3 - 0.002i, and the wavelength is 3.1835 µm.

Equations (47)

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Qabs=-Imm2-1kVP,
Qsca=16 |m2-1|2k4V2πP,
Qabs=c1x+c2x3,
Qsca=c3x4,
x=ka,
c1=-Im4m2-1m2+2,
c2=-Im415m2-1m2+22m4+27m2+382m2+3,
c3=83m2-1m2+22,
Qabs=c1x+c2x3 exp-c4x3.
Qsca,small=c39k4V216πP,
Qabs,small=c13kV4P+c23k3V4πexp-c43k3V4π.
ϕ=m-1kl.
S0=k22πP 1-exp-iϕdP,
Cext=4πk2ReS0,
Qad=2PReP1-exp-iϕdP.
Qedge=c0k2/3PB R1/3ds,
Qext,large=Qad1+Qedge/Qad.
Qext,largeQad1+Qedge/2.
Qext,large=QadZ,
Z=1+12/Qedge+1/c5Qad+1,
Qad=4 Re12-i exp-iρρ+1-exp-iρρ2,
Qedge=4c0u2/3πkb2/3g20π/2 q4/3dχ,
u=a/b, g=cos2 θ+u2 sin2 θ1/2, q=sin2 χ+g2 cos2 χ1/2,
P=πb2g, V=4π3 ab2.
ρ=3m-1kV2P.
Qad=π ReH1ρ+iJ1ρ.
Qedge=4c00π/2a/Lcos2 θ cos2 χ+sin2 χ1/2cos2 χ/sin2 θ+sin2 χ1/2dχ+2c0ka sin θ2/32+πa/Lcot θ,
ρ=4m-1kVπP.
Qad=Re2-exp-iρ+i 1-exp-iρρ,
Qedge=c0ka2/3.
QadQρ, ρ=3m-1kV2P,
Q¯adρQρ¯, ρ¯3m-1kV2P¯.
Q¯adρ¯Q6m-1kVS.
fy=f1yf2yf3y+f4y,
f2y=f4y=F2y=Qext,large,
F1y=Qabs,small+Qsca,small.
f1y=Qabs,small+Qsca,small+c6Qsca,smallc7,
f3y=c8Qabs,small+Qsca,small+c6Qsca,smallc7.
QadRe21-exp(-iϕeff.
Qad-Im2m-1kleff+Rem-12kleff2.
Qext,large-1+c5Im2m-1kVP+1+c5Rem-12kVP2.
c6=c5; c7=2c5.
Qext=Qabs,small+Qsca,small+c6Qsca,smallc7Qext,largeQsca,small+c6Qsca,smallc7+Qext,large.
Qext¯= QextP sin αdαdβdγ P sin αdαdβdγ,
Qext¯=Qabs,small¯+Qsca,small¯+c6Qsca,small¯c7Qext,large¯Qsca,small¯+c6Qsca,small¯c7+Qext,large¯.
Qsca,small=π28ka3|m2-1|2+4m2-1m2+12,
Qabs,small=-kaπ2Im12m2-1+m2-1m2+1.

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