Abstract

We derive theoretically and validate numerically general relationships for the elements of the backscattering matrix and for the linear, δL, and circular, δC, backscattering depolarization ratios for nonspherical particles in random orientation. For the practically important case of randomly oriented particles with a plane of symmetry or particles and their mirror particles occurring in equal numbers and in random orientation, δC = 2δL/(1 − δL). Extensive T-matrix computations for randomly oriented spheroids demonstrate that, although both δL and δC are indicators of particle nonsphericity, they cannot be considered a universal measure of the departure of particle shape from that of a sphere and have no simple dependence on particle size and refractive index.

© 1995 Optical Society of America

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References

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  1. K. Sassen, Bull. Am. Meteorol. Soc. 72, 1848 (1991).
    [CrossRef]
  2. S. J. Ostro, Rev. Mod. Phys. 65, 1235 (1993).
    [CrossRef]
  3. O. B. Toon, E. V. Browell, S. Kinne, J. Jordan, Geophys. Res. Lett. 17, 393 (1990).
    [CrossRef]
  4. S. Y. Matrosov, J. Geophys. Res. 98, 20675 (1993).
    [CrossRef]
  5. E. Rignot, “Backscatter model for the unusual radar properties of the Greenland ice sheet,” J. Geophys. Res. (to be published).
  6. H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).
  7. J. W. Hovenier, H. C. van de Hulst, C. V. M. van der Mee, Astron. Astrophys. 157, 301 (1986).
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    [CrossRef] [PubMed]
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  10. M. I. Mishchenko, D. W. Mackowski, L. D. Travis, “Scattering of light by bispheres with touching and separated components,” Appl. Opt. (to be published).
  11. M. I. Mishchenko, Appl. Opt. 32, 4652 (1993); M. I. Mishchenko, L. D. Travis, Opt. Commun. 109, 16 (1994); M. I. Mishchenko, D. W. Mackowski, Opt. Lett. 19, 1604 (1994).
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1994 (1)

1993 (3)

1991 (1)

K. Sassen, Bull. Am. Meteorol. Soc. 72, 1848 (1991).
[CrossRef]

1990 (1)

O. B. Toon, E. V. Browell, S. Kinne, J. Jordan, Geophys. Res. Lett. 17, 393 (1990).
[CrossRef]

1987 (1)

1986 (1)

J. W. Hovenier, H. C. van de Hulst, C. V. M. van der Mee, Astron. Astrophys. 157, 301 (1986).

1980 (1)

Asano, S.

Browell, E. V.

O. B. Toon, E. V. Browell, S. Kinne, J. Jordan, Geophys. Res. Lett. 17, 393 (1990).
[CrossRef]

Herb, P.

Hovenier, J. W.

J. W. Hovenier, H. C. van de Hulst, C. V. M. van der Mee, Astron. Astrophys. 157, 301 (1986).

Hu, C.-R.

Jordan, J.

O. B. Toon, E. V. Browell, S. Kinne, J. Jordan, Geophys. Res. Lett. 17, 393 (1990).
[CrossRef]

Kattawar, G. W.

Kinne, S.

O. B. Toon, E. V. Browell, S. Kinne, J. Jordan, Geophys. Res. Lett. 17, 393 (1990).
[CrossRef]

Mackowski, D. W.

M. I. Mishchenko, D. W. Mackowski, L. D. Travis, “Scattering of light by bispheres with touching and separated components,” Appl. Opt. (to be published).

Matrosov, S. Y.

S. Y. Matrosov, J. Geophys. Res. 98, 20675 (1993).
[CrossRef]

Mishchenko, M. I.

Ostro, S. J.

S. J. Ostro, Rev. Mod. Phys. 65, 1235 (1993).
[CrossRef]

Parkin, M. E.

Rignot, E.

E. Rignot, “Backscatter model for the unusual radar properties of the Greenland ice sheet,” J. Geophys. Res. (to be published).

Sassen, K.

K. Sassen, Bull. Am. Meteorol. Soc. 72, 1848 (1991).
[CrossRef]

Sato, M.

Toon, O. B.

O. B. Toon, E. V. Browell, S. Kinne, J. Jordan, Geophys. Res. Lett. 17, 393 (1990).
[CrossRef]

Travis, L. D.

M. I. Mishchenko, L. D. Travis, Appl. Opt. 33, 7206 (1994).
[CrossRef] [PubMed]

M. I. Mishchenko, D. W. Mackowski, L. D. Travis, “Scattering of light by bispheres with touching and separated components,” Appl. Opt. (to be published).

van de Hulst, H. C.

J. W. Hovenier, H. C. van de Hulst, C. V. M. van der Mee, Astron. Astrophys. 157, 301 (1986).

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

van der Mee, C. V. M.

J. W. Hovenier, H. C. van de Hulst, C. V. M. van der Mee, Astron. Astrophys. 157, 301 (1986).

Appl. Opt. (4)

Astron. Astrophys. (1)

J. W. Hovenier, H. C. van de Hulst, C. V. M. van der Mee, Astron. Astrophys. 157, 301 (1986).

Bull. Am. Meteorol. Soc. (1)

K. Sassen, Bull. Am. Meteorol. Soc. 72, 1848 (1991).
[CrossRef]

Geophys. Res. Lett. (1)

O. B. Toon, E. V. Browell, S. Kinne, J. Jordan, Geophys. Res. Lett. 17, 393 (1990).
[CrossRef]

J. Geophys. Res. (1)

S. Y. Matrosov, J. Geophys. Res. 98, 20675 (1993).
[CrossRef]

Rev. Mod. Phys. (1)

S. J. Ostro, Rev. Mod. Phys. 65, 1235 (1993).
[CrossRef]

Other (3)

M. I. Mishchenko, D. W. Mackowski, L. D. Travis, “Scattering of light by bispheres with touching and separated components,” Appl. Opt. (to be published).

E. Rignot, “Backscatter model for the unusual radar properties of the Greenland ice sheet,” J. Geophys. Res. (to be published).

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

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Figures (3)

Fig. 1
Fig. 1

Domain (shaded area) of possible combinations of b5/a1 and a2/a1 for backscattering by randomly oriented particles [see inequality (7)]. In the darker region δC < δL, whereas in the lighter region δC > δL.

Fig. 2
Fig. 2

δC versus δL for randomly oriented particles with the backscattering matrix given by Eq. (3).

Plate I
Plate I

Color diagram of δL, as a function of the aspect ratio (ratio of the larger to the smaller spheroidal axes) and the equal-surface-area-sphere size parameter for prolate (upper panels) and oblate (lower panels) spheroids with indices of refraction 1.5 + 0 005i; (left panels) and 1.78 + 0.005i (right panels).

Equations (10)

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F = [ a 1 0 0 b 5 0 a 2 0 0 0 0 - a 2 0 b 5 0 0 a 4 ] ,
a 4 = a 1 - 2 a 2
F = diag [ a 1 , a 2 , - a 2 , a 1 - 2 a 2 ] .
δ L = I - Q I + Q = a 1 - a 2 a 1 + a 2 ,
δ C = I + V I - V = a 1 + 2 b 5 + a 4 a 1 - a 4 = a 1 - a 2 + b 5 a 2 ,
a 1 - a 2 + b 5 0 ,
( a 2 / a 1 - 1 ) b 5 / a 1 [ 1 - ( a 2 / a 1 ) 2 ] 1 / 2 .
b 5 / a 1 > ( a 2 / a 1 - 1 ) ( a 2 / a 1 + 1 ) - 1 = - δ L .
δ C = 2 δ L / ( 1 - δ L ) .
0 2 δ L δ C .

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