Abstract

Within the geometric optics approximation, the phase functions of randomly oriented ice crystals are calculated as a series relative to multiplicity of internal collisions of light inside the particles. In the case of convex crystals, it is shown that the coefficients of the series provide the most information about the crystal shapes, while the angular functions of this series are weakly dependent on the shapes. The prevailing role of the term corresponding to one internal collision is emphasized. Three numbers describing a distribution of the single-collision scattered light among the aureole and halos of 22° and 46° prove to be the basic parameters by which to characterize scattering by hexagonal ice crystals.

© 2006 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. P. Yang and K. N. Liou, J. Opt. Soc. Am. A 14, 2278 (1997).
    [CrossRef]
  2. A. Macke, J. Mueller, and E. Raschke, J. Atmos. Sci. 53, 2813 (1996).
    [CrossRef]
  3. K. Muinonen, K. Lumme, J. Peltoniemi, and W. M. Irvine, Appl. Opt. 28, 3051 (1989).
    [CrossRef] [PubMed]
  4. M. Hess and M. Wiegner, Appl. Opt. 33, 7740 (1994).
    [CrossRef] [PubMed]
  5. V. Noel, G. Ledanois, H. Chepfer, and P. H. Flamant, Appl. Opt. 40, 4365 (2001).
    [CrossRef]
  6. A. G. Borovoi and I. A. Grishin, J. Opt. Soc. Am. A 20, 2071 (2003).
    [CrossRef]
  7. S. Chandrasekhar, Radiative Transfer (Dover, 1960).
  8. M. Born and E. Wolf, Principles of Optics (Pergamon, 1968).
  9. A. Borovoi, I. Grishin, and U. Oppel, Opt. Lett. 25, 1388 (2000).
    [CrossRef]
  10. A. G. Borovoi, N. V. Kustova, and U. G. Oppel, Opt. Eng. 44, 071208 (2005).
    [CrossRef]

2005 (1)

A. G. Borovoi, N. V. Kustova, and U. G. Oppel, Opt. Eng. 44, 071208 (2005).
[CrossRef]

2003 (1)

2001 (1)

2000 (1)

1997 (1)

1996 (1)

A. Macke, J. Mueller, and E. Raschke, J. Atmos. Sci. 53, 2813 (1996).
[CrossRef]

1994 (1)

1989 (1)

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon, 1968).

Borovoi, A.

Borovoi, A. G.

A. G. Borovoi, N. V. Kustova, and U. G. Oppel, Opt. Eng. 44, 071208 (2005).
[CrossRef]

A. G. Borovoi and I. A. Grishin, J. Opt. Soc. Am. A 20, 2071 (2003).
[CrossRef]

Chandrasekhar, S.

S. Chandrasekhar, Radiative Transfer (Dover, 1960).

Chepfer, H.

Flamant, P. H.

Grishin, I.

Grishin, I. A.

Hess, M.

Irvine, W. M.

Kustova, N. V.

A. G. Borovoi, N. V. Kustova, and U. G. Oppel, Opt. Eng. 44, 071208 (2005).
[CrossRef]

Ledanois, G.

Liou, K. N.

Lumme, K.

Macke, A.

A. Macke, J. Mueller, and E. Raschke, J. Atmos. Sci. 53, 2813 (1996).
[CrossRef]

Mueller, J.

A. Macke, J. Mueller, and E. Raschke, J. Atmos. Sci. 53, 2813 (1996).
[CrossRef]

Muinonen, K.

Noel, V.

Oppel, U.

Oppel, U. G.

A. G. Borovoi, N. V. Kustova, and U. G. Oppel, Opt. Eng. 44, 071208 (2005).
[CrossRef]

Peltoniemi, J.

Raschke, E.

A. Macke, J. Mueller, and E. Raschke, J. Atmos. Sci. 53, 2813 (1996).
[CrossRef]

Wiegner, M.

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Pergamon, 1968).

Yang, P.

Appl. Opt. (3)

J. Atmos. Sci. (1)

A. Macke, J. Mueller, and E. Raschke, J. Atmos. Sci. 53, 2813 (1996).
[CrossRef]

J. Opt. Soc. Am. A (2)

Opt. Eng. (1)

A. G. Borovoi, N. V. Kustova, and U. G. Oppel, Opt. Eng. 44, 071208 (2005).
[CrossRef]

Opt. Lett. (1)

Other (2)

S. Chandrasekhar, Radiative Transfer (Dover, 1960).

M. Born and E. Wolf, Principles of Optics (Pergamon, 1968).

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 (3)

Fig. 1
Fig. 1

Phase function of a randomly oriented hexagonal ice plate ( Q = height diameter = 0.5 ) and its components with zero (dashed curve) and two (dotted curve) internal collisions of photons. The lower part is presented on a large scale to show the cumulative contribution from photons with three and more collisions.

Fig. 2
Fig. 2

Partial phase functions of the halos of 22° and 46° [ p 11 ( θ ) and p 12 ( θ ) , respectively] for hexagonal ice columns and plates.

Fig. 3
Fig. 3

Probabilities that photons will abandon a crystal after one internal collision and distributions of the one-internal-collision photons among the aureole (bottom part of each bar) and halos of 22° and 46° (middle and top parts, respectively) for hexagonal ice columns and plates.

Tables (1)

Tables Icon

Table 1 Cumulative Probabilities (%) that Photons Will Abandon Ice Crystals of Different Shapes after m Internal Collisions

Equations (2)

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

p ( θ ) = m = 0 a m p m ( θ ) , m = 0 a m = 1 , 2 π 0 π p m ( θ ) sin θ d θ = 1.
p 1 ( θ ) = i b i p 1 i ( θ ) ; i b i = 1 , 2 π 0 π p 1 i ( θ ) sin θ d θ = 1.

Metrics