Abstract

A simple analytical formula is developed to describe light diffraction by chaotically oriented particles of arbitrary shape. The formula expresses the angular pattern through three well-defined microphysical characteristics of an ensemble: the average cross-sectional area, the average area squared, and the average length of the contour bordering the particle projection.

© 2010 Optical Society of America

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  1. L. R. Bissonnette, P. Bruscaglioni, A. Ismaeli, G. Zaccanti, A. Cohen, Y. Benayahu, M. Kleiman, S. Egert, C. Flesia, P. Schwendimann, A. V. Starkov, M. Noormohammadian, U. G. Oppel, D. M. Winker, E. P. Zege, I. L. Katsev, and I. N. Polonsky, Appl. Phys. B 60, 355 (1995).
    [CrossRef]
  2. J. Reichardt, M. Hess, and A. Macke, Appl. Opt. 39, 1895(2000).
    [CrossRef]
  3. A. A. Kokhanovsky and A. Macke, Appl. Opt. 36, 8785(1997).
    [CrossRef]
  4. A. Macke, J. Mueller, and E. Raschke, J. Atmos. Sci. 53, 2813 (1996).
    [CrossRef]
  5. V. Shcherbakov, J.-F. Gayet, B. Baker, and P. Lawson, J. Atmos. Sci. 63, 1513 (2006).
    [CrossRef]
  6. P. Yang and K. N. Liou, Appl. Opt. 35, 6568 (1996).
    [CrossRef] [PubMed]
  7. H. C. vande Hulst, Light Scattering by Small Particles(Wiley, 1957).
  8. B. A. Baum, A. J. Heymsfield, P. Yang, and S. T. Bedka, J. Appl. Meteorol. 44, 1885 (2005).
    [CrossRef]
  9. A. L. Jones, Part. Charact. 4, 123 (1987).
    [CrossRef]
  10. A. Malinka and E. Zege, J. Opt. Soc. Am. A 26, 1762(2009).
    [CrossRef]
  11. W. H. Wells, in Optics of the Sea, AGARD Lect. Ser. No. 61 (NATO, 1973).
  12. J. W. McLean and K. J. Voss, Appl. Opt. 30, 2027 (1991).
    [CrossRef] [PubMed]
  13. E. P. Zege, I. L. Katsev, A. S. Prikhach, G. Gilbert, and N. Witherspoon, Appl. Opt. 45, 6577 (2006).
    [CrossRef] [PubMed]
  14. M. G. Kendall and P. A. P. Moran, Geometrical Probability, No. 5 of Griffin’s Statistical Monographs and Courses(Griffin, 1963).

2009

2006

E. P. Zege, I. L. Katsev, A. S. Prikhach, G. Gilbert, and N. Witherspoon, Appl. Opt. 45, 6577 (2006).
[CrossRef] [PubMed]

V. Shcherbakov, J.-F. Gayet, B. Baker, and P. Lawson, J. Atmos. Sci. 63, 1513 (2006).
[CrossRef]

2005

B. A. Baum, A. J. Heymsfield, P. Yang, and S. T. Bedka, J. Appl. Meteorol. 44, 1885 (2005).
[CrossRef]

2000

1997

1996

P. Yang and K. N. Liou, Appl. Opt. 35, 6568 (1996).
[CrossRef] [PubMed]

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

1995

L. R. Bissonnette, P. Bruscaglioni, A. Ismaeli, G. Zaccanti, A. Cohen, Y. Benayahu, M. Kleiman, S. Egert, C. Flesia, P. Schwendimann, A. V. Starkov, M. Noormohammadian, U. G. Oppel, D. M. Winker, E. P. Zege, I. L. Katsev, and I. N. Polonsky, Appl. Phys. B 60, 355 (1995).
[CrossRef]

1991

1987

A. L. Jones, Part. Charact. 4, 123 (1987).
[CrossRef]

1973

W. H. Wells, in Optics of the Sea, AGARD Lect. Ser. No. 61 (NATO, 1973).

1963

M. G. Kendall and P. A. P. Moran, Geometrical Probability, No. 5 of Griffin’s Statistical Monographs and Courses(Griffin, 1963).

1957

H. C. vande Hulst, Light Scattering by Small Particles(Wiley, 1957).

Baker, B.

V. Shcherbakov, J.-F. Gayet, B. Baker, and P. Lawson, J. Atmos. Sci. 63, 1513 (2006).
[CrossRef]

Baum, B. A.

B. A. Baum, A. J. Heymsfield, P. Yang, and S. T. Bedka, J. Appl. Meteorol. 44, 1885 (2005).
[CrossRef]

Bedka, S. T.

B. A. Baum, A. J. Heymsfield, P. Yang, and S. T. Bedka, J. Appl. Meteorol. 44, 1885 (2005).
[CrossRef]

Benayahu, Y.

L. R. Bissonnette, P. Bruscaglioni, A. Ismaeli, G. Zaccanti, A. Cohen, Y. Benayahu, M. Kleiman, S. Egert, C. Flesia, P. Schwendimann, A. V. Starkov, M. Noormohammadian, U. G. Oppel, D. M. Winker, E. P. Zege, I. L. Katsev, and I. N. Polonsky, Appl. Phys. B 60, 355 (1995).
[CrossRef]

Bissonnette, L. R.

L. R. Bissonnette, P. Bruscaglioni, A. Ismaeli, G. Zaccanti, A. Cohen, Y. Benayahu, M. Kleiman, S. Egert, C. Flesia, P. Schwendimann, A. V. Starkov, M. Noormohammadian, U. G. Oppel, D. M. Winker, E. P. Zege, I. L. Katsev, and I. N. Polonsky, Appl. Phys. B 60, 355 (1995).
[CrossRef]

Bruscaglioni, P.

L. R. Bissonnette, P. Bruscaglioni, A. Ismaeli, G. Zaccanti, A. Cohen, Y. Benayahu, M. Kleiman, S. Egert, C. Flesia, P. Schwendimann, A. V. Starkov, M. Noormohammadian, U. G. Oppel, D. M. Winker, E. P. Zege, I. L. Katsev, and I. N. Polonsky, Appl. Phys. B 60, 355 (1995).
[CrossRef]

Cohen, A.

L. R. Bissonnette, P. Bruscaglioni, A. Ismaeli, G. Zaccanti, A. Cohen, Y. Benayahu, M. Kleiman, S. Egert, C. Flesia, P. Schwendimann, A. V. Starkov, M. Noormohammadian, U. G. Oppel, D. M. Winker, E. P. Zege, I. L. Katsev, and I. N. Polonsky, Appl. Phys. B 60, 355 (1995).
[CrossRef]

Egert, S.

L. R. Bissonnette, P. Bruscaglioni, A. Ismaeli, G. Zaccanti, A. Cohen, Y. Benayahu, M. Kleiman, S. Egert, C. Flesia, P. Schwendimann, A. V. Starkov, M. Noormohammadian, U. G. Oppel, D. M. Winker, E. P. Zege, I. L. Katsev, and I. N. Polonsky, Appl. Phys. B 60, 355 (1995).
[CrossRef]

Flesia, C.

L. R. Bissonnette, P. Bruscaglioni, A. Ismaeli, G. Zaccanti, A. Cohen, Y. Benayahu, M. Kleiman, S. Egert, C. Flesia, P. Schwendimann, A. V. Starkov, M. Noormohammadian, U. G. Oppel, D. M. Winker, E. P. Zege, I. L. Katsev, and I. N. Polonsky, Appl. Phys. B 60, 355 (1995).
[CrossRef]

Gayet, J.-F.

V. Shcherbakov, J.-F. Gayet, B. Baker, and P. Lawson, J. Atmos. Sci. 63, 1513 (2006).
[CrossRef]

Gilbert, G.

Hess, M.

Heymsfield, A. J.

B. A. Baum, A. J. Heymsfield, P. Yang, and S. T. Bedka, J. Appl. Meteorol. 44, 1885 (2005).
[CrossRef]

Ismaeli, A.

L. R. Bissonnette, P. Bruscaglioni, A. Ismaeli, G. Zaccanti, A. Cohen, Y. Benayahu, M. Kleiman, S. Egert, C. Flesia, P. Schwendimann, A. V. Starkov, M. Noormohammadian, U. G. Oppel, D. M. Winker, E. P. Zege, I. L. Katsev, and I. N. Polonsky, Appl. Phys. B 60, 355 (1995).
[CrossRef]

Jones, A. L.

A. L. Jones, Part. Charact. 4, 123 (1987).
[CrossRef]

Katsev, I. L.

E. P. Zege, I. L. Katsev, A. S. Prikhach, G. Gilbert, and N. Witherspoon, Appl. Opt. 45, 6577 (2006).
[CrossRef] [PubMed]

L. R. Bissonnette, P. Bruscaglioni, A. Ismaeli, G. Zaccanti, A. Cohen, Y. Benayahu, M. Kleiman, S. Egert, C. Flesia, P. Schwendimann, A. V. Starkov, M. Noormohammadian, U. G. Oppel, D. M. Winker, E. P. Zege, I. L. Katsev, and I. N. Polonsky, Appl. Phys. B 60, 355 (1995).
[CrossRef]

Kendall, M. G.

M. G. Kendall and P. A. P. Moran, Geometrical Probability, No. 5 of Griffin’s Statistical Monographs and Courses(Griffin, 1963).

Kleiman, M.

L. R. Bissonnette, P. Bruscaglioni, A. Ismaeli, G. Zaccanti, A. Cohen, Y. Benayahu, M. Kleiman, S. Egert, C. Flesia, P. Schwendimann, A. V. Starkov, M. Noormohammadian, U. G. Oppel, D. M. Winker, E. P. Zege, I. L. Katsev, and I. N. Polonsky, Appl. Phys. B 60, 355 (1995).
[CrossRef]

Kokhanovsky, A. A.

Lawson, P.

V. Shcherbakov, J.-F. Gayet, B. Baker, and P. Lawson, J. Atmos. Sci. 63, 1513 (2006).
[CrossRef]

Liou, K. N.

Macke, A.

Malinka, A.

McLean, J. W.

Moran, P. A. P.

M. G. Kendall and P. A. P. Moran, Geometrical Probability, No. 5 of Griffin’s Statistical Monographs and Courses(Griffin, 1963).

Mueller, J.

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

Noormohammadian, M.

L. R. Bissonnette, P. Bruscaglioni, A. Ismaeli, G. Zaccanti, A. Cohen, Y. Benayahu, M. Kleiman, S. Egert, C. Flesia, P. Schwendimann, A. V. Starkov, M. Noormohammadian, U. G. Oppel, D. M. Winker, E. P. Zege, I. L. Katsev, and I. N. Polonsky, Appl. Phys. B 60, 355 (1995).
[CrossRef]

Oppel, U. G.

L. R. Bissonnette, P. Bruscaglioni, A. Ismaeli, G. Zaccanti, A. Cohen, Y. Benayahu, M. Kleiman, S. Egert, C. Flesia, P. Schwendimann, A. V. Starkov, M. Noormohammadian, U. G. Oppel, D. M. Winker, E. P. Zege, I. L. Katsev, and I. N. Polonsky, Appl. Phys. B 60, 355 (1995).
[CrossRef]

Polonsky, I. N.

L. R. Bissonnette, P. Bruscaglioni, A. Ismaeli, G. Zaccanti, A. Cohen, Y. Benayahu, M. Kleiman, S. Egert, C. Flesia, P. Schwendimann, A. V. Starkov, M. Noormohammadian, U. G. Oppel, D. M. Winker, E. P. Zege, I. L. Katsev, and I. N. Polonsky, Appl. Phys. B 60, 355 (1995).
[CrossRef]

Prikhach, A. S.

Raschke, E.

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

Reichardt, J.

Schwendimann, P.

L. R. Bissonnette, P. Bruscaglioni, A. Ismaeli, G. Zaccanti, A. Cohen, Y. Benayahu, M. Kleiman, S. Egert, C. Flesia, P. Schwendimann, A. V. Starkov, M. Noormohammadian, U. G. Oppel, D. M. Winker, E. P. Zege, I. L. Katsev, and I. N. Polonsky, Appl. Phys. B 60, 355 (1995).
[CrossRef]

Shcherbakov, V.

V. Shcherbakov, J.-F. Gayet, B. Baker, and P. Lawson, J. Atmos. Sci. 63, 1513 (2006).
[CrossRef]

Starkov, A. V.

L. R. Bissonnette, P. Bruscaglioni, A. Ismaeli, G. Zaccanti, A. Cohen, Y. Benayahu, M. Kleiman, S. Egert, C. Flesia, P. Schwendimann, A. V. Starkov, M. Noormohammadian, U. G. Oppel, D. M. Winker, E. P. Zege, I. L. Katsev, and I. N. Polonsky, Appl. Phys. B 60, 355 (1995).
[CrossRef]

vande Hulst, H. C.

H. C. vande Hulst, Light Scattering by Small Particles(Wiley, 1957).

Voss, K. J.

Wells, W. H.

W. H. Wells, in Optics of the Sea, AGARD Lect. Ser. No. 61 (NATO, 1973).

Winker, D. M.

L. R. Bissonnette, P. Bruscaglioni, A. Ismaeli, G. Zaccanti, A. Cohen, Y. Benayahu, M. Kleiman, S. Egert, C. Flesia, P. Schwendimann, A. V. Starkov, M. Noormohammadian, U. G. Oppel, D. M. Winker, E. P. Zege, I. L. Katsev, and I. N. Polonsky, Appl. Phys. B 60, 355 (1995).
[CrossRef]

Witherspoon, N.

Yang, P.

B. A. Baum, A. J. Heymsfield, P. Yang, and S. T. Bedka, J. Appl. Meteorol. 44, 1885 (2005).
[CrossRef]

P. Yang and K. N. Liou, Appl. Opt. 35, 6568 (1996).
[CrossRef] [PubMed]

Zaccanti, G.

L. R. Bissonnette, P. Bruscaglioni, A. Ismaeli, G. Zaccanti, A. Cohen, Y. Benayahu, M. Kleiman, S. Egert, C. Flesia, P. Schwendimann, A. V. Starkov, M. Noormohammadian, U. G. Oppel, D. M. Winker, E. P. Zege, I. L. Katsev, and I. N. Polonsky, Appl. Phys. B 60, 355 (1995).
[CrossRef]

Zege, E.

Zege, E. P.

E. P. Zege, I. L. Katsev, A. S. Prikhach, G. Gilbert, and N. Witherspoon, Appl. Opt. 45, 6577 (2006).
[CrossRef] [PubMed]

L. R. Bissonnette, P. Bruscaglioni, A. Ismaeli, G. Zaccanti, A. Cohen, Y. Benayahu, M. Kleiman, S. Egert, C. Flesia, P. Schwendimann, A. V. Starkov, M. Noormohammadian, U. G. Oppel, D. M. Winker, E. P. Zege, I. L. Katsev, and I. N. Polonsky, Appl. Phys. B 60, 355 (1995).
[CrossRef]

Appl. Opt.

Appl. Phys. B

L. R. Bissonnette, P. Bruscaglioni, A. Ismaeli, G. Zaccanti, A. Cohen, Y. Benayahu, M. Kleiman, S. Egert, C. Flesia, P. Schwendimann, A. V. Starkov, M. Noormohammadian, U. G. Oppel, D. M. Winker, E. P. Zege, I. L. Katsev, and I. N. Polonsky, Appl. Phys. B 60, 355 (1995).
[CrossRef]

J. Appl. Meteorol.

B. A. Baum, A. J. Heymsfield, P. Yang, and S. T. Bedka, J. Appl. Meteorol. 44, 1885 (2005).
[CrossRef]

J. Atmos. Sci.

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

V. Shcherbakov, J.-F. Gayet, B. Baker, and P. Lawson, J. Atmos. Sci. 63, 1513 (2006).
[CrossRef]

J. Opt. Soc. Am. A

Part. Charact.

A. L. Jones, Part. Charact. 4, 123 (1987).
[CrossRef]

Other

W. H. Wells, in Optics of the Sea, AGARD Lect. Ser. No. 61 (NATO, 1973).

M. G. Kendall and P. A. P. Moran, Geometrical Probability, No. 5 of Griffin’s Statistical Monographs and Courses(Griffin, 1963).

H. C. vande Hulst, Light Scattering by Small Particles(Wiley, 1957).

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Figures (1)

Fig. 1
Fig. 1

Diffraction phase function calculated strictly for the mono- (thin curve) and polydispersed (o) ensembles of randomly oriented prisms and its approximation by Eq. (9) (thick curve).

Equations (16)

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

d C d Ω | θ λ / L = 2 λ L ( 2 π ) 3 θ 3 ,
d C d Ω d Ω = S ,
d C d Ω | θ = 0 = S 2 λ 2 ,
p ( θ ) = 2 π S d C d Ω ,
0 p ( θ ) θ d θ = 1 .
p ( θ ) | θ λ / L = a θ 3 , a = λ L 2 π 2 S ,
p ( 0 ) = 2 π S 2 λ 2 S ,
p ( θ ) = ρ 2 ( 1 + ρ 2 θ 2 ) 3 / 2
p ( θ ) = 1 2 V exp ( θ 2 2 V ) + ρ 2 2 ( 1 + ρ 2 θ 2 ) 3 / 2 .
ρ = 1 2 a ,
V = 4 a 2 8 p ( 0 ) a 2 1 .
L = π T .
S = 3 3 16 D 2 + 3 4 D H ,
S 2 = 9 64 D 4 + 3 3 4 π D 3 H + 2 π + 3 3 6 π D 2 H 2 ,
L = 3 π 4 D + π 2 H ,
d p d D = D m D 0 m + 1 m ! exp ( D D 0 ) ,

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