Abstract

Scattered light for preferentially oriented ice crystals is divided into specular and diffuse components, where the specular scattering is created by horizontally oriented facets of fluttering crystals. The specular component for a fluttering thin plate modeling these crystals is found analytically. The solution obtained is a two-dimensional (2D) convolution of a geometric optics pattern depending only on flutter and an independent diffraction function. The geometric optics pattern is explicitly expressed through the probability density for particle tilts, and the diffraction function is taken in the Fraunhofer diffraction approximation. The 2D convolution calculated numerically reveals a cumulative enhancement of scattered light in the scattering domain center. Certain possibilities to retrieve both flutter parameters and particle sizes from the specular patterns are discussed.

© 2009 Optical Society of America

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References

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  1. K. N. Liou, Radiation and Cloud Processes in the Atmosphere: Theory, Observation and Modelling (Oxford University, 1992).
  2. M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles (Cambridge University, 2002).
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    [CrossRef]
  4. V. Noel, G. Roy, L. Bissonnette, H. Chepfer, and P. Flamant, “Analysis of lidar measurements of ice clouds at multiple incidence angles,” Geophys. Res. Lett. 29, 1338 (2002)
    [CrossRef]
  5. V. Noel and K. Sassen, “Study of planar ice crystal orientations in ice clouds from scanning polarization lidar observations,” J. Appl. Meteorol. 44, 653-664 (2005).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2009 (1)

A. Borovoi and N. Kustova, “Display of ice crystal flutter in atmospheric light pillars,” Geophys. Res. Lett. 36, L04804(2009).
[CrossRef]

2008 (3)

2005 (2)

V. Noel and K. Sassen, “Study of planar ice crystal orientations in ice clouds from scanning polarization lidar observations,” J. Appl. Meteorol. 44, 653-664 (2005).
[CrossRef]

A. G. Borovoi, N. V. Kustova, and U. G. Oppel, “Light backscattering by hexagonal ice crystal particles in the geometrical optics approximation,” Opt. Eng. 44, 071208 (2005).
[CrossRef]

2004 (2)

V. Noel and H. Chepfer, “Study of ice crystal orientation in cirrus clouds based on satellite polarized radiance measurements,” J. Atmos. Sci. 61, 2073-2081 (2004).
[CrossRef]

F.-M. Breon and B. Dubrulle, “Horizontally oriented plated in clouds,” J. Atmos. Sci. 61, 2888-2898 (2004).
[CrossRef]

2003 (1)

2002 (1)

V. Noel, G. Roy, L. Bissonnette, H. Chepfer, and P. Flamant, “Analysis of lidar measurements of ice clouds at multiple incidence angles,” Geophys. Res. Lett. 29, 1338 (2002)
[CrossRef]

2001 (1)

1999 (1)

H. Chepfer, G. Brogniez, P. Goloub, F. M. Breon, and P. H. Flamant, “Observations of horizontally oriented ice crystals in cirrus clouds with POLDER-1/ADEOS-1,” J. Quant. Spectrosc. Radiat. Transfer 63, 521-543 (1999).
[CrossRef]

1990 (1)

1978 (1)

C. M. R. Platt, N. L. Abshire, and G. T. McNice, “Some microphysical properties of an ice cloud from lidar observations of horizontally oriented crystals,” J. Appl. Meteorol. 17, 1220-1224 (1978).
[CrossRef]

Abshire, N. L.

C. M. R. Platt, N. L. Abshire, and G. T. McNice, “Some microphysical properties of an ice cloud from lidar observations of horizontally oriented crystals,” J. Appl. Meteorol. 17, 1220-1224 (1978).
[CrossRef]

Bissonnette, L.

V. Noel, G. Roy, L. Bissonnette, H. Chepfer, and P. Flamant, “Analysis of lidar measurements of ice clouds at multiple incidence angles,” Geophys. Res. Lett. 29, 1338 (2002)
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge University, 1999).
[PubMed]

Borovoi, A.

Borovoi, A. G.

A. G. Borovoi, N. V. Kustova, and U. G. Oppel, “Light backscattering by hexagonal ice crystal particles in the geometrical optics approximation,” Opt. Eng. 44, 071208 (2005).
[CrossRef]

A. G. Borovoi and I. A. Grishin, “Scattering matrices for large ice crystal particles,” J. Opt. Soc. Am. A 20, 2071-2080(2003).
[CrossRef]

A. G. Borovoi, “Multiple scattering of short waves by uncorrelated and correlated scatterers,” in Light Scattering Reviews, A. A. Kokhanovsky, ed. (Springer-Praxis, 2006), Vol. 1, pp. 181-252.
[CrossRef]

Breon, F. M.

H. Chepfer, G. Brogniez, P. Goloub, F. M. Breon, and P. H. Flamant, “Observations of horizontally oriented ice crystals in cirrus clouds with POLDER-1/ADEOS-1,” J. Quant. Spectrosc. Radiat. Transfer 63, 521-543 (1999).
[CrossRef]

Breon, F.-M.

F.-M. Breon and B. Dubrulle, “Horizontally oriented plated in clouds,” J. Atmos. Sci. 61, 2888-2898 (2004).
[CrossRef]

Brogniez, G.

H. Chepfer, G. Brogniez, P. Goloub, F. M. Breon, and P. H. Flamant, “Observations of horizontally oriented ice crystals in cirrus clouds with POLDER-1/ADEOS-1,” J. Quant. Spectrosc. Radiat. Transfer 63, 521-543 (1999).
[CrossRef]

Chepfer, H.

V. Noel and H. Chepfer, “Study of ice crystal orientation in cirrus clouds based on satellite polarized radiance measurements,” J. Atmos. Sci. 61, 2073-2081 (2004).
[CrossRef]

V. Noel, G. Roy, L. Bissonnette, H. Chepfer, and P. Flamant, “Analysis of lidar measurements of ice clouds at multiple incidence angles,” Geophys. Res. Lett. 29, 1338 (2002)
[CrossRef]

V. Noel, G. Ledanois, H. Chepfer, and P. H. Flamant, “Computation of a single-scattering matrix for nonspherical particles randomly or horizontally oriented in space,” Appl. Opt. 40, 4365-4375 (2001).
[CrossRef]

H. Chepfer, G. Brogniez, P. Goloub, F. M. Breon, and P. H. Flamant, “Observations of horizontally oriented ice crystals in cirrus clouds with POLDER-1/ADEOS-1,” J. Quant. Spectrosc. Radiat. Transfer 63, 521-543 (1999).
[CrossRef]

Chervet, P.

Cho, H.-M.

Cohen, A.

Dubrulle, B.

F.-M. Breon and B. Dubrulle, “Horizontally oriented plated in clouds,” J. Atmos. Sci. 61, 2888-2898 (2004).
[CrossRef]

Flamant, P.

V. Noel, G. Roy, L. Bissonnette, H. Chepfer, and P. Flamant, “Analysis of lidar measurements of ice clouds at multiple incidence angles,” Geophys. Res. Lett. 29, 1338 (2002)
[CrossRef]

Flamant, P. H.

V. Noel, G. Ledanois, H. Chepfer, and P. H. Flamant, “Computation of a single-scattering matrix for nonspherical particles randomly or horizontally oriented in space,” Appl. Opt. 40, 4365-4375 (2001).
[CrossRef]

H. Chepfer, G. Brogniez, P. Goloub, F. M. Breon, and P. H. Flamant, “Observations of horizontally oriented ice crystals in cirrus clouds with POLDER-1/ADEOS-1,” J. Quant. Spectrosc. Radiat. Transfer 63, 521-543 (1999).
[CrossRef]

Galileiskii, V.

Goloub, P.

H. Chepfer, G. Brogniez, P. Goloub, F. M. Breon, and P. H. Flamant, “Observations of horizontally oriented ice crystals in cirrus clouds with POLDER-1/ADEOS-1,” J. Quant. Spectrosc. Radiat. Transfer 63, 521-543 (1999).
[CrossRef]

Grishin, I. A.

Hu, Y.

Kattawar, G. W.

Kustova, N.

A. Borovoi and N. Kustova, “Display of ice crystal flutter in atmospheric light pillars,” Geophys. Res. Lett. 36, L04804(2009).
[CrossRef]

Kustova, N. V.

A. G. Borovoi, N. V. Kustova, and U. G. Oppel, “Light backscattering by hexagonal ice crystal particles in the geometrical optics approximation,” Opt. Eng. 44, 071208 (2005).
[CrossRef]

Lacis, A. A.

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles (Cambridge University, 2002).

Lavigne, C.

Ledanois, G.

Liou, K. N.

Y. Takano and K. N. Liou, “Halo phenomena modified by multiple scattering,” J. Opt. Soc. Am. A 7, 885-889 (1990).
[CrossRef]

K. N. Liou, Radiation and Cloud Processes in the Atmosphere: Theory, Observation and Modelling (Oxford University, 1992).

McNice, G. T.

C. M. R. Platt, N. L. Abshire, and G. T. McNice, “Some microphysical properties of an ice cloud from lidar observations of horizontally oriented crystals,” J. Appl. Meteorol. 17, 1220-1224 (1978).
[CrossRef]

Minnis, P.

Mishchenko, M. I.

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles (Cambridge University, 2002).

Moilanen, J.

W. Tape and J. Moilanen, Atmospheric Halos and the Search for Angle X (American Geophysical Union, 2006).
[CrossRef]

Morozov, A.

Nasiri, S. L.

Noel, V.

V. Noel and K. Sassen, “Study of planar ice crystal orientations in ice clouds from scanning polarization lidar observations,” J. Appl. Meteorol. 44, 653-664 (2005).
[CrossRef]

V. Noel and H. Chepfer, “Study of ice crystal orientation in cirrus clouds based on satellite polarized radiance measurements,” J. Atmos. Sci. 61, 2073-2081 (2004).
[CrossRef]

V. Noel, G. Roy, L. Bissonnette, H. Chepfer, and P. Flamant, “Analysis of lidar measurements of ice clouds at multiple incidence angles,” Geophys. Res. Lett. 29, 1338 (2002)
[CrossRef]

V. Noel, G. Ledanois, H. Chepfer, and P. H. Flamant, “Computation of a single-scattering matrix for nonspherical particles randomly or horizontally oriented in space,” Appl. Opt. 40, 4365-4375 (2001).
[CrossRef]

Oppel, U. G.

A. G. Borovoi, N. V. Kustova, and U. G. Oppel, “Light backscattering by hexagonal ice crystal particles in the geometrical optics approximation,” Opt. Eng. 44, 071208 (2005).
[CrossRef]

Platt, C. M. R.

C. M. R. Platt, N. L. Abshire, and G. T. McNice, “Some microphysical properties of an ice cloud from lidar observations of horizontally oriented crystals,” J. Appl. Meteorol. 17, 1220-1224 (1978).
[CrossRef]

Roblin, A.

Roy, G.

V. Noel, G. Roy, L. Bissonnette, H. Chepfer, and P. Flamant, “Analysis of lidar measurements of ice clouds at multiple incidence angles,” Geophys. Res. Lett. 29, 1338 (2002)
[CrossRef]

Sassen, K.

V. Noel and K. Sassen, “Study of planar ice crystal orientations in ice clouds from scanning polarization lidar observations,” J. Appl. Meteorol. 44, 653-664 (2005).
[CrossRef]

Takano, Y.

Tape, W.

W. Tape and J. Moilanen, Atmospheric Halos and the Search for Angle X (American Geophysical Union, 2006).
[CrossRef]

Travis, L. D.

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles (Cambridge University, 2002).

Trepte, C.

Winker, D.

Wolf, E.

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge University, 1999).
[PubMed]

Yang, P.

Appl. Opt. (2)

Geophys. Res. Lett. (2)

V. Noel, G. Roy, L. Bissonnette, H. Chepfer, and P. Flamant, “Analysis of lidar measurements of ice clouds at multiple incidence angles,” Geophys. Res. Lett. 29, 1338 (2002)
[CrossRef]

A. Borovoi and N. Kustova, “Display of ice crystal flutter in atmospheric light pillars,” Geophys. Res. Lett. 36, L04804(2009).
[CrossRef]

J. Appl. Meteorol. (2)

V. Noel and K. Sassen, “Study of planar ice crystal orientations in ice clouds from scanning polarization lidar observations,” J. Appl. Meteorol. 44, 653-664 (2005).
[CrossRef]

C. M. R. Platt, N. L. Abshire, and G. T. McNice, “Some microphysical properties of an ice cloud from lidar observations of horizontally oriented crystals,” J. Appl. Meteorol. 17, 1220-1224 (1978).
[CrossRef]

J. Atmos. Sci. (2)

V. Noel and H. Chepfer, “Study of ice crystal orientation in cirrus clouds based on satellite polarized radiance measurements,” J. Atmos. Sci. 61, 2073-2081 (2004).
[CrossRef]

F.-M. Breon and B. Dubrulle, “Horizontally oriented plated in clouds,” J. Atmos. Sci. 61, 2888-2898 (2004).
[CrossRef]

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

J. Quant. Spectrosc. Radiat. Transfer (1)

H. Chepfer, G. Brogniez, P. Goloub, F. M. Breon, and P. H. Flamant, “Observations of horizontally oriented ice crystals in cirrus clouds with POLDER-1/ADEOS-1,” J. Quant. Spectrosc. Radiat. Transfer 63, 521-543 (1999).
[CrossRef]

Opt. Eng. (1)

A. G. Borovoi, N. V. Kustova, and U. G. Oppel, “Light backscattering by hexagonal ice crystal particles in the geometrical optics approximation,” Opt. Eng. 44, 071208 (2005).
[CrossRef]

Opt. Express (2)

Other (5)

K. N. Liou, Radiation and Cloud Processes in the Atmosphere: Theory, Observation and Modelling (Oxford University, 1992).

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles (Cambridge University, 2002).

A. G. Borovoi, “Multiple scattering of short waves by uncorrelated and correlated scatterers,” in Light Scattering Reviews, A. A. Kokhanovsky, ed. (Springer-Praxis, 2006), Vol. 1, pp. 181-252.
[CrossRef]

W. Tape and J. Moilanen, Atmospheric Halos and the Search for Angle X (American Geophysical Union, 2006).
[CrossRef]

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge University, 1999).
[PubMed]

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Figures (8)

Fig. 1
Fig. 1

Scattering by a thin plate.

Fig. 2
Fig. 2

Shapes and location of the scattering domains [ T = 15 ° , θ i = 0 ° (solid), 40 ° (dashed), and 85 ° (thin solid)]. The dots indicate the domain centers. The right figure shows only shapes.

Fig. 3
Fig. 3

Scattering efficiencies for the uniform tilt distribution with the maximum tilt T : (a) absolutely reflecting interface R = 1 , and (b) the reflection coefficient R corresponding to an interface with the refraction index of 1.31 and unpolarized incident light.

Fig. 4
Fig. 4

Scheme illustrating the forming of the total scattered light. The solid curve shows a shape of the geometric optics scattering domain ( θ i = 60 ° , T = 15 ° ), and the half-tone pictures are the diffraction functions at λ / a = 0.05 drawn for several points inside the domain.

Fig. 5
Fig. 5

Total phase functions for (a) the uniform and (b) the Gaussian tilt distributions ( T = 5 ° , θ i = 50 ° , λ / a = 0.027 , and the reflection coefficient R corresponds to an interface with the refraction index of 1.31 and unpolarized incident light).

Fig. 6
Fig. 6

Profiles of the phase functions of Fig. 5 along the meridian crossing the scattering domain center of ( φ 0 = 0 ° , θ 0 = 130 ° ). The corresponding geometric optics profiles are shown by dashed curves.

Fig. 7
Fig. 7

Same as in Fig. 5 at the incident angle of 70 ° .

Fig. 8
Fig. 8

Same as in Fig. 6 at the incident angle of 70 ° .

Equations (17)

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E = E s + E d
r = i 2 ( i · N ) N ,
N = ( i r ) / | i r | .
A = S ( ρ ) d ρ .
S ( ρ ) = S ( ρ ( ρ ) ) ,
σ ( s , i ) = A | i · N | R ( i · N ) F i , N ( s r ) ,
F i , N ( s r ) | ( k / 2 π ) exp ( i k [ ( s r ) · ρ ] ) S ( ρ ) d ρ | 2 / A ,
σ ( s , i ) = A | i · N | R ( i · N ) F i , N ( s r ( N ) ) p ( N ) d N = A | i · N ( r ) | R ( i · N ( r ) ) F i , N ( r ) ( s r ) p ( N ( r ) ) ( D N / D r ) d r .
D N / D r = | ( sin θ 1 d θ 1 d φ 1 ) / ( sin θ 2 d θ 2 d φ 2 ) | = | 4 cos θ 1 ) | 1 = ( 4 | i · N | ) 1 .
σ ( s , i ) = ( A / 4 ) R ( i · N ( r ) ) F i , N ( r ) ( s r ) p ( N ( r ) ) d r .
γ ( s , i ) = ( A / 4 ) R ( i · N ( s ) ) p ( N ( s ) ) .
σ ( s , i ) = γ ( r , i ) F i , N ( r ) ( s r ) d r .
P ( s , i ) = σ ( s , i ) / S ( i ) , P g ( s , i ) = γ ( s , i ) / S ( i ) ,
Q ( i ) = | i · N | R ( i · N ) p ( N ) d N = ( 1 / 4 ) R ( i · N ( s ) ) p ( N ( s ) ) d s .
γ ( θ s , θ i ) = ( π a 2 / 4 ) p ( | θ s θ 0 | / 2 ) R ( | cos [ ( θ s + θ 0 ) / 2 ] | ) ,
F i , N ( s r ) = β ( k a ) 2 4 π ( 2 J 1 [ k a ( w | | β ) 2 + w 2 ] k a ( w | | β ) 2 + w 2 ) 2 ,
t = ρ f / ρ d

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