Abstract

The shape effect of inelastic scattering by small particles is investigated using geometrical optics. The particles considered are described by surfaces composed of triangles. In order to determine the accuracy of this model, the results for an approximated sphere with different degrees of discretization are compared with the result for a smooth sphere. The triangulation method is then used for describing a superellipsoid. This enables us to consider inelastic scattering for a variety of particles by changing only a few parameters.

© 2006 Optical Society of America

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    [CrossRef]
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    [CrossRef]

2005 (1)

2001 (1)

1999 (1)

1997 (1)

T. Möller and B. Trumbore, "Fast, minimum storage ray-triangle intersection," J. Graphics Tools 2, 21-28 (1997).

1996 (2)

P. Chýlek, G. B. Lesins, G. Videen, J. G. D. Wong, R. G. Pinnick, D. Ngo, and J. D. Klett, "Black carbon and absorption of solar radiation by clouds," J. Geophys. Res. 101, 23317-23365 (1996).
[CrossRef]

A. Macke, M. I. Mishchenko, and B. Cairns, "The influence of inclusions on light scattering by large ice particles," J. Geophys. Res. 101, 23311-23316 (1996).
[CrossRef]

1992 (2)

1986 (1)

1984 (1)

P. Chýlek, V. Ramaswamy, and R. J. Cheng, "Effect of graphitic carbon on the albedo of clouds," J. Atmos. Sci. 41, 3076-3084 (1984).
[CrossRef]

1981 (1)

A. H. Barr, "Superquadrics and angle preserving transformations," IEEE Comput. Graphics Appl. 1, 11-23, (1981).
[CrossRef]

1978 (1)

1976 (2)

H. Chew, M. Kerker, and P. J. McNulty, "Raman and fluorescent scattering by molecules embedded in concentric spheres," J. Opt. Soc. Am. 66, 440-444 (1976).
[CrossRef]

H. Chew, P. J. McNulty, and M. Kerker, "Model for Raman and fluorescent scattering by molecules embedded in small particles," Phys. Rev. A 13, 396-404 (1976).
[CrossRef]

Alexander, D.

Barr, A. H.

A. H. Barr, "Superquadrics and angle preserving transformations," IEEE Comput. Graphics Appl. 1, 11-23, (1981).
[CrossRef]

Bottiger, J.

Bronk, B. V.

Cairns, B.

A. Macke, M. I. Mishchenko, and B. Cairns, "The influence of inclusions on light scattering by large ice particles," J. Geophys. Res. 101, 23311-23316 (1996).
[CrossRef]

Chang, R. K.

Cheng, R. J.

P. Chýlek, V. Ramaswamy, and R. J. Cheng, "Effect of graphitic carbon on the albedo of clouds," J. Atmos. Sci. 41, 3076-3084 (1984).
[CrossRef]

Chew, H.

Chýlek, P.

P. Chýlek, G. B. Lesins, G. Videen, J. G. D. Wong, R. G. Pinnick, D. Ngo, and J. D. Klett, "Black carbon and absorption of solar radiation by clouds," J. Geophys. Res. 101, 23317-23365 (1996).
[CrossRef]

P. Chýlek, V. Ramaswamy, and R. J. Cheng, "Effect of graphitic carbon on the albedo of clouds," J. Atmos. Sci. 41, 3076-3084 (1984).
[CrossRef]

Cooke, D. D.

Fell, N. F.

Figdor, C. G.

Hill, S. C.

Holler, S.

Kerker, M.

Klett, J. D.

P. Chýlek, G. B. Lesins, G. Videen, J. G. D. Wong, R. G. Pinnick, D. Ngo, and J. D. Klett, "Black carbon and absorption of solar radiation by clouds," J. Geophys. Res. 101, 23317-23365 (1996).
[CrossRef]

Lesins, G. B.

P. Chýlek, G. B. Lesins, G. Videen, J. G. D. Wong, R. G. Pinnick, D. Ngo, and J. D. Klett, "Black carbon and absorption of solar radiation by clouds," J. Geophys. Res. 101, 23317-23365 (1996).
[CrossRef]

Macke, A.

A. Macke, M. I. Mishchenko, and B. Cairns, "The influence of inclusions on light scattering by large ice particles," J. Geophys. Res. 101, 23311-23316 (1996).
[CrossRef]

McNulty, P. J.

Mishchenko, M. I.

A. Macke, M. I. Mishchenko, and B. Cairns, "The influence of inclusions on light scattering by large ice particles," J. Geophys. Res. 101, 23311-23316 (1996).
[CrossRef]

Möller, T.

T. Möller and B. Trumbore, "Fast, minimum storage ray-triangle intersection," J. Graphics Tools 2, 21-28 (1997).

Ngo, D.

P. Chýlek, G. B. Lesins, G. Videen, J. G. D. Wong, R. G. Pinnick, D. Ngo, and J. D. Klett, "Black carbon and absorption of solar radiation by clouds," J. Geophys. Res. 101, 23317-23365 (1996).
[CrossRef]

Niles, S.

Pan, Y.

Pinnick, R. G.

Ramaswamy, V.

P. Chýlek, V. Ramaswamy, and R. J. Cheng, "Effect of graphitic carbon on the albedo of clouds," J. Atmos. Sci. 41, 3076-3084 (1984).
[CrossRef]

Schulte, J.

Schweiger, G.

Sculley, M.

Sloot, P. M. A.

Trumbore, B.

T. Möller and B. Trumbore, "Fast, minimum storage ray-triangle intersection," J. Graphics Tools 2, 21-28 (1997).

Velesco, N.

Videen, G.

P. Chýlek, G. B. Lesins, G. Videen, J. G. D. Wong, R. G. Pinnick, D. Ngo, and J. D. Klett, "Black carbon and absorption of solar radiation by clouds," J. Geophys. Res. 101, 23317-23365 (1996).
[CrossRef]

Weigel, T.

Wong, J. G. D.

P. Chýlek, G. B. Lesins, G. Videen, J. G. D. Wong, R. G. Pinnick, D. Ngo, and J. D. Klett, "Black carbon and absorption of solar radiation by clouds," J. Geophys. Res. 101, 23317-23365 (1996).
[CrossRef]

Zhang, J.

Appl. Opt. (5)

IEEE Comput. Graphics Appl. (1)

A. H. Barr, "Superquadrics and angle preserving transformations," IEEE Comput. Graphics Appl. 1, 11-23, (1981).
[CrossRef]

J. Atmos. Sci. (1)

P. Chýlek, V. Ramaswamy, and R. J. Cheng, "Effect of graphitic carbon on the albedo of clouds," J. Atmos. Sci. 41, 3076-3084 (1984).
[CrossRef]

J. Geophys. Res. (2)

P. Chýlek, G. B. Lesins, G. Videen, J. G. D. Wong, R. G. Pinnick, D. Ngo, and J. D. Klett, "Black carbon and absorption of solar radiation by clouds," J. Geophys. Res. 101, 23317-23365 (1996).
[CrossRef]

A. Macke, M. I. Mishchenko, and B. Cairns, "The influence of inclusions on light scattering by large ice particles," J. Geophys. Res. 101, 23311-23316 (1996).
[CrossRef]

J. Graphics Tools (1)

T. Möller and B. Trumbore, "Fast, minimum storage ray-triangle intersection," J. Graphics Tools 2, 21-28 (1997).

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (1)

Phys. Rev. A (1)

H. Chew, P. J. McNulty, and M. Kerker, "Model for Raman and fluorescent scattering by molecules embedded in small particles," Phys. Rev. A 13, 396-404 (1976).
[CrossRef]

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Figures (9)

Fig. 1
Fig. 1

Angular dependence of light polarized perpendicular to the scattering plane inelastically scattered by a spherical particle (solid curve, x = 80 , n = 1.5 ) for various degrees of discretization. The intensity of the scattered light is normalized by the particle volume.

Fig. 2
Fig. 2

Ratio of light scattered inelastically by a sphere as a function of the degree of discretization at three different scattering angles. The scattered intensity is normalized by the volume of the sphere.

Fig. 3
Fig. 3

Paths of the rays within a DP whose surface is approximated by triangles. The heavy rays are totally reflected.

Fig. 4
Fig. 4

Dependence of the energy of the transmitted field W tot * normalized by the particle volume and the energy within a smooth sphere on n ϑ . Solid curve, the axis of symmetry and the direction of the incident light coincide. Dashed curve, the angle between the incident light and the axis of symmetry of the DP is α = 15 ° .

Fig. 5
Fig. 5

Dependence of the shape of superellipsoids on the parameters ϵ 1 and ϵ ( a 1 = a 2 = a 3 = 1 . )

Fig. 6
Fig. 6

Angular dependence of light scattered inelastically by barrel-shaped particles ( ϵ 1 = 0.5 , ϵ 2 = 1.0 ) with (1) a 1 = a 2 = a 3 = 400 ; (2) a 1 = a 2 = 400 , a 3 = 200 ; (3) a 1 = a 2 = 200 , a 3 = 400 ; and where a 1 , a 2 , a 3 are multiples of the wavenumber k = 2 π λ . The inelastic scattered intensity is normalized to the particle volume, and the incident light is polarized perpendicular to the scattering plane.

Fig. 7
Fig. 7

Same as Fig. 6, but the incident light is polarized parallel to the scattering plane.

Fig. 8
Fig. 8

Same as Fig. 6 but for inelastic scattering by a superellipsoid of ϵ 1 = ϵ 2 = 1.5 with (1) a 1 = a 2 = a 3 = 400 ; (2) a 1 = a 2 = 400 , a 3 = 200 ; (3) a 1 = a 2 = 200 , a 3 = 400 .

Fig. 9
Fig. 9

Same as Fig. 8, but the incident light is polarized parallel to the scattering plane.

Equations (6)

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

I * = I DP I s p h e r e V s p h e r e V DP ,
W * = ( W tot V ) DP ( W tot V ) DP ) s p h e r e ,
[ ( x a 1 ) 2 ϵ 2 + ( y a 2 ) 2 ϵ 2 ] ϵ 2 ϵ 1 + ( z a 3 ) 2 ϵ 1 1 = 0 .
x 2 = a 1 2 sin 2 ϵ 1 ϑ cos 2 ϵ 2 φ ,
y 2 = a 2 2 sin 2 ϵ 1 ϑ sin 2 ϵ 2 φ ,
z 2 = a 3 2 cos 2 ϵ 1 ϑ .

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