Abstract

Scattering phase matrices are calculated for randomly oriented hexagonal cylinders and equivalent spheroids. The scattering solution for spheroids utilizes a numerical integral equation technique called the T-matrix method, while that for hexagonal cylinders employs a geometric ray-tracing method. Computational results show that there is general agreement for the phase functions P11 for hexagonal cylinders and spheroids with the same overall dimensions or surface area, except for the 22 and 46° halo features and the backscattering maximum produced by the hexagonal geometry. Values of P12 which are associated with linear polarization when the incident light is unpolarized differ in the forward directions where hexagonal cylinders have two positive polarization maxima. Large differences are observed in the P33 and P44 elements.

© 1983 Optical Society of America

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References

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    [CrossRef] [PubMed]
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1982 (1)

1980 (1)

1977 (2)

P. W. Barber, IEEE Trans. Microwave Theory Tech. MTT-25, 373 (1977).
[CrossRef]

T. B. A. Senior, H. Weil, Appl. Opt. 16, 2979 (1977).
[CrossRef] [PubMed]

1975 (1)

1971 (1)

P. C. Waterman, Phys. Rev. D 3, 825 (1971).
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

Comparison of the normalized scattering phase function P11/4π for randomly oriented hexagonal ice columns and prolate spheroids as a function of the scattering angle. The prolate spheroid case in dots has the same surface area as the column. Cross at 0° scattering angle is obtained from diffraction only in the geometric optics program for hexagons.

Fig. 2
Fig. 2

Comparison of the phase matrix elements −P12/P11, P22/P11, and P43/P11 for hexagonal ice columns and prolate spheroids as a function of the scattering angle.

Fig. 3
Fig. 3

Comparison of the phase matrix elements P33/P11 and P41/P11 for hexagonal ice columns and prolate spheroids as a function of the scattering angle.

Fig. 4
Fig. 4

Same as Fig. 1, except for hexagonal plates and oblate spheroids.

Fig. 5
Fig. 5

Same as Fig. 2, except for hexagonal plates and oblate spheroids.

Fig. 6
Fig. 6

Same as Fig. 3, except for hexagonal plates and oblate spheroids.

Tables (1)

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Table I Basic Geometrical Parameters for Hexagonal Cylinders and Spheroids

Equations (2)

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P ( θ ) [ P 11 P 12 0 0 P 12 P 22 0 0 0 0 P 33 - P 43 0 0 P 43 P 44 ] ,
4 π P 11 ( Ω ) d Ω / 4 π = 1.

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