The brightness of a ring or a portion of a ring is dependent on both the total reflectivity (albedo) of the particles within that ring or ring portion and on the directional distribution of the reflected radiation (phase function). The phase function is the variation in brightness of the target as the phase angle varies between 0° (back-scattered light) and 180° (forward-scattered light). Sometimes the term scattering angle is utilized. The scattering angle is simply the supplement of the phase angle; or, in other words, the scattering angle is the difference between the phase angle and 180°. In mathematical terms,
0 = 180° - a, where 0 is the scattering angle and a is the phase angle.
The phase function for the bulk of the A and B rings peaks strongly at 0° phase angle. This characteristic is known as the opposition effect. Saturn's A and B rings have a much sharper opposition surge than any other natural objects in the solar system. Cassini observations have brought a much better understanding of this effect (Chapter 10).
In marked contrast with the strongly back-scattering A and B rings, the D, G, and E rings are strongly forward-scattering. This behavior is typical for rings which are dominated by particles in a size range that is comparable with the wavelength of the light incident on the rings (approximately a micrometer in radius).
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