  The two major factors contributing to the opposition brightening of Saturn's
rings are i) the intrinsic brightening of particles due to coherent
backscattering and/or shadow-hiding on their surfaces, and ii) the reduced
interparticle shadowing. We utilize the Hubble Space Telescope observations for
different elevation angles B to disentangle these contributions. We assume that
the intrinsic contribution is independent of B, so that any B dependence of the
phase curves is due to interparticle shadowing, which must also act similarly
for all colors. We construct a grid of dynamical/photometric simulation models
to fit the elevation-dependent part of opposition brightening. Eliminating the
modeled interparticle component yields the intrinsic contribution to the
opposition effect: for the B and A rings it is almost entirely due to coherent
backscattering; for the C ring, an intraparticle shadow hiding contribution may
also be present.
  Based on our simulations, the width of the interparticle shadowing effect is
roughly proportional to B. This follows from the observation that as B
decreases, the scattering is primarily from the rarefied low filling factor
upper ring layers, whereas at larger $B$'s the dense inner parts are visible.
The elevation angle dependence of interparticle shadowing also explains most of
the B ring tilt effect (the increase of brightness with elevation). From
comparison of the magnitude of the tilt effect at different filters, we show
that multiple scattering can account for at most a 10% brightness increase as B
-> 26^o, whereas the remaining 20% brightening is due to a variable degree of
interparticle shadowing. The negative tilt effect of the middle A ring is well
explained by the the same self-gravity wake models that account for the
observed A ring azimuthal brightness asymmetry.
