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 when the solar phase angle α → 0 • . We utilize the extensive set of Hubble Space Telescope observations (Cuzzi et al. 2002, Icarus 158, 199-223) for different elevation angles B and wavelengths λ 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 λ's. Our study complements that of Poulet et al. (2002, Icarus 158, 224), who used a subset of data for a single B ∼ 10 • , and the French et al. (2007b, PASP 119, 623-642) study for the B ∼ 23 • data set that included exact opposition. We construct a grid of dynamical/photometric simulation models, with the method of Salo and Karjalainen (2003, Icarus 164, 428-460), and use these simulations 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. Vertical segregation of particle sizes further enhances this effect. The elevation angle dependence of interparticle shadowing also explains most arXiv:1007.0349v1 [astro-ph.EP] 2 Jul 2010 -2of 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 • , 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 (Salo et al. 2004, Icarus 170, 70-90; French et al. 2007a, Icarus 189, 493-522).