  The appearance of debris disks around distant stars depends upon the
scattering/phase function (SPF) of the material in the disk. However,
characterizing the SPFs of these extrasolar debris disks is challenging because
only a limited range of scattering angles are visible to Earth-based observers.
By contrast, Saturn's tenuous rings can be observed over a much broader range
of geometries, so their SPFs can be much better constrained. Since these rings
are composed of small particles released from the surfaces of larger bodies,
they are reasonable analogs to debris disks and so their SPFs can provide
insights into the plausible scattering properties of debris disks. This work
examines two of Saturn's dusty rings: the G ring (at 167,500 km from Saturn's
center) and the D68 ringlet (at 67,600 km). Using data from the cameras onboard
the Cassini spacecraft, we are able to estimate the rings' brightnesses at
scattering angles ranging from 170 to 0.5 degrees. We find that both of the
rings exhibit extremely strong forward-scattering peaks, but for scattering
angles above 60 degrees their brightnesses are nearly constant. These SPFs can
be well approximated by a linear combination of three Henyey-Greenstein
functions, and are roughly consistent with the SPFs of irregular particles from
laboratory measurements. Comparing these data to Fraunhofer and Mie models
highlights several challenges involved in extracting information about particle
compositions and size distributions from SPFs alone. The SPFs of these rings
also indicate that the degree of forward scattering in debris disks may be
greatly underestimated.
