  We present new calculations of X-ray polarization from black hole accretion
disks in the thermally-dominated state, using a Monte-Carlo ray-tracing code in
full general relativity. In contrast to many previously published studies, our
approach allows us to include returning radiation that is deflected by the
strong-field gravity of the BH and scatters off of the disk before reaching a
distant observer. Although carrying a relatively small fraction of the total
observed flux, the scattered radiation tends to be highly polarized and in a
direction perpendicular to the direct radiation. We show how these new features
of the polarization spectra may be developed into a powerful tool for measuring
black hole spin and probing the gas flow in the innermost disk.
