  We have observed Bragg scattering of photons from quantum degenerate
$^{87}$Rb atoms in a three-dimensional optical lattice. Bragg scattered light
directly probes the microscopic crystal structure and atomic wavefunction whose
position and momentum width is Heisenberg-limited. The spatial coherence of the
wavefunction leads to revivals in the Bragg scattered light due to the atomic
Talbot effect. The decay of revivals across the superfluid to Mott insulator
transition indicates the loss of superfluid coherence.
