  We study the scattering of a weak and far-detuned light from a system of
ultracold bosons in 1D and 3D optical lattices. We show the connection between
angular distributions of the scattered light and statistical properties of a
Bose gas in a periodic potential. The angular patterns are determined by the
Fourier transform of the second-order correlation function, and thus they can
be used to retrieve information on particle number fluctuations and
correlations. We consider superfluid and Mott insulator phases of the Bose gas
in a lattice, and we analyze in detail how the scattering depends on the system
dimensionality, temperature and atom-atom interactions.
