  We theoretically study the superradiant gain and the direction of this
coherent radiant for an array of Bose-Einstein condensates in an optical
lattice. We find that the density grating is formed to amplify the scattering
light within the phase match condition. The scattering spectroscopy in the
momentum space can provide a method for measuring the overlap of wavefunction
between the neighboring sites, which is related to their inner-site and
inter-site coherence.
