  We present a theoretical treatment of coherent light scattering from an
interacting 1D Bose gas at finite temperatures. We show how this can provide a
nondestructive measurement of the atomic system states. The equilibrium states
are determined by the temperature and interaction strength, and are
characterized by the spatial density-density correlation function. We show how
this correlation function is encoded in the angular distribution of the
fluctuations of the scattered light intensity, thus providing a sensitive,
quantitative probe of the density-density correlation function and therefore
the quantum state of the gas.
