  We measure the two-point density correlation function of freely expanding
quasicondensates in the weakly interacting quasi-one-dimensional (1D) regime.
While initially suppressed in the trap, density fluctuations emerge gradually
during expansion as a result of initial phase fluctuations present in the
trapped quasicondensate. Asymptotically, they are governed by the thermal
coherence length of the system. Our measurements take place in an intermediate
regime where density correlations are related to near-field diffraction effects
and anomalous correlations play an important role. Comparison with a recent
theoretical approach described by Imambekov et al. yields good agreement with
our experimental results and shows that density correlations can be used for
thermometry of quasicondensates.
