  We investigate the coherence properties of an array of one-dimensional Bose
gases with short-scale phase fluctuations. The momentum distribution is
measured using Bragg spectroscopy and an effective coherence length of the
whole ensemble is defined. In addition, we propose and demonstrate that
time-of-flight absorption imaging can be used as a simple probe to directly
measure the coherence-length of 1D gases in the regime where phase-fluctuations
are strong. This method is suitable for future studies such as investigating
the effect of disorder on the phase coherence.
