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.
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