  We measure the spatial correlation function of Bose-Einstein condensates in
the cross-over region between phase-coherent and strongly phase-fluctuating
condensates. We observe the continuous path from a gaussian-like shape to an
exponential-like shape characteristic of one-dimensional phase-fluctuations.
The width of the spatial correlation function as a function of the temperature
shows that the condensate coherence length undergoes no sharp transition
between these two regimes.
