  We studied the spatial coherence of a Bosonic two-dimensional multi-mode
condensate both through measurements and simulations. It is shown that
condensates with a constant spatial density must be described as the
superposition of several quantized modes which reduces the overall coherence.
In this case, the spatial coherence can appear to decay faster than allowed by
the Berezinskii-Kosterlitz-Thouless (BKT) theory. However, we find through
spectroscopic measurements that the individual modes show a slower decay of the
spatial coherence than the overall system.
