  We study the coherence and density modulation of a non-equilibrium
exciton-polariton condensate in a one-dimensional valley with disorder. By
means of interferometric measurements we evidence a modulation of the
first-order coherence function and we relate it to a disorder-induced
modulation of the condensate density, that increases as the pump power is
increased. The non-monotonous spatial coherence function is found to be the
result of the strong non-equilibrium character of the one-dimensional system,
in the presence of disorder.
