The initial dynamics of resonantly excited secondary emission from quantum wells are dominated by Rayleigh scattering due to excitons localized in the disordered quantum well potential. We show experimentally and theoretically how the temporal shape of the early response is related to details of the two-dimensional disorder potential, and we determine the mean amplitude of the fluctuations and the correlation length. Spectral interferometry performed with a. single speckle allows to investigate the phase of the electric field emitted by the ensemble of excitons. We find evidence for a correlation between the degree of localization and the fluctuations of the phase as a function of energy.