  Most statistical tools used to characterize the complex structures of the
interstellar medium can be related to the power spectrum, and therefore to the
Fourier amplitudes of the observed fields. To tap into the vast amount of
information contained in the Fourier phases, one may consider the probability
distribution function (PDF) of phase increments, and the related concepts of
phase entropy and phase structure quantity. We use these ideas here with the
purpose of assessing the ability of radio-interferometers to detect and recover
this information. By comparing current arrays such as the VLA and Plateau de
Bure to the future ALMA instrument, we show that the latter is definitely
needed to achieve significant detection of phase structure, and that it will do
so even in the presence of a fair amount of atmospheric phase fluctuations. We
also show that ALMA will be able to recover the actual "amount'' of phase
structure in the noise-free case, if multiple configurations are used.
