  We adapt the smooth tests of goodness of fit developed by Rayner and Best to
the study of the non-Gaussianity of interferometric observations of the cosmic
microwave background (CMB). The interferometric measurements (visibilities) are
transformed into signal-to-noise eigenmodes, and then the method is applied
directly in Fourier space. This transformation allows us to perform the
analysis in different subsets of eigenmodes according to their signal-to-noise
level. The method can also deal with non-uniform or incomplete coverage of the
UV plane. We explore here two possibilities: we analyse either the real and
imaginary parts of the complex visibilities (Gaussianly distributed under the
Gaussianity hypothesis) or their phases (uniformly distributed under the
Gaussianity hypothesis). The power of the method in discriminating between
Gaussian and non-Gaussian distributions is studied by using several kinds of
non-Gaussian simulations. On the one hand, we introduce a certain degree of
non-Gaussianity directly into the Fourier space using the Edgeworth expansion,
and afterwards the desired correlation is introduced. On the other hand, we
consider interferometric observations of a map with topological defects (cosmic
strings). To these previous non-Gaussian simulations we add different noise
levels and quantify the required signal-to-noise ratio necessary to achieve a
detection of these non-Gaussian features. Finally, we have also studied the
ability of the method to constrain the so-called nonlinear coupling constant
f_{NL} using chi^2 simulations.The whole method is illustrated here by
application to simulated data from the Very Small Array interferometer.
