The robustness of phase mapping as a non-Gaussianity test

The identification and extraction of non-Gaussian signals are two of the main cosmological challenges facing future experimental measurements of the cosmic microwave background temperature pattern. In this Letter we present a detailed account and test the robustness of a generalized statistical measure based on a novel method of representation of Fourier phases using the return map. We demonstrate the usefulness (and limitations) of this method by testing it on controlled simulated maps, which show that it is both robust and powerful, particularly in detecting non-Gaussianity from systematics.