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Modern (sub)millimeter interferometers, such as ALMA and NOEMA, offer highangular resolution and unprecedented sensitivity. This provides the possibilityto characterize the morphology of the gas and dust in distant galaxies. Toassess the capabilities of current softwares in recovering morphologies andsurface brightness profiles in interferometric observations, we test theperformance of the Spergel model for fitting in the $uv$-plane, which has beenrecently implemented in the IRAM software GILDAS (uv$\_$fit). Spergel profilesprovide an alternative to the Sersic profile, with the advantage of having ananalytical Fourier transform, making them ideal to model visibilities in the$uv$-plane. We provide an approximate conversion between Spergel index andSersic index, which depends on the ratio of the galaxy size to the angularresolution of the data. We show through extensive simulations that Spergelmodeling in the $uv$-plane is a more reliable method for parameter estimationthan modeling in the image-plane, as it returns parameters that are lessaffected by systematic biases and results in a higher effective signal-to-noiseratio (S/N). The better performance in the $uv$-plane is likely driven by thedifficulty of accounting for correlated signal in interferometric images. Evenin the $uv$-plane, the integrated source flux needs to be at least 50 timeslarger than the noise per beam to enable a reasonably good measurement of aSpergel index. We characterise the performance of Spergel model fitting indetail by showing that parameters biases are generally low (< 10%) and thatuncertainties returned by uv$\_$fit are reliable within a factor of two.Finally, we showcase the power of Spergel fitting by re-examining two claims ofextended halos around galaxies from the literature, showing that galaxies andhalos can be successfully fitted simultaneously with a single Spergel model.

Fitting pseudo-S${\rm \acute{e}}$rsic(Spergel) light profiles to galaxies in interferometric data: the excellence of the $uv$-plane