Comparison of Fourier and model-based estimators in single-mode multi-axial interferometry

There are several solutions to code the signal arising from optical long-baseline multi-aperture interferometers. In this paper, we focus on the non-homothetic spatial coding scheme (multi-axial) with the fringe pattern coded along one dimension on one detector (all-in-one). After describing the physical principles governing single-mode interferometers using that sort of recombination scheme, we analyse two different existing methods that measure the source visibility. The first technique, the so-called Fourier estimator, consists of integrating the high-frequency peak of the power spectral density of the interferogram. The second method, the so-called model-based estimator, has been specifically developed for the Astronomical Multi-BEam combineR (AMBER) instrument of the Very Large Telescope Interferometer (VLTI) and deals with directly modelling the interferogram recorded on the detector. Performances of both estimators are computed in terms of the signal-to-noise ratio (S/N) of the visibility, assuming that the interferograms are perturbed by photon and detector noises. Theoretical expressions of the visibility S/N are provided, validated through numerical computations and then compared. We show that the model-based estimator offers up to 5 times better performances than the Fourier one.