Statistical characterisation of polychromatic absolute and differential squared visibilities obtained from AMBER/VLTI instrument

Context. In optical interferometry, the visibility squared moduli are generally assumed to follow a Gaussian distribution and to be independent of each other. A quantitative analysis of the relevance of such assumptions is important to help improving the exploitation of existing and upcoming multi-wavelength interferometric instruments. Aims. The aims of this study are to analyse the statistical behaviour of both the absolute and the colour-differential squared visibilities: distribution laws, correlations and cross-correlations between different baselines. Methods. We use observations of stellar calibrators obtained with the AMBER instrument on the Very Large Telescope Interferometer (VLTI) in different instrumental and observing configurations, from which we extract the frame-by-frame transfer function. Statistical hypotheses tests and diagnostics are then systematically applied. We also compute the same analysis after correcting the instantaneous squared visibilities from the piston and jitter chromatic effects, using a low-order fit subtraction. Results. For both absolute and differential squared visibilities and under all instrumental and observing conditions, we find a better fit for the Student distribution than for the Gaussian, log-normal, and Cauchy distributions. We find and analyse clear correlation effects caused by atmospheric perturbations. The differential squared visibilities allow us to keep a larger fraction of data with respect to selected absolute squared visibilities and thus benefit from reduced temporal dispersion, while their distribution is more clearly characterised. Conclusions. The frame selection based on the criterion of a fixed signal-to-noise value might result in either a biased sample of frames or one with severe selection. Instead, we suggest an adaptive frame selection procedure based on the stability of the modes of the observed squared visibility distributions. In addition, taking into account the correlations effects between measured squared visibilities should help improve the models used in inverse problems and, thus, the accuracy of model fits and image reconstruction results. Finally, our results indicate that re-scaled differential squared visibilities usually constitute a valuable alternative estimator of squared visibility.