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

TL;DR

This study analyzes the statistical properties of squared visibilities from optical interferometry data, revealing that Student distribution better models the data than Gaussian, and highlights the impact of atmospheric effects and frame selection biases.

Contribution

It provides a comprehensive statistical analysis of squared visibilities from VLTI/AMBER data, demonstrating the superiority of Student distribution modeling and examining atmospheric and selection effects.

Findings

Student distribution fits squared visibilities better than Gaussian.

Atmospheric perturbations cause observable correlation effects.

Differential visibilities retain more data with less dispersion.

Abstract

In optical interferometry, the visibility squared modulus 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. Analyze the statistical behaviour of both the absolute and the colour-differential squared visibilities: distribution laws, correlations and cross-correlations between different baselines. We use observations of stellar calibrators obtained with AMBER instrument on 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. 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 analyze clear correlation effects caused by atmospheric perturbations. The differential squared visibilities allow 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 characterized. The frame selection based on the criterion of a fixed SNR value might result in either a biased sample of frames or in a too severe selection.