Spatio-spectral encoding of fringes in optical long-baseline interferometry Example of the 3T and 4T recombining mode of VEGA/CHARA

Context. One of the main challenges of optical stellar interferometers is to increase the number of telescopes in the recombining unit to provide a larger number of measurements and an improved imaging capability. At the same time there is a need to preserve the spectroscopic capabilities, which leads to complex recombining schemes that may inhibit development. Aims. We describe the possibilities of combining the spatial and spectral encoding of fringes for the design of more compact beam combiners and for minimizing the number of pixels that must be read. Methods. We establish the formalism of the spatio-spectral fringe encoding, discuss general applications, and describe an implementation in the 3T/4T observing mode of the VEGA (Visible spEctroGraph and polArimeter) instrument installed at the coherent focus of the CHARA Array located on Mt Wilson in California. We finally present the science cases made possible by this instrumental implementation in the case of VEGA/CHARA. Results. We demonstrate the interest in implementing an optimized spatio-spectral encoding of fringes in a multi-telescope beam combiner. On-sky results, obtained with the 3T mode of the VEGA combiner are presented. At visible wavelengths and with the hectometric baselines of CHARA, sub-mas stellar diameters could be determined with a precision of a few percent with a spectral resolution of 5000. Our first estimates of closure phase show that accuracies better than 1 degree can be achieved. Conclusions. The first on-sky results obtained with the 3T-4T VEGA instrument using spatio-spectral fringe encoding show the validity of using this principle in the design of future complex beam combiners.