Bandwidth smearing in infrared long-baseline interferometry. Application to stellar companion search in fringe-scanning mode

In long-baseline interferometry, bandwidth smearing of an extended source occurs at finite bandwidth when its different components produce interference packets that only partially overlap. In this case, traditional model fitting or image reconstruction using standard formulas and tools lead to biased results. In this paper, we propose and implement a method to overcome this effect by calculating analytically a corrective term for the conventional interferometric observables: the visibility amplitude and closure phase. For that purpose, we model the interferogram taking into account the finite bandwidth and the instrumental differential phase. We obtain generic expressions for the visibility and closure phase in the case of temporally modulated interferograms, either processed using Fourier analysis or with the ABCD method. The expressions can be used to fit arbitrary models to the data. We then apply our results to the search and charactrization of stellar companions with the Precision Integrated-Optics Near-infrared Imaging ExpeRiment at the Very Large Telescope Interferometer, assessing the bias on observables and model-fitted parameters of a binary star. Finally, we consider the role of the atmosphere, first with an analytic model to identify the main contributions to bias and, secondly, by confirming the model with a numerical simulation of the atmospheric turbulence. In addition to the analytic expressions, the main results of our study are as follows: (i) the chromatic dispersion in the beam transport in the instrument has a strong impact on the closure phase and introduces additional biases even at separations where smearing is not expected to play an important role; (ii) the atmospheric turbulence introduces additional biases when smearing is present, but the impact is important only at very low spectral resolution; (iii) the bias on the observables strongly depends on the recombination scheme and data processing; (iv) the goodness of model fits is improved by modelling a Gaussian bandpass as long as the smearing is moderate.