Interferometric visibility of single-lens models: the thin-arcs approximation.

Long-baseline interferometry of microlensing events can resolve the individual images of the source produced by the lens, which combined with the modeling of the microlensing light curve, lead to the exact lens mass and distance. Interferometric observations thus offer a unique opportunity to constrain the mass of exoplanets detected by microlensing, and to precisely measure the mass of distant isolated objects such as stars, brown dwarfs and stellar remnants like white dwarfs, neutron stars or stellar black holes. Having accurate models and reliable numerical methods is of particular importance, as the number of targets is expected to increase significantly in the near future. In this work, we discuss the different approaches to calculating the fringe complex visibility for the important case of a single lens. We propose a robust integration scheme to calculate the exact visibility, and introduce a novel approximation, that we call `thin-arcs approximation', which applies over a wide range of lens-source separations. We find that this approximation runs $\times6$ to $\times10$ times faster than the exact calculation, depending of the characteristics of the event and the required accuracy. This approximation provides accurate results for microlensing events of medium to higher magnification observed around the peak, i.e. a large fraction of potential observational targets.