  Aims. We used realistic three-dimensional (3D) radiative hydrodynamical (RHD)
simulations from the Stagger-grid and synthetic images computed with the
radiative transfer code Optim3D to provide interferometric observables to
extract the signature of stellar granulation and transiting planets. Methods.
We computed intensity maps from RHD simulations for twelve interferometric
instruments covering wavelengths ranging from optical to infrared. The stellar
surface asymmetries in the brightness distribution mostly affect closure
phases. We compared the closure phases of the system star with a transiting
planet and the star alone and considered the impact of magnetic spots
constructing a hypothetical starspots image. Results. All the simulations show
departure from the axisymmetric case at all wavelengths. We presented two
possible targets (Beta Com and Procyon) and found that departures up to 16 deg
can be detected on the 3rd lobe and higher. In particular, MIRC is the most
appropriate instrument because it combines good UV coverage and long baselines.
Moreover, we explored the impact of convection on interferometric planet
signature for three prototypes of planets. It is possible to disentangle the
signature of the planet at particular wavelengths (either in the infrared or in
the optical) by comparing the closure phases of the star at difference phases
of the planetary transit. Conclusions. The detection and characterisation of
planets must be based on a comprehensive knowledge of the host star; this
includes the detailed study of the stellar surface convection with
interferometric techniques. In this context, RHD simulations are crucial to
reach this aim. We emphasize that interferometric observations should be pushed
at high spatial frequencies by accumulating observations on closure phases at
short and long baselines.
