Context. The direct detection of exoplanets with high-contrast imaging requires advanced data processing methods to disentangle potential planetary signals from bright quasi-static speckles. Among them, angular differential imaging (ADI) permits potential planetary signals with a known rotation rate to be separated from instrumental speckles that are either statics or slowly variable. The method presented in this paper, called ANDROMEDA for ANgular Differential OptiMal Exoplanet Detection Algorithm, is based on a maximum likelihood approach to ADI and is used to estimate the position and the flux of any point source present in the field of view. Aims. In order to optimize and experimentally validate this previously proposed method,...