  The final performance of current and future instruments dedicated to
exoplanet detection and characterization (such as SPHERE on the European Very
Large Telescope, GPI on Gemini North, or future instruments on Extremely Large
Telescopes) is limited by uncorrected quasi-static aberrations. These
aberrations create long-lived speckles in the scientific image plane, which can
easily be mistaken for planets. Common adaptive optics systems require
dedicated components to perform wave-front analysis. The ultimate wave-front
measurement performance is thus limited by the unavoidable differential
aberrations between the wavefront sensor and the scientific camera. To reach
the level of detectivity required by high-contrast imaging, these differential
aberrations must be estimated and compensated for. In this paper, we
characterize and experimentally validate a wave-front sensing method that
relies on focal-plane data. Our method, called COFFEE (for COronagraphic
Focal-plane wave-Front Estimation for Exoplanet detection), is based on a
Bayesian approach, and it consists in an extension of phase diversity to
high-contrast imaging. It estimates the differential aberrations using only two
focal-plane coronagraphic images recorded from the scientific camera itself. In
this paper, we first present a thorough characterization of COFFEE's
performance by means of numerical simulations. This characterization is then
compared with an experimental validation of COFFEE using an in-house adaptive
optics bench and an apodized Roddier & Roddier phase mask coronagraph. An
excellent match between experimental results and the theoretical study is
found. Lastly, we present a preliminary validation of COFFEE's ability to
compensate for the aberrations upstream of a coronagraph.
