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SPHERE (Spectro Polarimetric High contrast Exoplanet REsearch), the planetfinder instrument for the VLT is designed to study relatively bright extrasolargiant planets around young or nearby stars. SPHERE is a set of threeinstruments fed by the same AO-system, two of them share the same coronagraph.This complex system has been modeled with Fourier Optics to investigate theperformance of the whole instrument. In turns, this end-to-end model was usefulto analyze the sensitivity to various parameters (WFE, alignment of thecoronagraph, differential aberrations) and to put some specifications on thesub-systems. This paper presents some example of sensitivity analysis and somecontrast performance of the instruments as a function of the flux for the mainobserving mode of SPHERE: the Dual Band Imaging (DBI), equivalent to theSpectral Differential Imaging technique.

End to End Simulation of AO-assisted coronagraphic differential imaging: estimation of performance for SPHERE