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