  The Low Frequency Instrument on board the ESA Planck satellite is coupled to
the Planck 1.5 meter off-axis dual reflector telescope by an array of 27
corrugated feed horns operating at 30, 44, 70, and 100 GHz. We briefly present
here a detailed study of the optical interface devoted to optimize the angular
resolution (10 arcmin at 100 GHz as a goal) and at the same time to minimize
all the systematics coming from the sidelobes of the radiation pattern. Through
optical simulations, we provide shapes, locations on the sky, angular
resolutions, and polarization properties of each beam.
