Rough illustration of vignetting for exoplanet imaging using starshade. Top-left panel: example of an external occulter with 12 petals and a shaped profile following a Sonine curve of the form (1 − ρ²)². The background image gives its Fresnel diffraction pattern at the level of the pupil of the telescope. The discs give the illumination on the pupil for 3 directions of point sources in the sky (in fact the pupil is fixed and the shadow moves according to the direction of observation, but the relative effect is the same). Bottom panel: PSFs corresponding to the three above directions on the sky.