Forward and inverse problems for symmetric starbursts

Visual starbursts are images perceived by people watching a bright light source with a dilated pupil. They are generated by the optical aberrations of a person's eye. The problem of starbursts is considered for two families of symmetric aberration functions. The first is homogeneous polynomials, and the second is aberration functions that are invariants under rotation by 2<i>π</i>/<i>q</i> for any integer <i>q</i>. A complete geometrical characterization of the starbursts is given in both cases. The theory is used to solve the inverse problem of estimating the high-order aberrations from the observed starbursts.