The point spread function (PSF) for astronomical telescopes and instruments depends not only on geometric aberrations and scalar wave diffraction, but also on the apodization and wavefront errors introduced by coatings on reflecting and transmitting surfaces within the optical system. The functional form of these aberrations, called polarization aberrations, result from the angles of incidence and the variations of the coatings as a function of angle. These coatings induce small modifications to the PSF, which consists of four separate components, two nearly Airy-disk PSF components, and two faint components, we call ghost PSF components, with a spatial extent about twice the size of the diffraction limited image. As the specifications of optical systems constantly improve, these small effects become increasingly important. It is shown how the magnitude of these ghost PSF components, at ∼10-5 in the example telescope, can interfere with exoplanet detection with coronagraphs.