As we saw in Figs. B.3, B.4, and B.8, we frequently see lensed emission from extended components of the source. These arcs and rings are important because they can supply the extra constraints needed to determine the radial mass distribution that we lack in a simple two-image of four-image lens (Section B.4.1). The magnification produced by gravitational lensing also allows us to study far fainter quasar host galaxies than is otherwise possible. Comparisons of the luminosities and colors of high and low redshift host galaxies and the relative luminosities of the host and the quasar are important for understanding the growth of supermassive black holes and their relationships with their parent halos.
Modeling extended emission is more difficult than modeling point sources largely because of the complications introduced by the finite resolution of the observations. In this section we first discuss a simple theory of Einstein ring images, then some methods for modeling extended emission, and finally some results about the mass distributions of lenses and the properties of quasar host galaxies. All models of extended lenses sources start from the fact that lensing preserves the surface brightness of the source - what we perceive as magnification is only an artifact of the finite resolution of our observations. This can be modified by absorption in the ISM of the lens galaxy (e.g. see, Koopmans et al. ), but we will neglect this complication in what follows. We start with a simple analytic model for the formation of Einstein rings, then discuss numerical reconstructions of lensed sources and their ability to constrain mass distributions, and end with a survey of the properties of quasar host galaxies.