Finite source gravitational lensing: Theory and applications

We develop a semi-analytic model for the magnification of a finite source by an isothermal sphere. With this model we are able to place lower bounds on the mass scale of substructure perturbers in quasar lensing which we do for the lens systems B1422+231, B2045+265, B1555+375, and B0712+472. Numerous galaxy-galaxy lenses have been discovered by spectroscopic searches of large data sets and we formulate the theory of finite source lens statistics as is applicable to galaxy-galaxy lenses. Using parameters from the Sloan Lens ACS survey, we quote predictions of the expected number of rogue lines which should be found in their spectra and the fraction of those which will show evidence of strong lensing upon follow up observations. We then turn our focus to microlensing and, inspired by the recent discovery of the first central image in a multiply imaged quasar system, calculate microlensing effects on the magnification of the central image. The analysis is essential when using properties of the central image to constraint mass models for the lens system because the optical depth near the center of the lens galaxy is so high. Lastly, the with large number of new galaxy-galaxy lens systems and upcoming surveys such as the Supernova Acceleration Probe comes the possibility that a multiply imaged supernova will be observed in the near future. We predict that the size of the supernova and the stellar optical depth at the image positions will make microlensing by stars in the main lens galaxy ubiquitous in the light curves of these objects. We explore changes in the light curves due to different properties of the stellar population