  In this paper we present the theoretical basis for the modeling of weakly
gravitationally lensed extended sources that are polarized. This technique has
been used in the past to constrain the mass profiles of galaxies projected
against the jet of the quasar 3C9. Since then, work has been done to improve
both the measurement and theoretical modeling of the lensing signal, which
manifests itself as an alignment breaking between the morphology and the
polarization, parametrized as eta-g. To this end, we present the mathematical
derivation of the theoretical value of eta-g as well as numerical simulations
of expected signals in polarized radio jets. We use the radio jet sources 3C9
and 1253+104 as illustrative examples of the measurement and modeling of the
eta-g signal. For 3C9, we present constraints on the parameters of the two
intervening lenses and quantify their confidence intervals. One lens has no
measured redshift and in this case, we show the dependence of mass and
mass-to-light ratio on assumed redshift.
