  Lens time delays are a powerful probe of cosmology, provided that the
gravitational potential of the main deflector can be modeled with sufficient
precision. Recent work has shown that this can be achieved by detailed modeling
of the host galaxies of lensed quasars, which appear as "Einstein Rings" in
high resolution images. We carry out a systematic exploration of the high
resolution imaging required to exploit the thousands of lensed quasars that
will be discovered by current and upcoming surveys with the next decade.
Specifically, we simulate realistic lens systems as imaged by the Hubble Space
Telescope (HST), James Webb Space Telescope (JWST), and ground based adaptive
optics images taken with Keck or the Thirty Meter Telescope (TMT). We compare
the performance of these pointed observations with that of images taken by the
Euclid (VIS), Wide-Field Infrared Survey Telescope (WFIRST) and Large Synoptic
Survey Telescope (LSST) surveys. We use as our metric the precision with which
the slope $\gamma'$ of the total mass density profile $\rho_{tot}\propto
r^{-\gamma'}$ for the main deflector can be measured. Ideally, we require that
the statistical error on $\gamma'$ be less than 0.02, such that it is
subdominant to other sources of random and systematic uncertainties. We find
that survey data will likely have sufficient depth and resolution to meet the
target only for the brighter gravitational lens systems, comparable to those
discovered by the SDSS survey. For fainter systems, that will be discovered by
current and future surveys, targeted follow-up will be required. However, the
exposure time required with upcoming facilitites such as JWST, the Keck Next
Generation Adaptive Optics System, and TMT, will only be of order a few minutes
per system, thus making the follow-up of hundreds of systems a practical and
efficient cosmological probe.
