  High precision cosmological distance measurements towards individual objects
such as time delay gravitational lenses or type Ia supernovae are affected by
weak lensing perturbations by galaxies and groups along the line of sight. In
time delay gravitational lenses, "external convergence," kappa, can dominate
the uncertainty in the inferred distances and hence cosmological parameters. In
this paper we attempt to reconstruct kappa, due to line of sight structure,
using a simple halo model. We use mock catalogues from the Millennium
Simulation, and calibrate and compare our reconstructed P(kappa) to ray-traced
kappa "truth" values; taking into account realistic observational
uncertainties. We find that the reconstruction of kappa provides an improvement
in precision of ~50% over galaxy number counts. We find that the lowest-kappa
lines of sight have the best constrained P(kappa). In anticipation of large
future samples of lenses, we find that selecting the third of the systems with
the highest precision kappa estimates gives a sample of unbiased time delay
distance measurements with just ~1% uncertainty due to line of sight external
convergence effects. Photometric data are sufficient to pre-select the
best-constrained lines of sight, and can be done before investment in
light-curve monitoring. Conversely, we show that selecting lines of sight with
high external shear could, with the reconstruction model presented, induce
biases of up to 1% in time delay distance. We find that a major potential
source of systematic error is uncertainty in the high mass end of the stellar
mass-halo mass relation; this could introduce ~2% biases on the time-delay
distance if completely ignored. We suggest areas for the improvement of this
general analysis framework (including more sophisticated treatment of high mass
structures) that should allow yet more accurate cosmological inferences to be
made.
