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High precision cosmological distance measurements towards individual objectssuch as time delay gravitational lenses or type Ia supernovae are affected byweak lensing perturbations by galaxies and groups along the line of sight. Intime delay gravitational lenses, "external convergence," kappa, can dominatethe uncertainty in the inferred distances and hence cosmological parameters. Inthis paper we attempt to reconstruct kappa, due to line of sight structure,using a simple halo model. We use mock catalogues from the MillenniumSimulation, and calibrate and compare our reconstructed P(kappa) to ray-tracedkappa "truth" values; taking into account realistic observationaluncertainties. We find that the reconstruction of kappa provides an improvementin precision of ~50% over galaxy number counts. We find that the lowest-kappalines of sight have the best constrained P(kappa). In anticipation of largefuture samples of lenses, we find that selecting the third of the systems withthe highest precision kappa estimates gives a sample of unbiased time delaydistance measurements with just ~1% uncertainty due to line of sight externalconvergence effects. Photometric data are sufficient to pre-select thebest-constrained lines of sight, and can be done before investment inlight-curve monitoring. Conversely, we show that selecting lines of sight withhigh external shear could, with the reconstruction model presented, inducebiases of up to 1% in time delay distance. We find that a major potentialsource of systematic error is uncertainty in the high mass end of the stellarmass-halo mass relation; this could introduce ~2% biases on the time-delaydistance if completely ignored. We suggest areas for the improvement of thisgeneral analysis framework (including more sophisticated treatment of high massstructures) that should allow yet more accurate cosmological inferences to bemade.

Reconstructing the Lensing Mass in the Universe from Photometric Catalogue Data