Lensed sources are rare and must be searched for in the optical and near-IR surveys in both hemispheres. Searches involve automated processes, visual post-selection and follow-up observations to confirm or demote candidates.
The small photometric variations of the lensed sources are followed on weekly or even daily basis using medium-sized optical telescopes. Image deconvolution is applied to the data to derive the light curves of each lensed image.
Numerical techniques are used to measure the time delays in the observed light curves. This process is complicated by the presence of microlensing by stars in the lensing galaxy, by the irregular sampling of the light curves, and by season gaps.
Positions and fluxes of the lensed images coming from high resolution optical data, as well as kinematics of the deflector are used to constrain a model of the lensing galaxy and to reconstruct its gravitational potential.
Mocks for light curves and microlensing variations, as well as N-body hydro simulations of lens galaxies are used to test all possible sources of systematic errors. Eventually, a full end-to-end simulation chain will be created to generate a detailed account of all sources of errors.
The results from all the steps are combined together to infer the value of the Hubble parameter within standard or more exotic cosmological models. The analysis steps must be blinded, i.e. carried out without any knowledge of the derived Hubble constant, to avoid the confirmation bias.