2019ApJ...883....3L

Strongly lensed quasars with time-delay measurements are well known to provide the "time-delay distances" D_Δt_=(1+zL_)DL_DS_/DLS_, and the angular diameter distances to the lens galaxies D_L. These two kinds of distances give stringent constraints on cosmological parameters. In this work, we explore a different use of time-delay observables: under the assumption of a flat universe, strong lensing observations can accurately measure the angular diameter distances to the sources D_S. The corresponding redshifts of the quasars may be up to z_S ∼ 4 according to the forecast. The high-redshift distances would sample the Hubble diagram between SNe Ia and the cosmic microwave background, model-independently providing direct information on the evolution of the nature of our universe, for example, the dark energy equation of state parameter w(z). We apply our method to the existing lensing system SDSS 1206+4332 and get D_S=2388_–978⁺²⁶³²Mpc at z_S = 1.789. We also make a forecast for the era of Large Synoptic Survey Telescope. The uncertainty of D_S depends on the redshifts of the lens and the source, the uncertainties of D_Δt and D_L, and the correlation between D_Δt and D_L. Larger correlation would result in tighter D_S determination.