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We present the measurement of the Hubble constant, H 0, with three strong gravitational lens systems. We describe a blind analysis of both PG 1115+080 and HE 0435−1223 as well as an extension of our previous analysis of RXJ 1131−1231. For each lens, we combine new adaptive optics (AO) imaging from the Keck Telescope, obtained as part of the SHARP (Strong-lensing High Angular Resolution Programme) AO effort, with Hubble Space Telescope (HST) imaging, velocity dispersion measurements, and a description of the line-of-sight mass distribution to build an accurate and precise lens mass model. This mass model is then combined with the COSMOGRAIL-measured time delays in these systems to determine H 0. We do both an AO-only and an AO + HST analysis of the systems and find that AO and HST results are consistent. After unblinding, the AO-only analysis gives |$H_{0}=82.8^{+9.4}_{-8.3}~\rm km\, s^{-1}\, Mpc^{-1}$| for PG 1115+080, |$H_{0}=70.1^{+5.3}_{-4.5}~\rm km\, s^{-1}\, Mpc^{-1}$| for HE 0435−1223, and |$H_{0}=77.0^{+4.0}_{-4.6}~\rm km\, s^{-1}\, Mpc^{-1}$| for RXJ 1131−1231. The joint AO-only result for the three lenses is |$H_{0}=75.6^{+3.2}_{-3.3}~\rm km\, s^{-1}\, Mpc^{-1}$|⁠. The joint result of the AO + HST analysis for the three lenses is |$H_{0}=76.8^{+2.6}_{-2.6}~\rm km\, s^{-1}\, Mpc^{-1}$|⁠. All of these results assume a flat Λ cold dark matter cosmology with a uniform prior on Ωm in [0.05, 0.5] and H 0 in [0, 150] |$\rm km\, s^{-1}\, Mpc^{-1}$|⁠. This work is a collaboration of the SHARP and H0LiCOW teams, and shows that AO data can be used as the high-resolution imaging component in lens-based measurements of H 0. The full time-delay cosmography results from a total of six strongly lensed systems are presented in a companion paper. [ABSTRACT FROM AUTHOR]

Strong gravitational lenses with measured time delays between the multiple images allow a direct measurement of the time-delay distance to the lens, and thus a measure of cosmological parameters, particularly the Hubble constant, H0. We present a blind lens model analysis of the quadruply imaged quasar lens HE 0435-1223 using deep Hubble Space Telescope imaging, updated time-delay measurements from the COSmological MOnitoring of GRAvItational Lenses (COSMOGRAIL), a measurement of the velocity dispersion of the lens galaxy based on Keck data, and a characterization of the mass distribution along the line of sight. HE 0435-1223 is the third lens analysed as a part of the H0 Lenses in COSMOGRAIL's Wellspring (H0LiCOW) project. We account for various sources of systematic uncertainty, including the detailed treatment of nearby perturbers, the parametrization of the galaxy light and mass profile, and the regions used for lens modelling. We constrain the effective time-delay distance to be DΔt=2612-191+208Mpc, a precision of 7.6 per cent. From HE 0435-1223 alone, we infer a Hubble constant of H0=73.1-6.0+5.7kms-1Mpc-1 assuming a flat ΛCDM cosmology. The cosmographic inference based on the three lenses analysed by H0LiCOW to date is presented in a companion paper (H0LiCOW Paper V). [ABSTRACT FROM AUTHOR]