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 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 \substack { +9.4 \ -8.3 } ~ { } km s ^ { -1 } Mpc ^ { -1 } for PG 1115 + 080 , H _ { 0 } = 70.1 \substack { +5.3 \ -4.5 } ~ { } km s ^ { -1 } Mpc ^ { -1 } for HE 0435 - 1223 , and H _ { 0 } = 77.0 \substack { +4.0 \ -4.6 } ~ { } km s ^ { -1 } Mpc ^ { -1 } for RXJ 1131 - 1231 .
The joint AO-only result for the three lenses is H _ { 0 } = 75.6 \substack { +3.2 \ -3.3 } ~ { } km s ^ { -1 } Mpc ^ { -1 } .
The joint result of the AO+ HST analysis for the three lenses is H _ { 0 } = 76.8 \substack { +2.6 \ -2.6 } ~ { } km s ^ { -1 } Mpc ^ { -1 } .
All of the above results assume a flat \Lambda cold dark matter cosmology with a uniform prior on \Omega _ { \textrm { m } } in [ 0.05 , 0.5 ] and H _ { 0 } in [ 0 , 150 ] 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 .