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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]

Accurate and precise measurements of the Hubble constant are critical for testing our current standard cosmological model and revealing possibly new physics. With Hubble Space Telescope (HST) imaging, each strong gravitational lens system with measured time delays can allow one to determine the Hubble constant with an uncertainty of ∼7 per cent. Since HST will not last forever, we explore adaptive-optics (AO) imaging as an alternative that can provide higher angular resolution than HST imaging but has a less stable point spread function (PSF) due to atmospheric distortion. To make AO imaging useful for time-delay-lens cosmography, we develop a method to extract the unknown PSF directly from the imaging of strongly lensed quasars. In a blind test with two mock data sets created with different PSFs, we are able to recover the important cosmological parameters (time-delay distance, external shear, lens-mass profile slope, and total Einstein radius). Our analysis of the Keck AO image of the strong lens system RXJ 1131−1231 shows that the important parameters for cosmography agree with those based on HST imaging and modelling within 1σ uncertainties. Most importantly, the constraint on the model time-delay distance by using AO imaging with 0.09 arcsec resolution is tighter by ∼50 per cent than the constraint of time-delay distance by using HST imaging with 0.09 arcsec when a power-law mass distribution for the lens system is adopted. Our PSF reconstruction technique is generic and applicable to data sets that have multiple nearby point sources, enabling scientific studies that require high-precision models of the PSF. [ABSTRACT FROM AUTHOR]