Astrometric precision and knowledge of the point spread function are key ingredients for a wide range of astrophysical studies including time-delay cosmography in which strongly lensed quasar systems are used to determine the Hubble constant and other cosmological parameters. Astrometric uncertainty on the positions of the multiply-imaged point sources contributes to the overall uncertainty in inferred distances and therefore the Hubble constant. Similarly, knowledge of the wings of the points spread function (PSF) is necessary to disentangle light from the background sources and the foreground deflector. We analyze adaptive optics (AO) images of the strong lens system J0659+1629 obtained with the W. M. Keck Observatory using the laser guide star AO system. We show that by using a reconstructed point spread function we can i) obtain astrometric precision of $< 1$ milliarcsecond (mas), which is more than sufficient for time-delay cosmography; and ii) subtract all point-like images resulting in residuals consistent with the noise level. The method we have developed is not limited to strong lensing, and is generally applicable to a wide range of scientific cases that have multiple point sources nearby.
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