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ABSTRACT Strong gravitational lensing is a powerful probe of the distribution of matter on sub-kpc scales. It can be used to test the existence of completely dark sub-haloes surrounding galaxies, as predicted by the standard cold dark matter model, or to test alternative dark matter models. The constraining power of the method depends strongly on photometric and astrometric precision and accuracy. We simulate and quantify the capabilities of upcoming adaptive optics systems and advanced instruments on ground-based telescopes, focusing as an illustration on the Keck Telescope (OSIRIS + KAPA, LIGER + KAPA) and the Thirty Meter Telescope (TMT; IRIS + NFIRAOS). We show that these new systems will achieve dramatic improvements over current ones in both photometric and astrometric precision. Narrow line flux ratio errors below 2 per cent, and submilliarcsecond astrometric precision will be attainable for typical quadruply imaged quasars. With TMT, the exposure times required will be of order a few minutes per system, enabling the follow-up of 100–1000 systems expected to be discovered by the Rubin, Euclid, and Roman Telescopes.