Adaptive optics (AO) have been used to correct wavefronts to achieve diffraction limited point spread functions in a broad range of optical applications, prominently ground-based astronomical telescopes operating in near infra-red. While most AO systems cannot provide diffraction-limited performance in the optical passband (400 nm - 900 nm), AO can improve image concentration, as well as both near and far field image stability, within an AO-fed spectrograph. Enhanced near and far field stability increase wavelength-scale stability in high dispersion spectrographs. In this work, we describe detailed modelling of the stability improvements achievable on extremely large telescopes. These improvements in performance may enable the mass measurement of Earth Twins by the precision radial velocity method, and the discovery of evidence of exobiotic activity in exoplanet atmospheres with the next generation of extremely large telescopes (ELTs). In this paper, we report on numerical simulations of the impact of AO on the performance of the GMT-Consortium Large Earth Finder (G-CLEF) instrument for the future Giant Magellan Telescope (GMT). The proximate cause of this study is to evaluate what improvements AO offer for exoplanet mass determination by the precision radial velocity (PRV) method and the discovery of biomarkers in exoplanet atmospheres. A modified AO system capable of achieving this improved stability even with changing conditions is proposed.
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