  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.
