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Ground-based high contrast exoplanet imaging requires state-of-the-art adaptive optics (AO) systems in order to detect extremely faint planets next to their brighter host stars. For such extreme AO systems (with high actuator count deformable mirrors over a small field of view), the lag time of the correction (which can impact our system by the amount the wavefront has changed by the time the system is able to apply the correction) which can be anywhere from 1-5 milliseconds, can cause wavefront errors on spatial scales that lead to speckles at small angular separations from the central star in the final science image. One avenue for correcting these aberrations is predictive control, wherein previous wavefront information is used to predict the future state of the wavefront in one-system-lag's time, and this predicted state is applied as a correction with a deformable mirror. Here, we consider two methods for predictive control: data-driven prediction using empirical orthogonal functions1 and the physically-motivated predictive Fourier control.2 The performance and robustness of these methods have not previously been compared side-by-side. In this paper, we compare these predictors by applying them as post-facto methods to simulated atmospheres and on-sky telemetry, to investigate the circumstances in which their performance differs, including testing them under different wind speeds, C2N profiles, and time lags. We also discuss future plans for testing both algorithms on the Santa Cruz Extreme AO Laboratory (SEAL) testbed.3 This work will inform the next generation of extremely large telescopes (including the European Extremely Large Telescope, as well as plans for the Giant Magellan Telescope and the Thirty Meter Telescope), which will depend on predictive control as a key technology to reach the contrasts necessary to directly image rocky planets in the habitable zones of the nearest low-mass stars.
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