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Register a new userAdaptive Optics Predictive Control with Empirical Orthogonal Functions (EOFs)
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Authors
Olivier Guyon
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Atmospheric wavefront prediction based on previous wavefront sensor measurements can greatly enhance the performance of adaptive optics systems. We propose an optimal linear approach based on the Empirical Orthogonal Functions (EOF) framework commonly employed for atmospheric predictions. The approach offers increased robustness and significant performance advantages over previously proposed wavefront prediction algorithms. It can be implemented as a linear pattern matching algorithm, which decomposes in real time the input (most recent wavefront sensor measurements) into a linear sum of previously encountered patterns, and uses the coefficients of this linear expansion to predict the future state. The process is robust against evolving conditions, unknown spatio-temporal correlations and non-periodic transient events, and enables multiple sensors (for example accelerometers) to contribute to the wavefront estimation. We illustrate the EOFs advantages through numerical simulations, and demonstrate filter convergence within 1 minute on a 1 kHz rate system. We show that the EOFs approach provides significant gains in high contrast imaging by simultaneously reducing residual speckle halo and producing a residual speckle halo that is spatially and temporally uncorrelated.
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Predictive wavefront control is an important and rapidly developing field of adaptive optics (AO). Through the prediction of future wavefront effects, the inherent AO system servo-lag caused by the measurement, computation, and application of the wavefront correction can be significantly mitigated. This lag can impact the final delivered science image, including reduced strehl and contrast, and inhibits our ability to reliably use faint guidestars. We summarize here a novel method for training deep neural networks for predictive control based on an adversarial prior. Unlike previous methods in the literature, which have shown results based on previously generated data or for open-loop systems, we demonstrate our networks performance simulated in closed loop. Our models are able to both reduce effects induced by servo-lag and push the faint end of reliable control with natural guidestars, improving K-band Strehl performance compared to classical methods by over 55% for 16th magnitude guide stars on an 8-meter telescope. We further show that LSTM based approaches may be better suited in high-contrast scenarios where servo-lag error is most pronounced, while traditional feed forward models are better suited for high noise scenarios. Finally, we discuss future strategies for implementing our system in real-time and on astronomical telescope systems.
The search for exoplanets is pushing adaptive optics systems on ground-based telescopes to their limits. One of the major limitations at small angular separations, exactly where exoplanets are predicted to be, is the servo-lag of the adaptive optics systems. The servo-lag error can be reduced with predictive control where the control is based on the future state of the atmospheric disturbance. We propose to use a linear data-driven integral predictive controller based on subspace methods that is updated in real time. The new controller only uses the measured wavefront errors and the changes in the deformable mirror commands, which allows for closed-loop operation without requiring pseudo-open loop reconstruction. This enables operation with non-linear wavefront sensors such as the pyramid wavefront sensor. We show that the proposed controller performs near-optimal control in simulations for both stationary and non-stationary disturbances and that we are able to gain several orders of magnitude in raw contrast. The algorithm has been demonstrated in the lab with MagAO-X, where we gain more than two orders of magnitude in contrast.
The behavior of an adaptive optics (AO) system for ground-based high contrast imaging (HCI) dictates the achievable contrast of the instrument. In conditions where the coherence time of the atmosphere is short compared to the speed of the AO system, the servo-lag error becomes the dominate error term of the AO system. While the AO system measures the wavefront error and subsequently applies a correction (taking a total of 1 to 2 milli-seconds), the atmospheric turbulence above the telescope has changed. In addition to reducing the Strehl ratio, the servo-lag error causes a build-up of speckles along the direction of the dominant wind vector in the coronagraphic image, severely limiting the contrast at small angular separations. One strategy to mitigate this problem is to predict the evolution of the turbulence over the delay. Our predictive wavefront control algorithm minimizes the delay in a mean square sense and has been implemented on the Keck II AO bench. In this paper we report on the latest results of our algorithm and discuss updates to the algorithm itself. We explore how to tune various filter parameters on the basis of both daytime laboratory tests and on-sky tests. We show a reduction in residual-mean-square wavefront error for the predictor compare to the leaky integrator implemented on Keck. Finally, we present contrast improvements for both day time and on-sky tests. Using the L-band vortex coronagraph for Kecks NIRC2 instrument, we find a contrast gain of 2.03 at separation of 3~$lambda/D$ and up to 3 for larger separations (4-6~$lambda/D$).
An explanation for the origin of asymmetry along the preferential axis of the PSF of an AO system is developed. When phase errors from high altitude turbulence scintillate due to Fresnel propagation, wavefront amplitude errors may be spatially offset from residual phase errors. These correlated errors appear as asymmetry in the image plane under the Fraunhofer condition. In an analytic model with an open-loop AO system, the strength of the asymmetry is calculated for a single mode of phase aberration, which generalizes to two dimensions under a Fourier decomposition of the complex illumination. Other parameters included are the spatial offset of the AO correction, which is the wind velocity in the frozen flow regime multiplied by the effective AO time delay, and propagation distance or altitude of the turbulent layer. In this model, the asymmetry is strongest when the wind is slow and nearest to the coronagraphic mask when the turbulent layer is far away, such as when the telescope is pointing low towards the horizon. A great emphasis is made about the fact that the brighter asymmetric lobe of the PSF points in the opposite direction as the wind, which is consistent analytically with the clarification that the image plane electric field distribution is actually the inverse Fourier transform of the aperture plane. Validation of this understanding is made with observations taken from the Gemini Planet Imager, as well as being reproducible in end-to-end AO simulations.
Current and future high-contrast imaging instruments require extreme adaptive optics (XAO) systems to reach contrasts necessary to directly image exoplanets. Telescope vibrations and the temporal error induced by the latency of the control loop limit the performance of these systems. One way to reduce these effects is to use predictive control. We describe how model-free Reinforcement Learning can be used to optimize a Recurrent Neural Network controller for closed-loop predictive control. First, we verify our proposed approach for tip-tilt control in simulations and a lab setup. The results show that this algorithm can effectively learn to mitigate vibrations and reduce the residuals for power-law input turbulence as compared to an optimal gain integrator. We also show that the controller can learn to minimize random vibrations without requiring online updating of the control law. Next, we show in simulations that our algorithm can also be applied to the control of a high-order deformable mirror. We demonstrate that our controller can provide two orders of magnitude improvement in contrast at small separations under stationary turbulence. Furthermore, we show more than an order of magnitude improvement in contrast for different wind velocities and directions without requiring online updating of the control law.
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