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Ground control to major time-lag: on-sky results of data-driven predictive wavefront control at Keck Observatory

This paper presents on-sky results from Keck Observatory demonstrating that a new data-driven predictive wavefront control implementation using Empirical Orthogonal Functions (EOF) achieves a 20% improvement in wavefront residuals over a classic integrator, while maintaining comparable imaging performance and serving as a pathfinder for future extremely large telescopes.

Original authors: Jules Fowler, Rebeca Jensen-Clem, Sylvain Cetre, Maaike A. M. van Kooten, Maissa Salama, Antonin Bouchez, Avinash Surendran, Charlotte Guthery, Eduardo Marin, Mahawa Cisse, Max Service, Charlotte Z. B

Published 2026-06-23

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CC BY 4.0

Original authors: Jules Fowler, Rebeca Jensen-Clem, Sylvain Cetre, Maaike A. M. van Kooten, Maissa Salama, Antonin Bouchez, Avinash Surendran, Charlotte Guthery, Eduardo Marin, Mahawa Cisse, Max Service, Charlotte Z. Bond, Emiel Por, Nour Skaf, Will Gauvin

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The Big Problem: The "Wind-Driven Halo"

Imagine you are trying to take a perfect photo of a tiny, faint firefly (an exoplanet) sitting right next to a blindingly bright spotlight (a star). To do this, you need a camera that can block the spotlight's glare perfectly.

Astronomers use a system called Adaptive Optics (AO) to do this. Think of the AO system as a "smart mirror" that wiggles thousands of times per second to cancel out the blurring caused by Earth's atmosphere (the "turbulence").

However, there is a catch: Time.
The atmosphere is like a fast-moving river. By the time the smart mirror senses a ripple in the water, calculates how to fix it, and actually moves to fix it, the river has already moved on. The mirror is always reacting to where the water was, not where it is. This delay creates a specific kind of blur called a "wind-driven halo," which makes it hard to see the faint firefly next to the bright star.

The Solution: Predicting the Future

The paper describes a new way to fix this delay. Instead of just reacting to the past, the new system predicts the future.

Think of it like catching a ball.

The Old Way (Integral Controller): You watch the ball, wait until it hits your hand, and then try to move your hand to catch it. You are always a split-second late.
The New Way (Predictive Controller): You watch the ball's path, calculate where it will be in a split second, and move your hand there before the ball arrives.

The team at the Keck Observatory built a system that uses a mathematical tool called Empirical Orthogonal Functions (EOF). You can think of EOF as a "pattern recognizer." It looks at the history of how the atmosphere has been moving (like looking at the wake of a boat) and uses those patterns to guess exactly where the turbulence will be when the mirror finally moves.

What They Did

The researchers took this new "predictive" software and installed it directly into the computer brain (the Real-Time Controller) of the Keck-II telescope in Hawaii. They didn't just test it in a computer simulation; they tested it on the sky with real stars.

They ran two types of tests:

Lab Tests: They simulated wind and turbulence in a closed dome to see if the system worked.
Real Sky Tests: They pointed the telescope at bright stars and switched back and forth between the "Old Way" (reacting) and the "New Way" (predicting).

The Results: A Promising Step

The paper reports three main findings:

Smoother Sensor Readings: When they measured the "ripples" in the light using the telescope’s own internal sensor (the Shack-Hartmann wavefront sensor), the predictive system was 20% better at smoothing them out than the old system. It is important to note that this is a self-consistent internal metric: it proves the algorithm is doing exactly what it was designed to do (reducing the error signal the sensor sees). However, improving this internal sensor reading does not automatically guarantee that the final astronomical images are 20% sharper or clearer.
Robustness: They tried changing the settings (the "knobs" on the machine) to see if it was hard to tune. They found that even if the settings weren't perfect, the new system didn't get worse than the old system. It's a "safe" upgrade.
The Photos: When they took actual pictures of the stars, the difference was subtle. The "Strehl Ratio" (a score for how sharp the image is) was about the same for both systems (around 46–56%). The predictive system made the image slightly more stable, but the results for overall image quality and contrast were less clear-cut than the internal sensor data suggested.

Why This Matters (According to the Paper)

The authors explain that this is a "pathfinder."

For Keck: It demonstrates that predictive control can work on a real telescope, improving the internal consistency of the system.
For the Future: The next generation of telescopes (the "Extremely Large Telescopes") will be huge and segmented (made of many mirrors). These future telescopes will have even more complex timing issues. The Keck telescope is currently the only place where you can test this kind of predictive technology on a real, large, segmented mirror.

In short: The team successfully taught the Keck telescope to "look ahead" at the wind. The internal sensor data shows a 20% improvement in how well the system corrects for atmospheric errors, validating the algorithm's design. While the final images did not show a dramatic jump in sharpness, this successful test paves the way for future telescopes to potentially use similar predictive techniques to help find Earth-like planets.

Technical Summary: On-Sky Results of Data-Driven Predictive Wavefront Control at Keck Observatory

Problem Statement
Extreme adaptive optics (XAO) systems, essential for directly imaging exoplanets, are often limited by temporal errors. These errors arise when atmospheric turbulence evolves faster than the system's control loop latency (typically 1–5 ms). In standard integral control, corrections are applied as quickly as possible, but wind-driven turbulence can still cause wavefront errors to accumulate, leading to artifacts like the "wind-driven halo" in coronagraphic images. While predictive control has been theoretically discussed for three decades and briefly tested on other platforms (e.g., Subaru/SCExAO), there has been no facilitated, on-sky demonstration of such a system on an 8–10 meter class telescope that integrates directly into the real-time controller (RTC).

Methodology
The authors implemented a data-driven predictive controller using Empirical Orthogonal Functions (EOF) directly into the Keck-II RTC. The system utilizes a pseudo-open loop (POL) reconstruction of the wavefront, derived from wavefront sensor residuals and deformable mirror (DM) commands, to identify linear trends in atmospheric evolution.

Algorithm: The predictor calculates a correction based on a history vector ( $h$ ) of previous POL states (typically 3–10 frames) using a filter matrix ( $F$ ). The final correction is a weighted mix of a classic high-order integrator ( $C_i$ ) and the predictor ( $C_p$ ), governed by a mixing factor ( $m$ ) and a regularization parameter ( $\alpha$ ).
Hardware Integration: To accommodate the need for multiple historical frames in real-time, the Keck RTC was updated in 2024 to support the predictive business unit.
Testing Phases:
1. Bench Testing: The system was tested on the Keck-II AO bench using injected turbulence profiles (single wind layer and a seven-layer profile).
2. On-Sky Commissioning: Initial tests were conducted on targets BS 8088 and HD 189337 to verify loop closure and explore filter hyper-parameters ( $\alpha$ , mixing factor $m$ , history length $n$ , training data length $l$ ).
3. Parameter Optimization: A dedicated observing run on December 3, 2025, utilized three bright natural guide stars (BS 8936, BS 327, BS 1191) to scan hyper-parameters and compare the optimized predictor against a classic integrator.
Metrics: Performance was evaluated using Shack-Hartmann Wavefront Sensor (SHWFS) residuals (RMS wavefront error), NIRC2 imaging Strehl Ratios (SR) at 2190 nm (Brackett $\gamma$ ), coronagraph-free contrast, and principal component analysis (PCA) of PSF stability.

Key Contributions

First Facilitized On-Sky Demonstration: This work presents the first successful on-sky implementation of a data-driven EOF predictor integrated directly into the RTC of an 8–10 meter class telescope.
RTC Upgrade: The paper details the necessary updates to the Keck RTC to support the storage and processing of multiple wavefront sensor frames required for predictive algorithms.
Parameter Stability Analysis: The study provides empirical data on the robustness of the predictor, demonstrating that while hyper-parameter optimization yields gains, sub-optimal parameters do not significantly degrade performance below that of a classic integrator.

Results

Wavefront Residuals: On-sky engineering tests demonstrated a 20% performance improvement in wavefront residuals (measured by SHWFS) for the predictor compared to a classic integrator when using optimized parameters (mixing factor $m=0.4$ , history $n=10$ , training data $l=60,000$ frames, $\alpha=300$ ).
Strehl Ratio and Contrast: NIRC2 imaging through the Brackett $\gamma$ filter showed comparable performance between the integrator and the predictor, with Strehl Ratios around 46–56%. The difference in SR was less than 1.5%, which the authors note is likely negligible given other system noise sources and seeing variations. Coronagraph-free contrast curves also showed comparable results.
PSF Stability: Analysis of principal components revealed a modest improvement in image stability for the predictor, showing approximately 3% less power in the singular values (principal components) compared to the integrator, suggesting reduced noise and easier data reduction.
Robustness: The study found that mixing factors above 0.4 or $\alpha$ values below 300 led to instability. However, within a "reasonable regime," varying parameters did not result in performance notably worse than the integrator. A single filter matrix remained sufficient for up to ~20 minutes of on-sky turbulence.

Significance and Claims
The authors position this work as a critical "pathfinder" for predictive control methods destined for Extremely Large Telescopes (ELTs). They claim that:

Immediate Utility: The system improves current observing for the Keck community, particularly by mitigating temporal errors.
Future Relevance: As the Keck Observatory upgrades to the HAKA deformable mirror (increasing degrees of freedom by a factor of 7), fitting errors will decrease, making temporal errors the dominant error term. In this future context, the demonstrated 20% reduction in wavefront error is projected to yield a 2% improvement in Strehl Ratio for visible light instruments (e.g., ORKID).
Operational Viability: The results suggest that predictive control can be operated with "set and forget" parameters, as the system is robust against minor sub-optimizations, making it practical for routine use.
Unique Testbed: Keck remains a unique demonstrator for segmented telescope AO systems, providing essential data on the complexity of full telescope systems that simulations and lab benches cannot fully replicate.

The paper concludes modestly, acknowledging that current performance gains may be limited by model mismatch and non-common path aberrations, and that future work will focus on understanding system noise floors and extending these methods to slower control frequencies for fainter guide stars.