Focal plane wavefront control with model-based reinforcement learning

I. Proof of concept on simulated static and dynamic non-common path aberrations

¹ European Southern Observatory (ESO), Karl-Schwarzschild-Str. 2, 85748 Garching, Germany
² STAR Institute, Université de Liège, Allée du Six Août 19C, 4000 Liège, Belgium

^★ Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 10 December 2025
Accepted: 31 March 2026

Abstract

Context. The direct imaging of potentially habitable exoplanets is one prime science case for high-contrast imaging (HCI) instruments on ground-based, extremely large telescopes. Most such exoplanets orbit close to their host stars, where their observation is limited by fast-moving atmospheric speckles and quasi-static noncommon path aberrations (NCPA).

Aims. Conventional NCPA correction methods often use mechanical mirror probes, which compromise performance during operation. This work presents machine-learning-based NCPA control methods that automatically detect and correct both dynamic and static NCPA errors by leveraging past telemetry data and sequential phase diversity.

Methods. We extend previous work in reinforcement learning (RL) for adaptive optics (AO) to focal plane wavefront control. A new model-based RL algorithm, Policy Optimization for Noncommon Path Aberrations (PO4NCPA), interprets the focal plane image as input data and, through sequential phase diversity, determines phase corrections that optimize both non-coronagraphic and post-coronagraphic point spread functions (PSFs) without prior system knowledge. Furthermore, we demonstrate the effectiveness of this approach by numerically simulating static NCPA errors on a ground-based telescope and an infrared imager affected by water vapor-induced seeing (dynamic NCPAs).

Results. Simulations show that PO4NCPA robustly compensates static and dynamic NCPAs. In static cases, it achieves near-optimal focal plane light suppression with a coronagraph and near-optimal Strehl without one. With dynamic NCPA, it matches the performance of the modal least-squares reconstruction combined with a 1-step delay integrator in these metrics, though with a higher wavefront root mean square error (RMSE), especially for high-order modes. The method remains effective for the Extremely Large Telescope (ELT) pupil, the vector vortex coronagraph, under photon and background noise.

Conclusions. PO4NCPA is model-free and can be directly applied to standard imaging as well as to any type of coronagraphy; its submillisecond inference times and performance also make it suitable for real-time low-order correction of atmospheric turbulence beyond HCI requirements.