Upgrading SPHERE with the second stage AO system SAXO+: frequency-based data-driven controller for adaptive optics

TL;DR

This work tackles improving direct-imaging performance with a two-stage AO system (SAXO+) by introducing a PSD-based data-driven controller that designs an Infinite Impulse Response ($K(z)$) filter through convex optimization to minimize disturbance-induced residuals while respecting stroke and robustness constraints. By formulating a mixed $\mathcal{H}_2$/$\mathcal{H}_\infty$ objective and solving LMIs, the approach yields a robust, frequency-domain controller applicable to both Standalone and disentangled CAO (dCAO) configurations. Through COMPASS simulations of five science cases and a vibration scenario, the data-driven controller consistently improves contrast and Strehl, especially under fast wind, and demonstrates the ability to notch dominant vibration frequencies for a flatter residual spectrum. The findings highlight the practical potential of PSD-based data-driven AO control for SPHERE/SAXO+ and lay the groundwork for future non-stationary-atmosphere testing and on-sky validation.

Abstract

This study introduces a novel frequency-based data-driven controller for adaptive optics, using power spectral density for optimization while ensuring stability criteria. It addresses disturbance rejection, command amplitude constraints and system transfer functions through convex optimization to obtain an optimal control in an infinite input response filter form. Evaluated within the SAXO+ project, it demonstrates efficacy under diverse atmospheric conditions and operational scenarios. The proposed controller is tested in both standard and disentangled adaptive optics schemes, showcasing its adaptability and performance. Experimental validation is conducted using the COMPASS simulation tool, affirming the controller's promise for enhancing adaptive optics systems in real-world applications.

Figures (12)

• Figure 1: Block diagram of an AO system with modal control. With $\vec{\phi}$ the incoming wavefront, $\vec{e}$ the residual wavefront, $\vec{n}$ the noise, $\vec{s}$ the slopes, $\vec{m}$ the modal measurements, $\vec{u}$ the modal commands, $\vec{v}$ the voltages, S2M and M2V the modal projection matrices.
• Figure 2: Standalone cascaded system block diagram.
• Figure 3: dCAO system block diagram, the matrix $\mathbf{P}$ denotes the projection matrix used to project the first stage commands to the second stage command space.
• Figure 4: Tilt vibration power spectral density after filtering out the atmospheric disturbance.
• Figure 5: Tilt vibration power spectral density obtained by filtering the model with white noise.