Fast computation of an optimal controller for large-scale adaptive optics.

Area of Science:

• Astronomy and Astrophysics
• Optical Engineering
• Control Systems Theory

Background:

• Adaptive optics (AO) systems use minimum-variance control, often implemented via Kalman filters, for astronomical observations.
• Calculating the Kalman filter gain involves solving Riccati equations, which become computationally prohibitive for large telescope apertures due to the curse of dimensionality.

Purpose of the Study:

• To develop an efficient method for computing the Kalman gain in AO systems, specifically addressing the computational challenges posed by large telescopes.
• To reduce the computational complexity associated with the standard Riccati equation solvers for adaptive optics applications.

Main Methods:

• Proposed an approximation for computing the Kalman gain by treating the turbulence phase screen as a cropped version of an infinite-size screen.
• Evaluated the computational advantages (off- and on-line) of the proposed method compared to standard solvers.
• Assessed the performance of the approximation for both classical AO and wide-field tomographic AO with multiple natural guide stars.

Main Results:

• Demonstrated significant improvements in computational time for calculating the Kalman gain.
• The approximation effectively mitigates the 'curse of dimensionality' for large telescope apertures.
• Validated the method's performance across different AO configurations through simulations.

Conclusions:

• The proposed approximation offers a computationally efficient solution for Kalman gain calculation in adaptive optics.
• This method enables the application of minimum-variance control to extremely large telescopes and advanced AO systems.
• The findings pave the way for faster and more scalable adaptive optics control.