Adaptive optics (AO) is used in ground-based astronomical telescopes to improve the resolution by counteracting the effects of atmospheric turbulence. Most AO systems are based on a simple control law that neglects the temporal evolution of the distortions introduced by the atmosphere. This paper presents a datadriven control design approach that is able to exploit the spatiotemporal correlation in the wavefront, without assuming any form of decoupling. The approach consists of a dedicated subspace-identification algorithm to identify an atmospheric disturbance model from open-loop wavefront sensor data, followed by 2 -optimal control design. It is shown that in the case that the deformable mirror and wavefront sensor dynamics can be represented by a delay and a two taps impulse response, it is possible to derive an analytical expression for the 2 -optimal controller. Numerical simulations on AO test bench data demonstrate a performance improvement with respect to the common AO control approach.

A recently proposed data-driven H 2 -optimal control approach is demonstrated on a laboratory setup. Most adaptive optics (AO) systems are based on a control law that neglects the temporal evolution of the wavefront. The proposed control approach is able to exploit the spatiotemporal correlation in the wavefront without assuming any form of decoupling. By analyzing the dynamic behavior of the wavefront sensor (WFS), it is shown that if the wavefront correction device can be considered static, the transfer function from control input to WFS output reduces to a two-tap impulse response and an integer number of samples delay. Considering this model structure, a data-driven identification procedure is developed to estimate the relevant parameters from measurement data. The specific structure allows for an analytical expression of the optimal controller in terms of the system matrices of the minimum-phase spectral factor of the atmospheric disturbance model. The performance of the optimal controller is compared with that of the standard AO control law. An analysis of the dominant error sources shows that optimal control may reduce the temporal error.

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Even though the wavefront distortion introduced by atmospheric turbulence is a dynamic process, its temporal evolution is usually neglected in the adaptive optics (AO) control design. Most AO control systems consider only the spatial correlation in a separate wavefront reconstruction step. By accounting for the temporal evolution of the wavefront it should be possible to further reduce the residual phase error and enable the use of fainter guide stars. Designing a controller that takes full advantage of the spatio-temporal correlation in the wavefront requires a detailed model of the wavefront distortion. In this paper we present a dedicated subspace identification algorithm that is able to provide the required prior knowledge. On the basis of open-loop wavefront slope data it estimates a multi-variable state-space model of the wavefront disturbance. The model provides a full description of the spatio-temporal statistics in a form that is suitable for control. The algorithm is demonstrated on open-loop wavefront data.