Linear-quadratic-Gaussian control for adaptive optics systems using a hybrid model.

This paper presents a linear-quadratic-Gaussian (LQG) design based on the equivalent discrete-time model of an adaptive optics (AO) system. The design model incorporates deformable mirror dynamics, an asynchronous wavefront sensor and zero-order hold operation, and a continuous-time model of the incident wavefront. Using the structure of the discrete-time model, the dimensions of the Riccati equations to be solved are reduced. The LQG controller is shown to improve AO system performance under several conditions.

Discrete-time model of an adaptive optics systems.

The standard adaptive optics system can be viewed as a sampled-data feedback system with a continuous-time disturbance (the incident wavefront from the observed object) and discrete-time measurement noise. A common measure of the performance of adaptive optics systems is the time average of the pupil variance of the residual wavefront. This performance can be related to that of a discrete-time system obtained by lifting the incident and residual wavefronts. The corresponding discrete-time model is derived, and the computation of the adaptive optics system residual variance is based on that model. The predicted variance of a single mode of an adaptive optics system is shown to be the same as that obtained via simulation (as expected). The discrete-time prediction is also shown to be superior to a continuous-time approximation of the adaptive optics system.

Minimum variance control structure for adaptive optics systems.

The adaptive optics minimum variance control problem is formulated as a linear-quadratic-Gaussian optimization. The formulation incorporates the wavefront sensor frame integration in discrete-time models of the deformable mirror and incident wavefront. It shows that, under nearly ideal conditions, the resulting minimum variance controller approaches the integral controller commonly used in adaptive optics systems. The inputs to the controller dynamics are obtained from a reconstructor with the maximum a posteriori structure that uses the estimation error covariance of the wavefront error. The ideal conditions assumed to obtain the integral controller are as follows; isotropic first-order (but nonstationary) temporal atmospheric aberrations, no computational loop delay, and no deformable mirror dynamics. The effects of variations in these conditions are examined.

Fast calibration of high-order adaptive optics systems.

We present a new method of calibrating adaptive optics systems that greatly reduces the required calibration time or, equivalently, improves the signal-to-noise ratio. The method uses an optimized actuation scheme with Hadamard patterns and does not scale with the number of actuators for a given noise level in the wavefront sensor channels. It is therefore highly desirable for high-order systems and/or adaptive secondary systems on a telescope without a Gregorian focal plane. In the latter case, the measurement noise is increased by the effects of the turbulent atmosphere when one is calibrating on a natural guide star.