Design of a linear quadratic Gaussian controller for an adaptive optics system

The authors consider the control of a phase-correcting ground-based adaptive optical telescope. They present the design of a linear quadratic Gaussian controller for generating actuator voltages to a deformable mirror, given a set of slope measurements from a wavefront sensor. A truth model is developed based on theoretical developments and actual test data. The resulting state-space model has as its states the Zernike coefficients associated with the atmospheric turbulence and the deformable mirror. The reflected image can be described by combining the Zernike coefficients. As a result of the approach taken, modal control is accomplished as opposed to zonal control since the coupling of actuator influence functions is taken into account in developing the design models. The results of covariance and Monte Carlo analysis demonstrate the limits on performance imposed by the Kalman filter. Computer simulations predict that the controller presented can reduce phase distortion to an r.m.s. value of approximately 0.1 wavelengths