Control System Design for Retinal Imaging Adaptive Optics Systems Using Orthonormal Basis Functions

This paper presents a solution to control system design issues for membrane mirrors used in retinal imaging adaptive optics systems. Such systems allow for the early diagnosis of eye diseases through high resolution imaging of the retina. Optical defects in the eye, known as aberrations, distort the retinal images, hence reducing their resolution. A retinal imaging adaptive optics system makes use of a deformable mirror whose shape is adjusted in real time to cancel the aberration effects. Due to the unknown and time-varying nature of the aberrations in the eye, the main control problem addressed in this paper is the tracking of an unknown and time-varying shape for the membrane mirror. Since the desired shape of the mirror is unknown and time-varying, it is proposed in this paper to design a multivariable controller that is tuned online to converge to the controller needed to achieve regulation. This is done iteratively, by taking advantage of the Q-parameterization of stabilizing controllers, so that the controller will converge to the ideal controller. Most often, finite impulse response (FIR) filters are used to represent the Q-parameter. It is proposed in this paper to represent the Q-parameter using orthonormal infinite impulse response filter basis functions. Such basis functions yield faster convergence rates during parameter estimation, and a Q-parameter representation that is less sensitive to parameter variations from the desired parameters. This is particularly crucial for the proposed application, where small errors in a typical FIR representation for the Q-parameter can lead to significant performance degradation. Simulation results are presented to illustrate the performance of the proposed adaptive controller design approach.