Discrete-Time Model of an Adaptive Optics System

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 performance measure for 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. This paper derives the corresponding discrete-time model and the computation of the adaptive optics system residual variance based on that model. The predicted variance of a single mode of an adaptive optics system is shown, as expected, to be the same as that obtained via simulation. The discrete-time prediction is also shown to be superior to a continuous-time approximation of the adaptive optics system.