Discrete-time model for an adaptive optics system with input delay

Abstract

The standard adaptive optics (AO) 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 performance of AO 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 article derives the corresponding discrete-time model and the computation of the AO system residual variance based on that model. The predicted variance of a single mode of an AO system is shown to be the same as that obtained via simulation.

Keywords:

• adaptive optics
• feedback
• sampled-data

Notes

Notes

1. Because the loop delay is identical for all signals, the delay operator can be regarded as occurring anywhere in the loop. Here it is between the ZOH and the DM.

2. This article assumes that the integration is over the entire frame of the CCD camera (i.e. the time interval of integration is ). The model presented here can be suitably modified to handle integrations that are less than a frame.

3. The output of a curvature sensor can also be modelled by changing the geometry matrix H.

4. The lifting approach can be defined more generally. In particular, it can be applied to extended spaces, and H _∞-norms can be used in place of Euclidean norms.

5. They are exactly diagonal if the Karhunen–Loève basis is used.