Establish command–disturbance decorrelation in incremental telemetry

Demonstrate theoretically that the incremental deformable-mirror commands are uncorrelated with the incremental disturbance in the closed-loop adaptive-optics identification method, thereby establishing the validity and precision of the interaction-matrix parameter estimator.

Background

The paper estimates adaptive-optics interaction-matrix parameters from incremental measurements and commands recorded during closed-loop operation. For the method to be statistically reliable, the covariance of the incremental disturbance must be approximated adequately and the incremental command vector must not be correlated with the incremental disturbance vector.

The authors theoretically analyze the first requirement and justify approximating the disturbance covariance by twice the measurement-noise covariance. However, they explicitly state that the second requirement—establishing the absence of correlation between incremental commands and incremental disturbances—has not yet been clearly analyzed theoretically. This unresolved issue directly affects the claimed precision and reliability of the parameter estimates.