Active optics (AO) provides the fast, local image-plane correction in the hybrid architecture. It is not intended to correct every long-term disturbance. Its job is to reduce a small residual after the slower thermal loop has brought the spectrograph close enough to the desired state.
The centroid error is:
\[\mathbf{e}_k = \begin{bmatrix} dX_k \\ dY_k \end{bmatrix}.\]A local actuator calibration relates commanded AO steps to image-plane motion:
\[\mathbf{e}_k \approx \mathbf{M}_{\mathrm{AO}}\mathbf{s}_k,\]where $\mathbf{s}k$ is the two-axis AO command and $\mathbf{M}{\mathrm{AO}}$ is measured experimentally. The ideal corrective command is:
\[\mathbf{s}_k^{\ast}=-\mathbf{M}_{\mathrm{AO}}^{-1}\mathbf{e}_k.\]In practice, commands are rounded, bounded per update and bounded again by total available travel.
The AO unit was characterised by applying controlled movements in the cardinal directions and measuring the resulting detector centroid displacement. Repeated movements and return-to-centre tests were used to assess:
The study demonstrated that AO is capable of fine image-plane correction, but the response must be calibrated empirically rather than assumed to be perfectly symmetric or perfectly linear.
A raw pixel error is not an AO command. The mapping depends on the optical path, orientation and actuator response. A direction error, sign error or unmodelled cross-axis term can push the image farther from the reference.
A basic quality check compares the predicted and observed residual after a move:
\[\mathbf{e}_{\mathrm{pred},k+1}= \mathbf{e}_k+\mathbf{M}_{\mathrm{AO}}\mathbf{s}_k.\]If the measured response differs substantially from the prediction, the controller should reduce its authority, flag the event and avoid blindly repeating the same correction.
The component study established the correct division of labour:
This avoids a common hybrid-control failure mode: allowing the fast actuator to become a long-term drift integrator. That may look effective initially but it eventually consumes available travel and leaves no margin for genuine fine correction.
The public report does not include the measured calibration matrix, step table, firmware or serial protocol, actuator travel range, reversal procedure, target coordinates or per-run thresholds. The public scientific conclusion is that fine correction must be empirical, bounded and monitored for cumulative range usage.