Modal Identification of Mirror Vibrations at the VLT using Accelerometer Data

Recent advances in ground-based astronomy have made it possible to create optical telescopes with primary mirrors up to 40 m in size. With growing mirror diameter, the suppression of non-atmospheric disturbances becomes increasingly important. Precise knowledge of the movement of telescope mirrors is essential for understanding and compensating for vibration-based perturbations. A model from VLT accelerometer data for each individual mirror is developed, while the influence of wind buffeting is accounted for by a von Karman wind model. To describe the relevant rigid body motion, we consider the piston, tip and tilt modes of the mirrors. The identification is validated by comparing the power spectral density of the measured and identified modes. Additionally, we assess the robustness of the approach by calculating the identification error over different sections of the data. The study indicates that the employed methods are adequate for the identification of modal telescope vibrations. It is anticipated that said findings will serve as a significant foundation for the development of advanced model-based AO controllers for large telescopes, such as linear quadratic Gaussian control.