Modal Identification of Mirror Vibrations at the VLT using Accelerometer Data

TL;DR

This work tackles vibration-induced image degradation in extremely large telescopes by building a physically grounded, gray-box model of mirror dynamics driven by wind. It decomposes mirror motion into low-order modal components (piston, tip, tilt) and identifies their parameters from accelerometer PSDs, using a von Karman wind spectrum to describe the wind forcing. The approach successfully reproduces the main spectral energy in the accelerometer data and demonstrates robustness across nighttime data segments, laying a foundation for model-based AO controllers such as LQG. Limitations stem from sparse accelerometer coverage, but the authors outline practical improvements (e.g., more sensors) and future work integrating WFS data and targeted excitations to validate and extend the model's applicability.

Abstract

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.

Figures (7)

• Figure 1: Optical configuration of the VLT (Nasmyth) with accelerometer positions. Four sensors on M1 (orange dots), one sensor on M2 (blue dot), two sensors on M3 (green dots).
• Figure 2: VLT accelerometer position data. M1 sensors (), M2 sensor (), M3 sensors ().
• Figure 3: Calculation of tip-tilt from sensor signals.
• Figure 4: PSD of M1 piston. Eigenfrequencies of the mirror are indicated by green dots ($\bullet$), other disturbances by orange diamonds ($\blacklozenge$).
• Figure 5: The spectra of the identified wind and mirror dynamical models replicate the accelerometer data.