ETD

• position sensors
• Virgo

Gravitational wave detectors such as Advanced Virgo require extremely precise control of the position and orientation of their suspended optical components. The performance of the seismic isolation system, the Superattenuator, depends critically on the quality of the local position sensors used to stabilise the suspension stages at low frequency. At present, this task is performed by ironless Linear Variable Differential Transformers (LVDTs), which offer robustness and a large linear range. However, their ultimate sensitivity is limited. As next-generation gravitational wave observatories such as the Einstein Telescope evolve toward lower noise floors, alternative sensing technologies must be explored.

This thesis investigates the development, modelling and experimental characterisation of position sensors for gravitational wave interferometers. The work spans both traditional inductive sensors and emerging optical solutions.

The first part provides the theoretical and experimental context. After reviewing the foundations of General Relativity, the operating principles of interferometric detectors are presented. The optical configuration of Virgo is described in detail, including the Michelson interferometer with Fabry-Pérot arm cavities and the main noise sources limiting sensitivity. Particular attention is devoted to the Superattenuator, its hierarchical control architecture and the role of position sensors. This suspension concept is also the basis for the system foreseen for the Phase II-O5 upgrade and for the Einstein Telescope, within the framework of the CAOS project.

The second part focuses on ironless LVDTs. A complete electromagnetic model is developed, starting from a single-turn configuration and extending to realistic finite-size coils. The sensitivity, linearity range and noise contributions are quantified and the electrical sizing of primary and secondary coils is addressed. Two numerical tools were developed and used for the design of the new LVDTs for the Advanced Virgo Phase II-O5 upgrade: a simulation tool and a design/optimization tool, that explores feasible coil configurations under spatial and electrical constraints.

The third part explores optical alternatives to LVDTs. A fiber-optic Fabry-Pérot interferometer was designed, implemented and characterised in the laboratory. Cavity-length scanning, piezoelectric calibration, interferometer linearization and closed-loop operation were demonstrated. The locked cavity achieved a displacement sensitivity of $\approx 10^{-11}$ m/$\sqrt{\mathrm{Hz}}$ above a few hertz, already comparable to the requirements of Virgo’s local control. The long-term stability of the prototype was also investigated, identifying alignment drifts and parasitic cavities as the dominant limitations. Finally, a commercial sensor (Picomove by TeemPhotonics) was tested using the same external cavity, demonstrating correct operation, quadrature readout and direct phase reconstruction, with sensitivity and stability strongly dependent on alignment quality.

The results show that the developed LVDT design tools are directly applicable to current and future Virgo upgrades, while optical interferometric sensors represent promising candidates for the next-generation of suspension systems.