A state observer for the Virgo inverted pendulum.

We report an application of Kalman filtering to the inverted pendulum (IP) of the Virgo gravitational wave interferometer. Using subspace method system identification techniques, we calculated a linear mechanical model of Virgo IP from experimental transfer functions. We then developed a Kalman filter, based on the obtained state space representation, that estimates from open loop time domain data, the state variables of the system. This allows the observation (and eventually control) of every resonance mode of the IP mechanical structure independently.

In-vacuum Faraday isolation remote tuning.

In-vacuum Faraday isolators (FIs) are used in gravitational wave interferometers to prevent the disturbance caused by light reflected back to the input port from the interferometer itself. The efficiency of the optical isolation is becoming more critical with the increase of laser input power. An in-vacuum FI, used in a gravitational wave experiment (Virgo), has a 20 mm clear aperture and is illuminated by an almost 20 W incoming beam, having a diameter of about 5 mm. When going in vacuum at 10(-6) mbar, a degradation of the isolation exceeding 10 dB was observed. A remotely controlled system using a motorized lambda=2 waveplate inserted between the first polarizer and the Faraday rotator has proven its capability to restore the optical isolation to a value close to the one set up in air.

In-vacuum optical isolation changes by heating in a Faraday isolator.

We describe a model evaluating changes in the optical isolation of a Faraday isolator when passing from air to vacuum in terms of different thermal effects in the crystal. The changes are particularly significant in the crystal thermal lensing (refraction index and thermal expansion) and in its Verdet constant and can be ascribed to the less efficient convection cooling of the magneto-optic crystal of the Faraday isolator. An isolation decrease by a factor of 10 is experimentally observed in a Faraday isolator that is used in a gravitational wave experiment (Virgo) with a 10 W input laser when going from air to vacuum. A finite element model simulation reproduces with a great accuracy the experimental data measured on Virgo and on a test bench. A first set of measurements of the thermal lensing has been used to characterize the losses of the crystal, which depend on the sample. The isolation factor measured on Virgo confirms the simulation model and the absorption losses of 0.0016 +/- 0.0002/cm for the TGG magneto-optic crystal used in the Faraday isolator.