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Virgo interferometer
The Virgo interferometer is a large interferometer designed to detect gravitational waves predicted by the general theory of relativity. Virgo is a Michelson interferometer that is isolated from external disturbances: its mirrors and instrumentation are suspended and its laser beam operates in a vacuum. The instrument's two arms are three kilometres long and located in Santo Stefano a Macerata, near the city of Pisa, Italy.

Virgo is part of a scientific collaboration of laboratories from six countries: Italy and France, the Netherlands, Poland, Hungary and Spain. Other interferometers similar to Virgo have the same goal of detecting gravitational waves, including the two LIGO interferometers in the United States (at the Hanford Site and in Livingston, Louisiana). Since 2007, Virgo and LIGO have agreed to share and jointly analyze the data recorded by their detectors and to jointly publish their results.[1] Because the interferometric detectors are not directional (they survey the whole sky) and they are looking for signals which are weak, infrequent, one-time events, simultaneous detection of a gravitational wave in multiple instruments is necessary to confirm the signal validity and to deduce the angular direction of its source.

The interferometer is named for the Virgo Cluster of about 1,500 galaxies in the Virgo constellation, about 50 million light-years from Earth. As no terrestrial source of gravitational wave is powerful enough to produce a detectable signal, Virgo must observe the Universe. The more sensitive the detector, the further it can see gravitational waves, which then increases the number of potential sources. This is relevant as the violent phenomena Virgo is potentially sensitive to (coalescence of a compact binary system, neutron stars or black holes; supernova explosion; etc.) are rare: the more galaxies Virgo is surveying, the larger the probability of a detection.

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The detector
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Thermal Compensation System (TCS)
Thanks to Fabry-Perot (FP) optical cavities, the power circulating inside the Interferometer is by a factor around 300 with respect to simple Michelson configuration. On the other hand, the core optics coating absorptions, though optimized to be just of the order of parts per million, result in a radial temperature gradient within the mirrors [1] causing thermal effects. The two main ones are:


 * thermo-refractive substrate lenses in the recycling cavities, due to the refractive index dependence on the temperature;


 * thermo-elastic surface deformation in the Fabry–Perot mirrors, due to a non-zero material’s thermal expansion coefficient.

Both these mechanisms induce optical aberrations, that can decrease the circulating power inside the cavity or can generate higher order modes which if become resonant inside the cavity, spoil the control signals.

The optical aberrations are induced also by the cold defects coming from the residual imperfections due to the state of the art of the mirror production procedure.

The Thermal Compensation System (TCS) [2] is designed to contrast the aberrations coming both from cold defects and thermally driven effects. The strategy is to induce in the optics a complementary distortion, with respect to the one given by the aberrations, restoring the nominal optical configuration of the interferometer.

The Advanced Virgo TCS features both new high-performance sensors and actuators, making it a dynamical adaptive optical system.

Sensors.

Wavefront aberrations on each core optics are sensed by the Hartmann Wavefront Sensors (HWSs). They probe the optics through an auxiliary beam, usually a SLED (Super Luminescent Light Emitting Diode), which accumulates wavefront distortions after being transmitted through or reflected from the deformed optics of FP cavities. In particular, two HWS in transmission measure the thermal lens on the two input mirrors crossed by the laser beam, while four wavefront sensing setups, identified as HWS in reflection, have been designed to measure the thermoelastic deformation on the input and end mirrors.

The wavefront aberration local sensing provided by HWSs is complementary to the global one measured by the phase camera encoding the amplitude and phase of the main beam circulating into the detector [3]. This sensor scans over a photodiode the beam resulting from the recombination of the pick off of the main laser beam with the one picked up at the strategical ports of the detector. The heterodyne technique is used to independently assess the information in the carrier, upper and lower sidebands at different frequencies.

Actuators.

Two different actuators are designed to cope with thermal effects and cold defects. The CO2 lasers correct both cold and thermal lenses and the ring heaters (RHs) to decrease the radii of curvature of the mirrors.

The formers project the suitably shaped heating pattern on an additional transmissive fused silica plate[1], the so-called Compensation Plate (CP), installed between the beam splitter and the input mirrors. The projecting optical systems have been designed to produce two different actuation patterns on the CPs:


 * The Double Axicon System (DAS) is obtained by superimposing two annular beams with different sizes and radii in order to shape a donut. The name of this actuator derives from axicon, an optic with a conical surface, used to convert the CO2 Gaussian beam into an annular one. The DAS is used mainly to correct the thermal lensing due to uniform coating absorption in the input mirrors and the cold defects showing a high degree of spherical aberration.


 * The Central Heating (CH) having a Gaussian shape of the same size of the main laser beam, is used to mitigate the thermal transients when the interferometer loses lock.

RHs are thermal actuators conceived to precisely tune the radius of curvature (RoC) of the mirror’s surface, aberrated by the main laser beam that induces a bump on the mirror high-reflectivity surfaces making their profiles non-spherical. Advanced Virgo RHs, consisting of two parallel, thin o-rings made of borosilicate glass (Pyrex), surround each FP mirrors. Each ring is powered by Joule heating through a Nickel-Crome conductive wire tightly wrapped in helical coils around it, then acting as a radiator. To increase the efficiency of the system, the heat that radiates away is gathered and conveyed toward the mirror barrel by a c-shaped and internally polished copper shield enclosing the rings.

This complex system of thermal actuators and sensors composing the TCS is fundamental to guarantee the operation at high power of the GW detector. During O3, the thermal lensing induced by the main laser beam was compensated by the DAS shined the CPs, stabilizing the power recycling cavity and increasing the robustness of the detector. Furthermore, the CH actuator has been switched on during the lock acquisition sequence to mimic the main laser and to avoid thermal transients which slowed down the whole procedure. Finally, the end mirror’s RH have been used to tune the mirror’s radius of curvature in order to maximize the intra-cavity power and minimize the power at the anti-symmetric port. As result, the FP circulating power increased of about 15% and the power exiting the interferometer decreased by factor 2 [4].

In Figure, a scheme of the TCS sensors and actuators integrated in Advanced.

[1] Reitze, D.; Saulson, P.R.; Grote, H. Advanced Interferometric Gravitational-Wave Detectors; World Scientific Publishing Co.: Singapore, 2019; Volume 2.

[2] Lawrence, R.C. Active Wavefront Correction in Laser Interferometric Gravitational Wave Detectors. Ph.D. Thesis, MIT, Cambridge, MA, USA, 2003.

[3] Goda, K.; Ottaway, D.; Connelly, B.; Adhikari, R.; Mavalvala, N.; Gretarsson, A. Frequency-resolving spatiotemporal wave-front sensor. Opt. Lett. 2004, 29, 1452. [CrossRef] [PubMed]

[4] Nardecchia I., Detecting Gravitational Waves with Advanced Virgo, Galaxies 2022, 10, 28. https://doi.org/10.3390/galaxies10010028

[1] The CO2 laser’s wavelength (l = 10.6 μm) is completely absorbed by the fused silica, maximising their compensation effect.