(ed.). Gravitational waves (IOP, 2001)(422s).

106 The Earth-based large interferometer VirgoFigure 9.2. The interferometer with Fabry–Perot cavity and power recycling.and it is called the shot noise limit. The contrast C < 1 does not change thisresult. The large interferometer design has been optimized in order to enhance thesensitivity: inside the arm there is a resonant Fabry–Perot cavity; this is equivalentto increasing the interferometer armlength, by a coefficient proportional to thefinesse of the Fabry–Perot cavity. Moreover, as shown in equation (9.5), the SNRincreases with the square root of the power and, since the output is at the darkfringe, the unused light, reflected back from the interferometer, is re-injected witha technique called recycling. Figure 9.2 shows the basic scheme of most of theinterferometers under construction [3].The other fundamental noise of the interferometer is the so called ‘thermalnoise’ [11, 12]. The Virgo test masses are in thermal equilibrium with theenvironment. An average energy of kT, where k is the Boltzmann constantand T is the temperature, is associated with each degree of freedom, givingorigin, through the ‘fluctuation dissipation theorem’, to position fluctuations ofthe macroscopic coordinates. Using the equation of motion and the fluctuationdissipationtheorem, the displacement noise is estimated. There are two maindissipation mechanisms: the structural and the viscous damping. It is assumedthat mechanisms of viscous damping are pretty much reduced, and only thestructural one survives. Internal friction in materials is described by adding animaginary term to the elastic constant, and the equation of motion for a springbecomes:mẍ + K (1 + i)x = 0 (9.8)where x is the coordinate of interest, m is the mass associated with the oscillator,K is the elastic constant and takes care of the dissipation and is related to theusual Q of the oscillator.As most of the interferometers under construction, Virgo [6, 7] will be arecycled interferometer, with resonant Fabry–Perot cavity in each arm. Thearm length is 3 km, the recycling factor 40 and the finesse of the cavity 40;the light source is a 25 W Nd:YAG laser (λ = 1.06 µm). The Virgo Projectis under construction in Italy at Cascina, near Pisa, by CNRS (France) andINFN (Italy). The participating laboratories are: ESPCI-Paris, Nice, LAL-