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

30 Gravitational-wave detectorsThere are three main sources of noise in interferometers: thermal, shot andvibrational. To understand the way they are controlled, it is important to thinkin frequency space. Observations with ground-based detectors will be made in arange from perhaps 10 Hz up to 10 kHz, and initial detectors will have a muchsmaller observing bandwidth within this. Disturbances by noise that occur atfrequencies outside the observation band can simply be filtered out. The goal ofnoise control is to reduce disturbances in the observation band.• Thermal noise. Interferometers work at room temperature, and vibrations ofthe mirrors and of the suspending pendulum can mask gravitational waves.To control this noise, scientists take advantage of the fact that thermal noisehas its maximum amplitude at the frequency of the vibrational mode, andif the resonance of the mode is narrow (a high quality factor Q) then theamplitude at other frequencies is small. Therefore, pendulum suspensionsare designed with the pendulum frequency at about 1 Hz, well belowthe observing window, and mirror masses are designed to have principalvibration modes above 1 kHz, well above the optimum observing frequencyfor initial interferometers. These systems are constructed with high values ofQ (10 6 or more) to reduce the noise in the observing band. Even so, thermalnoise is typically a dominant noise below 100 or 200 Hz.• Shot noise. This is the principal limitation to sensitivity at higherfrequencies, above 200–300 Hz. It arises from the quantization of photons.When photons form interference fringes, they arrive at random timesand make random fluctuations in the light intensity that can look like agravitational wave signal; the more photons one uses, the smoother will bethe interference fringe. We can easily calculate this intrinsic noise. If N isthe number of photons emitted by the laser during our measurement, thenas a random process the fluctuation number δN is proportional to the squareroot of N. If we are using light with a wavelength λ (for example infraredlight with λ ∼ 1 µm) one can expect to measure lengths to an accuracy ofλδl shot ∼2π √ N .To measure a gravitational wave at a frequency f , one has to make at least 2 fmeasurements per second, so one can accumulate photons for a time 1/2 f .If P is the light power, one hasN =Phc 1λ ·2 f.It is easy to work out from this that, for δl shot to be equal to δl gw inequation (3.1), one needs light power of about 600 kW. No continuous lasercould provide this much light to an interferometer.The key to reaching such power levels inside the arms of a detector isa technique called power recycling (see Saulson 1994) first proposed by