The Advanced LIGO gravitational wave detectors are secondgeneration instruments designed and built for the two LIGO observatories in Hanford WA and Livingston LA USA. The two instruments are identical in design and are specialized versions of a Michelson interferometer with 4 km long arms. As in Initial LIGO FabryPerot cavities are used in the arms to increase the interaction time with a gravitational wave and power recycling is used to increase the effective laser power. Signal recycling has been added in Advanced LIGO to improve the frequency response. In the most sensitive frequency region around 100 Hz the design strain sensitivity is a factor of 10 better than Initial LIGO. In addition the low frequency end of the sensitivity band is moved from 40 Hz down to 10 Hz. All interferometer components have been replaced with improved technologies to achieve this sensitivity gain. Much better seismic isolation and test mass suspensions are responsible for the gains at lower frequencies. Higher laser power larger test masses and improved mirror coatings lead to the improved sensitivity at mid and high frequencies. Data collecting runs with these new instruments are planned to begin in mid2015.
['General Relativity and Quantum Cosmology', 'Astrophysics - Instrumentation and Methods for Astrophysics', 'Physics - Instrumentation and Detectors']
Advanced LIGO
{'LIGO Scientific Collaboration (August 2014 LSC author list)': 'Email: pf@ligo.mit.edu', 'Abstract': 'The  Advanced  LIGO  gravitational  wave  detectors  are  second  generation instruments designed and built for the two LIGO observatories in Hanford, WA and Livingston, LA. The two instruments are identical in design, and are specialized versions of a Michelson interferometer with 4 km long arms. As in  initial  LIGO,  Fabry-Perot  cavities  are  used  in  the  arms  to  increase  the interaction  time  with  a  gravitational  wave,  and  power  recycling  is  used  to increase  the  effective  laser  power.  Signal  recycling  has  been  added  in Advanced LIGO to improve the frequency response.  In  the  most  sensitive frequency region around 100 Hz, the design strain sensitivity is a factor of 10 better than initial LIGO. In addition, the low frequency end of the sensitivity band is moved from 40 Hz down to 10 Hz. All interferometer components have  been  replaced  with  improved  technologies  to  achieve  this  sensitivity gain. Much better seismic isolation and test mass suspensions are responsible for the gains at lower frequencies. Higher laser power, larger test masses and improved mirror coatings lead to the improved sensitivity at mid- and highfrequencies. Data collecting runs with these new instruments are planned to begin in mid-2015.  \nPACS numbers: 01.52.+r, 04.80.Nn, 07.60.Ly, 95.55.Ym', '1. Introduction': 'From  its  inception,  the  LIGO  project  was  planned  to  involve  the  development  and operation of multiple generations of increasingly sensitive gravitational wave detectors. The Advanced LIGO detectors are the second generation of interferometers designed and built for the two observatories operated by the LIGO Laboratory: one on the Hanford site in  Washington  state,  and  the  other  in  Livingston  Parish,  Louisiana.  The  Initial  LIGO detectors,  constructed  in  the  late  1990s,    operated  at  design  sensitivity  in  a  continuous data-taking mode from November 2005 to September 2007 [1]. Subsequently, upgrades were made to the interferometer laser sources and readout systems [2], which improved the  strain  sensitivity  at  the  most  sensitive  frequencies  by  approximately  30%;  the instrument  root-mean-square  (rms)  strain  noise  reached  an  unprecedented  level  of 2 × 10 ! !! in  a  100  Hz band. In this configuration, Enhanced LIGO collected data from July 2009 to October 2010. Although no gravitational wave signals were detected with Initial  or  Enhanced  LIGO,  they  produced  several  interesting  astrophysical  results; representative examples are listed in reference [3].  \nCompared to Initial LIGO, Advanced LIGO is designed to provide a factor of 10 increase in strain sensitivity over a broad frequency band, and to extend the low end of the band to 10 Hz (from 40 Hz). As the probed volume of the universe scales as the cube of  the  strain  sensitivity,  this  represents  an  enormous  increase  (of  order  10 3 x)  in  the number  of  potential  astrophysical  sources  detectable  by  these  instruments.  At  design sensitivity,  Advanced  LIGO  is  likely  to  detect  dozens  of  compact  binary  coalescence sources per year [4].  \nHoused within the vacuum system and facilities built for Initial LIGO, Advanced LIGO  completely  replaces  the  interferometer  components  with  new  designs  and technology. Each observatory hosts one Advanced LIGO interferometer with 4km long arms.  A  third  interferometer  (originally  planned  as  a  second  detector  at  Hanford)  is consigned for a planned later installation at a new, currently undetermined site in India. All three interferometers are intended to be identical in design and expected performance. The addition of the third site (India) will provide significantly better source localization for the Advanced LIGO network [5].  \nUS  National  Science  Foundation  funding  for  the  construction  and  installation  of Advanced LIGO began in April 2008. Installation of the new hardware began in early 2011, and was completed for the Livingston detector (L1) in mid-2014; installation of the Hanford detector (H1) will be completed by the end of 2014.', '2. Interferometer configuration and system design': 'The optical configuration of the Advanced LIGO interferometer is shown in figure 1. The basis of the design is a Michelson interferometer with a Fabry-Perot resonant cavity in each arm to build up the phase shift produced by an arm length change. Power recycling is  another  standard  feature  of  such  interferometers:  the  power  recycling  mirror  (PRM) forms  a  resonant  cavity  between  the  laser  source  and  the  Michelson  to  increase  the effective laser power.  \nWith Advanced LIGO, signal recycling [6]  has  been  added  to  the  interferometer. The signal recycling mirror (SRM) at the anti-symmetric output of the Michelson is used to  effectively  lower  the  arm  cavity  finesse  for  gravitational  wave  signals  and  thereby maintain  a  broad  detector  frequency  response.  The  choice  of  SRM  transmission  and tuning is discussed in the section on sensitivity (3). In principle, signal recycling can also be used to create a narrowband mode of operation, with enhanced sensitivity at, e.g., a likely pulsar frequency, though with higher noise at other frequencies. Though there are no current plans for narrowband operation, this option may be taken in the future.  \nFigure 1. Advanced LIGO optical configuration. ITM: input test mass; ETM: end test mass; ERM: end reaction mass; CP: compensation plate; PRM: power recycling mirror; PR2/PR3: power recycling mirror 2/3; BS: 50/50 beam splitter; SRM: signal recycling mirror; SR2/SR3: signal recycling mirror 2/3; FI: Faraday isolator; φ m: phase modulator; PD: photodetector. The laser power numbers correspond to full-power operation. All of the components shown, except the laser and phase modulator, are mounted in the LIGO ultra-high vacuum system on seismically isolated platforms.  \n<!-- image -->  \nThe  top-level  parameters  of  the  interferometers  are  listed  in  Table  1.  The motivations behind these and other system design choices are described in this section. The various interferometer subsystems and components are described in section 4.  \nTable 1. Main parameters of the Advanced LIGO interferometers. PRC: power recycling cavity; SRC: signal recycling cavity.', '2.1 Arm cavity design': 'With  signal  recycling,  the  quantum  noise-limited  strain  sensitivity  is  in  principle independent of the arm cavity finesse, and depends only on the power stored in the arms; thus the choice of finesse is guided by other practical considerations. Higher arm cavity finesse  carries  the  benefits  of  lower  laser  power  in  the  power  recycling  cavity  and reduced coupling from the vertex Michelson degree-of-freedom. Lower finesse reduces the  sensitivity  to  optical  loss  and  noise  in  the  signal  recycling  cavity.  The  arm  cavity finesse of 450 represents a trade-off between these effects.  \nIn order to reduce test mass thermal noise, the beam size on the test masses is made as large as practical so that it averages over more of the mirror surface. The dominant noise mechanism here is mechanical loss in the dielectric mirror coatings, for which the displacement thermal noise scales inversely with beam size. This thermal noise reduction is  balanced  against  increased  aperture  loss  and  decreased  mode  stability  with  larger beams. The slightly asymmetric design of the arm cavity takes advantage of the fact that the ITMs contribute less to thermal noise because their coatings are half as thick as on the ETMs.  Therefore  the  beam  can  be  somewhat  smaller  on  the  ITMsÑwith  negligible increase  in  thermal  noiseÑin  order  to  limit  aperture  losses  in  the  beam  splitter  and recycling  cavities;  the  ETM  beam  size  is  maximized  to  reduce  this  thermal  noise contribution. The resonator g parameter product for the arm cavity is g 1 g 2 = 0.83, which is  approaching the stability limit of g 1 g 2 ! 1.  Lower  thermal noise thus comes at the expense of greater sensitivity to angular misalignment.  \nThe  specified  mirror  beam  sizes  can  be  achieved  with  either  of  two  designs:  a nearly-planar cavity or a nearly-concentric one. The nearly-concentric design is preferred for  its  higher  stability  with  high  stored  power  operation  when  torques  due  to  optical radiation  pressure  become  significant.  In  this  case,  the  torsional  mode  with  the  higher optical  stiffness  is  statically  stable,  whereas  it  would  be  statically  unstable  for  a  nearplanar design [7].', '2.2 Recycling cavity design': 'Both the power recycling and signal recycling cavities are designed to be stable for the fundamental Gaussian modes they support. That is, the fundamental cavity mode accrues a non-negligible Gouy phase in a one-way propagation through the cavity. The benefit of this  design  (new  in  Advanced  LIGO)  is  that  both  recycling  cavities  have  well  defined spatial eigenmodes and transversal mode-spacings much greater than the linewidth of the cavities [8]. The modes become less sensitive to mirror imperfections, resulting in more efficient signal detection. The stable design results in the folded layout shown in figure 1 for these cavities. Each of the six recycling cavity mirrors is a curved optic; they produce a one-way Gouy phase of 25 and 19 degrees in the power and signal recycling cavities, respectively, and transform the beam radius from 5.3 cm at the ITMs to 2.2 mm at the PRM, and 2.1 mm at the SRM.', '2.3 Gravitational wave readout': 'Readout of the gravitational wave signal is accomplished using an output mode cleaner in conjunction with homodyne, or DC detection. In this scheme, a local oscillator field is generated  by  offsetting  the  arm  cavities  slightly  from  their  resonance  (typically  a  few picometers),  thereby  pulling  the  Michelson  slightly  off  the  dark  fringe  [2].  The  output mode  cleaner  filters  out  non-TEM00  mode  carrier  power,  and  any  power  in  RF modulation  sidebands,  so  that  only  the  carrier  TEM00  mode  is  detected.  This  greatly reduces the power that must be detected at the output. Homodyne readout is a significant departure  from  the  heterodyne  readout  used  in  Initial  LIGO.  Compared  to  heterodyne detection, it is less susceptible to a number of technical noise couplings, but its primary benefits lie in lower quantum noise [9] and compatibility with the future use of squeezed light [10].', '2.4 High power effects': 'Several  effects  may  hinder  interferometer  operation  at  high  power  and  need  to  be considered in the design: optical distortion produced by thermal effects from absorbed power; optical torques that can significantly impact alignment stability; and parametric instabilities  arising  from  coupling  between  test  mass  acoustic  modes  and  higher-order optical modes of the arm cavities.  \nAs mentioned above, the torque induced by radiation pressure becomes comparable to the mechanical restoring torque of the test mass suspension, and must be accounted for in the angular controls system. This problem is addressed in reference [11], where it is shown that the unstable alignment modes have very low frequency, and can be readily stabilized with a suitable control filter.  \nThe dominant source of thermal distortion is thermal lensing in the ITM substrates due to power absorbed in the ITM reflective coatings. Next in importance, at high power, coating absorption in the ITMs and ETMs causes a non-negligible change their radii of curvature through thermo-elastic distortion. The thermal compensation system, described in section 4.6, is designed to compensate both of these effects. The compensation plates (CP)  shown  in  figure  1  allow  some  of  the  distortion  correction  to  be  applied  to  these elements, which are more noise-tolerant than the ITMs. The use of ultra-low absorption  \nfused silica for the ITMs, the BS, and the CPs ensures that power absorbed in the bulk is negligible compared to that absorbed in the test mass high reflectivity coatings.  \nParametric acousto-optic couplings have the potential to lead to unstable build-up of such  coupled,  higher-order  modes  [12].  Unchecked,  this  could  impose  a  limit  on  the power stored in the arms. Uncertainties in the parameters relevant to the process prevent an  exact  calculation  of  the  situation.  Instead,  statistical  analyses  can  indicate  the probability of instability at a given power level. The general conclusion of these analyses is that there may be 5-10 modes per test mass that could become unstable at full power. One or more of several mitigation methods may thus need to be applied. The simplest is to  use  the  thermal compensation actuators to slightly change the radius of curvature of one or more test masses; this would shift the eigen-frequency of the higher-order optical mode to avoid overlap with the corresponding acoustic mode. A second technique would be  to  actively  damp  any  unstable  acoustic  modes.  Each  test  mass  is  equipped  with  an electro-static actuator (see section 4.4.2) that can be used to apply a damping feedback force at the acoustic mode frequencies. A third technique, still in the research phase, is to apply passive tuned dampers to the test masses.', '3. Strain sensitivity': 'The interferometer noise floor is determined by the fundamental noise sources, quantum noise  and  thermal  noise.  Thermal  noise  is  determined  by  fixed  parameters  in  the interferometer, such as material properties and beam size. Quantum noise, on the other hand, depends on the readily variable input laser power, and the (less readily) changeable SRM  transmission.  Other  noise  sources,  such  as  laser  frequency  or  amplitude  noise, photodetector  dark  noise,  actuator  noise,  etc.,  are  classified  as  ÔtechnicalÕ  noises. Technical  noises  are  controlled  by  design  so  that  the  equivalent  strain  noise  of  each source is no greater than 10% of the target strain sensitivity throughout the detection band (10Ñ7000 Hz). As these noise sources are typically statistically independent, they add as a root-square-sum to the total; an individual 10% noise source thus increases the noise floor by only 0.5%.  \nThe  projected  strain  noise  spectrum  for  the  nominal  Advanced  LIGO  mode  of operation is shown in figure 2. In the nominal mode, the input power at the PRM is 125 W, the SRM transmission is 20%, and the signal recycling cavity has zero detuning. The individual noise terms are described in the following sections.  \nBeyond the strain noise spectrum, a standard figure of merit for detector sensitivity is  the  distance  to  which  the  GW  signal  emitted  by  a  binary  neutron  star  (BNS) coalescence  is  detectable.  The  BNS range is  defined  as  the  volume-  and  orientationaveraged distance at which a coalescence gives a matched filter signal-to-noise ratio of 8 in a single detector [13]. The BNS range for the strain noise curve in figure 2 is 190 Mpc.  \nFigure 2 Principal noise terms for the nominal (high power, broadband) mode of operation of Advanced LIGO.  \n<!-- image -->', '3.1 Quantum noise': 'Quantum  noise  encompasses  the  effects  of  statistical  fluctuations  in  detected  photon arrival  rate  (shot  noise)  and  radiation  pressure  due  to  photon  number  fluctuations. Quantum  noise  is  calculated  using  the  formulation  of  Buonanno  and  Chen  [14].  We assume 75 ppm round-trip loss in each arm cavity, and 10 -3 loss in the power recycling cavity, which leads to 5.2 kW of power at the beamsplitter and 750 kW of power in each arm  cavity.  A  detection  efficiency  of  90%  is  assumed;  this  accounts  for  finite transmission  through  the  output  Faraday  isolator  and  output  mode  cleaner,  as  well  as photodetector quantum efficiency.', '3.2 Test mass thermal noise': 'Coating Brownian noise is the dominant of the various test mass thermal noise terms. It arises  from  mechanical  dissipation  in  the  coatings,  and  is  calculated  according  to reference [15]. The coating design and material parameters are described in section 4.3. Coating  thermo-optic  noise  arises  from  thermal  dissipation  in  the  coatings,  producing noise via the thermoelastic and thermorefractive coefficients of the coating materials. The two effects are calculated coherently, according to reference [16]. Mechanical loss in the  \nbulk  fused  silica  is  responsible  for  the  substrate  Brownian  noise  term.  Reference  [17] provides the calculation for  this  term,  using  the  bulk  and  surface  loss  model  for  fused silica found in reference [18].', '3.3 Suspension thermal noise': 'Thermal noise in the test mass suspension is primarily due to loss in the fused silica fibres used in the final suspension stage. As described in the suspension design section (4.4.2), these four glass fibres have a circular, but variable diameter cross-section: they are thin in the  main  (middle)  section  of  the  fibre,  and  about  twice  as  thick  near  the  ends.  This geometry minimizes thermal noise, while keeping the fibre violin mode frequency high (510 Hz fundamental) and the vertical stretching mode frequency low (9Hz). The thermal noise is calculated using  a finite-element model  of the last suspension stage, including loss  terms  for  the  bulk,  the  surface,  and  the  thermoelastic  components  of  the  fibre material [19].', '3.4 Gravity gradients': 'Seismic waves produce density perturbations in the earth close to the test masses, which in  turn  produce  fluctuating  gravitational  forces  on  the  masses.  This  seismic  gravitygradient noise is estimated using the transfer function formulation of reference [20], and a representative model for the seismic motion at an observatory site. The latter can be quite variable over time, and gravity gradient noise is predicted to be several times higher than shown in figure 2 for some time periods [21].  \nFigure 2 also shows the strain noise from the transmission of seismic noise through the  seismic  isolation  and  suspension  systems  to  the  test  masses  (the  ÔSeismic  noiseÕ curve). Due to the large mechanical isolation, this noise is negligible above 11 Hz.', '3.5 Residual gas noise': 'Residual gas in the 4 km long beam tubes will lead to statistical variations in the column density of gas particles in the beam path, producing fluctuations in the effective refractive index along the path. The resulting optical path length noise is modeled by calculating the impulsive change in the cavity fieldÕs phase as a molecule moves through the beam, and integrating over the molecular velocity distribution [22]. The noise curve includes only the most dominant residual gas component, hydrogen, at a pressure of 4 × 10 ! ! pascals.  \nThough  not  included  in  the  figure  2  noise  curve,  residual  gas  in  the  test  mass vacuum chambers will contribute some damping to the test mass suspension, potentially increasing  the  suspension  thermal  noise.  This  damping  effect  is  increased  by  the relatively narrow gap between the test mass and its suspended reaction mass Ñ so-called thin-film damping [23]. Gas damping noise is most significant in the 10Ñ40 Hz band, where it falls very nearly as ! ! ! . At an anticipated chamber pressure of 7 × 10 ! ! pascals of H2, the resulting strain noise is 5 × 10 ! !" / Hz at  20  Hz  Ð  a  factor  of  3-4  below  the interferometer strain noise in figure 2. To mitigate the effect, this gap is larger for the ITMs (20 mm) than the ETMs (5 mm), since the former do not require as much electrostatic  actuation  force.  This  noise  term  is  not  included  in  figure  2  because  it  will eventually  be  made  negligible  (i.e.,  another  factor  of  3  reduction),  through  some combination of lower chamber pressure, an increased gap for the ETMs, and possibly a more complicated (ring-like) geometry for the end reaction masses.', '3.6 Other modes of operation': 'As mentioned above, the laser input power and the signal recycling cavity parameters can be varied to implement different modes of operation than the nominal mode represented by  figure  2.  We  illustrate  the  potential  parameter  space  with  two  particular  alternate interferometer modes: a mode optimized for low input power; a mode optimized for BNS detection. The low power mode is of interest because achieving operation at full power is likely to take extended commissioning time; early operations and observation runs will therefore be carried out at reduced power. The BNS optimized mode shows the potential sensitivity  to  this  particular  source,  and  the  corresponding  trade-off  in  broadband sensitivity.  Table  2  gives  the  parameters  for  the  two  modes,  and  figure  3  shows  their strain noise spectra.  \nTable 2 Interferometer parameters for two alternate modes of operation  \nFigure 3 Advanced LIGO strain noise spectrum for the modes defined in table 2, and for the  nominal  sensitivity  shown  in  figure  2.  The  feature  at  500  Hz  is  the  (unresolved) fundamental vibrational mode of the test mass suspension fibres.  \n<!-- image -->', '4.1 Laser source': 'The interferometer employs a multi-stage Nd:YAG laser that can supply up to 180 W at the laser system output. The pre-stabilized laser (PSL) system [24] consists of this laser light source, and control systems that stabilize the laser in frequency, beam direction, and intensity.  The  laser  was  developed  and  supplied  by  the  Max  Planck  Albert  Einstein Institute in collaboration with Laser Zentrum Hannover e.V. A schematic drawing of the PSL is shown in Figure 4.  \nFigure  4 Schematic  of  the  pre-stabilized  laser  system.  The  Input  Mode  Cleaner  is discussed in section 4.2. AOM: acousto-optic modulator; EOM: electro-optic modulator; FI: Faraday isolator; PD: photodetector.  \n<!-- image -->  \nThe laser comprises three stages. The first stage is a commercial non-planar ringoscillator (NPRO) manufactured by InnoLight GmbH. The second stage (medium power amplifier) is a single-pass amplifier that boosts the NPRO power to 35 W, and the third stage is an injection-locked ring oscillator with a maximum output power of about 220 W. All stages are pumped by laser diodes; the pump diodes for the second and third stages are fibre coupled and located far from the laser table for easier management of power and cooling. The system may be configured for 35 W output by using the NPRO and medium power stages, bypassing the high power oscillator; this configuration will be in the early operations of Advanced LIGO.  \nThe source laser is passed through the pre-mode cleaner (PMC). The PMC is a bowtie cavity (2m round trip length) designed to strip higher-order modes from the beam, to reduce beam jitter  (amplitude  reduction  factor  for  TEM01/TEM10  modes of  63),  and  to provide low-pass filtering for RF intensity fluctuations (cavity pole at 560 kHz).  \nIntensity stabilization requirements are quite stringent across the GW band. At full laser power, radiation pressure effects in the arm cavities lead to a residual intensity noise specification of 2 × 10 -9 Hz -1/2 at 10 Hz, at the input to the PRM. This stability is achieved through cascaded sensors and feedback loops. The first sensor measures the power in the PMC mode, and the  second  sensor  samples  light  transmitted  through  the  Input  Mode Cleaner. To ensure that an accurate low-noise measurement is made, the second sensor profits from the beam stability post-mode-cleaner, is in vacuum, and consists of multiple diodes used at low power. An acousto-optic modulator (AOM1) is the actuator for the control loop.  \nThe initial frequency stabilization of the laser is performed in the PSL by locking its frequency to an isolated, high-finesse reference cavity (bandwidth of 77 kHz) using the standard  reflection  locking  technique.  Three  actuators  are  used  to  provide  wide  \nbandwidth  and  large  dynamic  range:  a  PZT  attached  to  the  NPRO  crystal;  an  electrooptic modulator (EOM1)Ñused as a broadband, phase correctorÑbetween the NPRO and medium power amplifier; and the NPRO crystal temperature for slow, wide-range control. The servo bandwidth is 400 kHz. The beam used for this frequency pre-stabilization is taken  after  the  PMC,  and  is  double-passed  through  an  AOM  before  being  sent  to  the reference cavity. This AOM is driven by a voltage-controlled oscillator to provide laser frequency  actuation  (1  MHz  range,  100  kHz  bandwidth)  for  subsequent  stages  of stabilization.  \nFigure 5 shows a mode scan of the L1 high-power laser beam when operating at full output power. The total power in higher-order (non-TEM00) modes is 5.3% of the total. This is measured before the PMC, which will filter out this high-order mode content. DBB - modescan  \nFigure 5 Mode scan of the high power laser used on the L1 interferometer. Close to 95% of the power is in the TEM00 mode. 4.2 Input optics The input optics subsystem (IO) accepts the light from the pre-stabilized laser, stabilizes and conditions it, and performs matching and pointing into the main interferometer core optics. A schematic view is shown in Figure 6. The optical efficiency of the IO, from the PSL output to the PRM, is designed to be at least 75%. The system can be broken down into the following functional units. 4.8 4.9 5 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 0 10 20 30 40 50 60 70 80 90 100 higher order mode power (%) scan 10 -6 10 -5 10 -4 10 -2 10 -1 0 5 10 relative power TEM lm order even l odd l  \n<!-- image -->  \n-3  \n10  \nDBB  \nDiagnostic breadboard:  \nDBID 0208, scan mode (3)  \nSelected laser beam:  \n200W laser (DBB shutter open)  \nPower in DBB (RPD.DC):  \n10.2 V  \nBeam alignment:  \npre-alignment off  \nModematching lens positions:  \nlens 1 (ML  \nMeasurement:  \n99 scans, 13. Jul 2011 17:21 CDT  \nScan ramp:  \n0.500 Hz, 30000 Cts  \nPZT calibration deviation:  \n-0.5%  \nResolution (samples):  \n65539  \nPhotodetector signal (TPD):  \n0.000 V  \nglyph[triangleright]glyph[triangleright]glyph[triangleright]  \n8.292 V  \nFinesse:  \n406.4  \nRoundtrip Gouy phase:  \n0.149917  \nRelative misalignment (X,Y):  \n0.013  \nRelative mismodematching:  \n0.087  \nHigher order mode count:  \n50.9  \nHigher order mode power:  \n5.3%  \n·  \n·  \n·  \n·  \n0.9  \n·  \n0.000000 FSR  \n0.015, 0.009  \n0.007  \n2.5  \n·  \n·  \n0.180%  \n·  \n0.010  \n·  \n0.0%  \n4.6 s/ramp, 11984  \n1  \n) = -0.6 mm, lens 2 (ML  \nMODESCAN  \n·  \n2  \n) = -1.8 mm, lenses latched  \n·  \n22.8 s/FSR, 29  \n0.1 s/linewidth  \ndbb\\_msc-016.pdf, page 1 of 2  \nFigure 6 Schematic of the input optics components. IFI: input Faraday isolator. P: periscope. IMn: input mirror 1-4.  \n<!-- image -->  \n4.2.1 RF Modulation . Radio-frequency (RF) phase modulation is impressed on the beam and used for global sensing of the interferometer (see section 4.8) and for sensing of the IMC. Three modulation frequencies are applied, all with small modulation depth: 9 MHz and  45  MHz  for  the  main  interferometer  sensing;  24  MHz  for  IMC  sensing.  The modulator  must  exhibit  good  phase  modulation  efficiency,  low  residual  amplitude modulation, and negligible thermal lensing up to a beam power of 165 W [25]. The EOM uses  a  40mm  long,  4 × 4  mm  cross-section,  wedged  RTP  (rubidium  titanyl  phosphate) crystal as the electro-optic material. Three pairs of electrodes are used to apply the three modulation frequencies to the crystal.  \n4.2.2 Input Mode Cleaner . The IMC supplies a key function of the IO system: to stabilize the PSL beam in position and mode content, and to provide a high-quality laser frequency reference. The beam pointing stability at the input to the PRM, expressed relative to the beam  radius  and  beam  divergence  angle,  must  be glyph<c=1,font=/BNXNOX+ArialUnicodeMS> 1x10 -8 Hz -1/2 at  100  Hz.  The frequency stability at the IMC output must be glyph<c=1,font=/BNXNOX+ArialUnicodeMS> 1x10 -3 Hz/Hz 1/2 at 100 Hz.  \nThe  IMC  is  a  three-mirror  ring  cavity  used  in  transmission.  Each  mirror  is suspended  in  a  triple  pendulum  suspension  with  metal  wire  loops  (see  section  4.4)  to provide  vibration  isolation  and  acceptable  thermal  noise.  The  IMC  finesse  is  500,  the round trip length is 32.9 m, and the linewidth is 18 kHz. The 24 MHz phase modulation sidebands are used both for reflection locking and wavefront-sensor alignment control of the  IMC.  Additionally,  the  IMC  is  used  as  a  frequency  actuator  for  the  final  level  of frequency stabilization to the long arm cavities.  \n4.2.3  Faraday Isolator .  An  in-vacuum  Faraday  Isolator  is  mounted  between  the  IMC output and the PRM; the isolator extracts the beam reflected from the interferometer and prevents this  beam  from  creating  parasitic  interference  in  the  input  chain.  The  isolator must deliver a minimum of 30dB of isolation up to 125 W of laser power. To compensate thermally  induced  birefringence,  the  isolator  uses  two  terbium  gallium  garnet  (TGG) crystals for Faraday rotation, with a quartz rotator in between. Compensation of thermal lensing  is  achieved  by  incorporating  a  negative dn/dT material  (deuterated  potassium dihydrogen phosphate, or ÔDKDPÕ) in the assembly [26].  \n4.2.4 Mode Matching . The IMC output beam must be matched to the interferometer mode, with a targeted efficiency of 95% or better. This mode matching is accomplished with two curved mirrors, in combination with two flat mirrors used for beam routing.  All four of these reflective optics are mounted in single stage suspensions for vibration isolation; the suspensions also have actuators to provide remote steering capability (see section 4.4).', '4.3 Core optics': 'The ÔCore OpticsÕ are central to the interferometer performance. For each interferometer they include (see Table 3):  \n- ∞ Two input and two end test masses which form the Fabry-Perot arms\n- ∞ A 50/50 beamsplitter at the vertex of the Michelson interferometer\n- ∞ Two compensation plates that serve as actuation reaction masses for the input test masses, and to which thermal compensation can be applied\n- ∞ Two actuation reaction masses for the end test masses\n- ∞ Four reflective curved mirrors in the signal and power recycling cavities\n- ∞ Signal and power recycling mirrors  \nTable 3 Parameters of the core optics. ETM/ITM: end/input test mass; CP: compensation plate;  ERM: end reaction mass; BS: beam splitter; PR3/2: power recycling mirror 3/2; SR3/2:  signal  recycling  mirror  3/2;  PRM/SRM:  power/signal  recycling  mirror.  ROC: radius of curvature; AR: anti-reflection. Transmission values are at 1064 nm, except for those in parentheses, which are for 532 nm.  \nAll the core optics are made with fused silica substrates. Their fabrication involves three components: material type; substrate polishing; and coatings. The test masses naturally have the most stringent requirements for all three aspects.  \nThe fused silica material used for the input test masses, the compensation plates, and the  beamsplitter  is  Heraeus  Suprasil  3001.  This  is  an  ultra-low  absorption  grade,  with absorption  at  1064  nm  of  <  0.2  ppm/cm.  The  material  also  has  a  low  level  of  \ninhomogeneity  and  low  mechanical  loss.  The  material  for  the  other  core  optics  is  less critical, and less expensive grades of fused silica are used (ETMs use Heraeus Suprasil 312).  \nThe surface quality required of the polishing is determined largely by the targeted round-trip  optical  loss  in  the  arm  cavities.  For  a  given  input  laser  power,  this  loss determines the achievable stored power in the arms, and thus the quantum noise level of the  interferometer.  For  Advanced  LIGO the arm round-trip loss goal is set at 75 ppm. This  would  allow  a  total  arm  cavity  stored  power  (both  arms)  of  up  to:  1/75  ppm  = 1.3x10 4 times  the  input  power.  Table  4  lists  the  test  mass  substrate  polishing requirements, as well as typical achieved levels. The substrates for the large core optics are produced by a combination of super-polishing for small scale smoothness, followed by ion-beam milling to achieve the large scale uniformity.  \nTable 4 Polishing specifications and results for the test masses  \nAll  the  optical  coatings  are  ion-beam  sputtered,  multi-layer  dielectrics.  The  test masses  are  coated  by  Laboratoire  MatŽriaux  AvancŽs  (LMA,  Lyon,  France);  all  other large core optics are coated by CSIRO (Sydney, Australia). The critical properties of the coating  materials  are  low  optical  absorption,  low  scatter,  and  low  mechanical  loss (particularly for the test masses). For all optics other than the test masses, the coatings are traditional  alternating  layers  of  silicon-dioxide  and  tantalum  pentoxide,  each  of ¼ -wavelength optical thickness. For the test masses, the TaO5 is doped with 25% titanium dioxide,  a  recipe  that  reduces  the  mechanical  loss  by  about  40%  [28].  In  addition,  the layer thicknesses are altered: the SiO2 layers are a little thicker and the Ti-TaO5 layers are a  little  thinner  than  a ¼ -wavelength.  This  design  not  only  achieves  the  transmission specifications at 532 nm, but it also gives a further, modest reduction in thermal noise because less  Ti-TaO5  is  used;  see  Table  5  for  the  coating  material  parameters  that  are used to calculate the thermal noise curve shown in Figure 2.  \nTable 5 Test mass coating material parameters used to calculate coating thermal noise (i.e., this represents our model of the coating).  \nAll  core  optics  are  characterized  with  high  precision  metrology,  before  and  after coating. As an example, Figure 7 shows power spectra of the measured phase maps of the test masses used in one arm of the L1 interferometer. The coating contributes additional non-uniformity greater  than  the  substrate  at  larger  spatial  scales.  Comparing  the  phase map residuals over the central 160 mm diameter, after subtracting tilt and power, gives:  \n- ∞ ETM substrate: 0.18 nm-rms coated: 0.69 nm-rms\n- ∞ ITM substrate: 0.15 nm-rms coated: 0.31 nm-rms  \nOptical simulations of an arm cavity formed with these two test mass mirrors predict a  total  round  trip  loss  of  about  44  ppm  (20  ppm  due  to  distortions  captured  in  the phasemap, 20 ppm due to smaller scale roughness that causes wider angle scatter, 4 ppm from  ETM  transmission).  This  is  well  within  the  goal  of  75  ppm,  though  particulate contamination of installed optics can contribute a few tens of ppm additional loss.  \nFigure 7 Power spectra of the surface maps, coated and un-coated, for the ITM and ETM used in one arm of the L1 interferometer.  \n<!-- image -->  \nThough coating absorption is a negligible component of the total loss, it is critical for higher power operation (see section 4.6). Absorption in the test mass high-reflectivity coatings is specified at less than 0.5 ppm, and actual coatings show measured absorption of 0.2Ñ0.4 ppm. Other coatings are specified to have absorption less than 1 ppm.  \nThe  test  mass  coatings  delivered  to  date  meet  many  of  their  challenging requirements such as absorption and scattering, but some of the properties are not ideal:  \n- ∞ For  the  ETMs,  a  systematic  error  in  the  layer  thicknesses  left  the  1064  nm transmission in spec, but caused the 532 nm transmission to be larger than desired by an order of magnitude. This has made the arm length stabilization system described in section 4.8.4 much more challenging.\n- ∞ Features  of  the  coating  planetary  system  produce  a  ~1  nm  peak-to-peak  thickness ripple, with an 8 mm period, in the outer regions of the mirror. This is the peak seen in the ETM07 coated curve in Figure 7. This surface ripple scatters light out of the arm cavity; the optical loss is not significant (6 ppm), but the scattered light impinges on the beam tube baffles and can cause excess phase noise (see section 4.7).\n- ∞ Spherical aberration of the ETM coatings is 2-3 times higher than the specification of 0.5 nm. This will alter slightly the shape of the cavity fundamental mode compared to an ideal Gaussian TEM00 mode. However, the aberration is very similar from ETM to ETM,  so  the  arm  cavity  modes  are  well  matched  and  this  defect  does  produce significant loss.\n- ∞ The anti-reflection coatings on the ITMs have 2-3 times higher reflectivity than the specification  of  50  ppm.  Though  not  significant  in  terms  of  loss,  the  higher  AR produces higher power ghost beams that may need better baffling to control scattered light noise (see section 4.7).', '4.4 Suspensions': 'All of the primary in-vacuum interferometer optical components (all depicted in Figure 1, with the exception of the input Faraday isolator) are suspended by pendulum systems of varying designs. These suspension systems provide passive isolation from motion of the seismically isolated optics tables in all degrees of freedom and acceptable thermal noise. The suspensions also provide low noise actuation capability, used to align and position the optics based on interferometer sensing and control signals.  \n4.4.1 Requirements. The suspension designs employed for each optical element depend upon the performance requirements and physical constraints, as listed in Table 6. Most of the suspensions employ multiple pendulum and vertical isolation stages.  \nTable 6 Suspension types. Auxiliary suspensions are for optical pick-off beams, beam steering and mode matching.  \n4.4.2  Design  description. The  most  challenging  design  is  the  quadruple  pendulum suspension  for  the  test  masses  [27].  Each  of  these  suspensions  is  comprised  of  two adjacent chains, each chain having four masses suspended from one another. The main chain  includes  the  test  mass  optic  as  the  lowest  mass.  The  adjacent,  reaction  chain provides  an  isolated  set  of  masses  for  force  reaction.  The  bottom  mass  in  the  reaction chain is the Compensation Plate (CP) optic in the case of an ITM suspension, and the End Reaction  Mass  (ERM)  in  the  case  of  an  ETM  suspension.  A  structure  surrounds  and cages the suspended masses and mounts to the seismically isolated optics table.  \nVibration isolation for the test mass is accomplished with a 4-stage pendulum and 3 stages  of  cantilevered  blade  springs,  providing  isolation  in  all  6  degrees-of-freedom above approximately 1 Hz. The suspension is designed to couple 22 of the 24 quasi-rigid body  modes  (all  but  the  2  highest  frequency)  of  each  isolation  chain  so  that  they  are observable and controllable at the top mass (4 wires between masses to couple pitch and roll modes; non-vertical wires to couple pendulum modes). The blade springs are made of maraging  steel  to  minimize  noise  resulting  from  discrete  dislocation  movements associated with creep under load [31].  \nFor each chain, all the quadruple suspension rigid body modes below 9 Hz can be actively damped from the top stage. Sensing for this local damping is accomplished with integral  optical  shadow  sensors  [32],  or  with  independent  optical  lever  sensors.  The shadow sensors are collocated with the suspension actuators and have a noise level of 3x10 -10 m/ √ Hz at 1 Hz.  \nForce  actuation  on  the  upper  three  masses  is  accomplished  with  coil/magnet actuators [32]. Six degree-of-freedom actuation is provided at the top mass of each chain, by  reacting  against  the  suspension  structure.  These  actuators  are  used  for  the  local damping of 22 modes (each chain). The next two masses can be actuated in the pitch, yaw and piston directions, by applying forces between adjacent suspended masses. These stages  are  used  for  global  interferometer  control.  Low  noise  current  drive  electronics, combined with the passive filtering of the suspension, limit the effect of actuation noise at the test mass.  \nFigure 8 Quadruple pendulum suspension for the Input Test Mass (ITM) optic.  \n<!-- image -->  \nDirect low-noise, high-bandwidth actuation on the test mass optic is accomplished with electro-static actuation [33]. The CP and ERM each have an annular pattern of gold electrodes, deposited on the face adjacent to the test mass, just outside the central optical aperture. The pattern is separated into 4 quadrants, which enables actuation in pitch, yaw and piston. The force coefficient is highly dependent on the separation between the test mass  and  its  reaction  mass.  The  ETM-ERM  separation  is  5  mm,  which  provides  a maximum force of about 200 micro-Newtons using a high-voltage driver. Less actuation is needed on the ITMs, so the CP-ITM gap is increased to 20 mm to mitigate the effect of squeezed film damping [23].  \nThe  test  mass  and  the  penultimate  mass  are  a  monolithic  fused  silica  assembly, designed  to  minimize  thermal  noise  [34].  Machined  fused  silica  elements  (ÒearsÓ)  are hydroxide-catalysis  (silicate)  bonded  to  flats  polished  onto  the  sides  of  the  TM  and penultimate mass. Custom drawn fused silica fibres are annealed and welded to the fused silica ears with a CO2 laser system [35]. The shape of the fibres is designed to minimize thermal noise (400 µ m dia. by 596 mm long with 800 µ m dia. by 20 mm long ends), while achieving a low suspension vertical ÒbounceÓ mode (9 Hz, below band) and high first  violin  mode  frequency  (510  Hz,  above  the  instrumentÕs  most  sensitive  frequency range). The fibre stress (800 MPa) is well below the immediate, static, breaking strength (5 GPa).  \nThe other suspension types employ the same basic key principles as the test mass quadruple suspensions, except for using steel wire in the final stage.  \n4.4.3  Performance. The  transfer  functions  (actuation  to  response)  in  all  degrees  of freedom  in  general  match  very  well  the  model  for  the  test  mass  suspension;  Figure  9  \nshows one such comparison. Furthermore, the transfer functions are well matched from suspension to suspension, so that very small, if any, parameter value changes are required for the control filters of the multi-input, multi-output control system.  \nThe  thermal  noise  performance  of  the  suspension  cannot  be  verified  until  the interferometer  is  fully  commissioned  and  operating  at  design  sensitivity.  The displacement thermal noise spectrum for the monolithic stage is made up of quadrature sum  of  contributions  from  the  horizontal  pendulum  mode,  the  vertical  mode  (with  a vertical-horizontal cross-coupling assumed of 0.1%), the first violin mode and the loss associated with the silicate  bonded ears. The  as-installed  quality  factor  (Q)  of  the  first violin modes of the fibres has been measured to be 1.1Ñ1.6 x 10 9 , which is about a factor of  2  higher  than  anticipated  from  prototype  testing  [34],  and  is  consistent  with  the anticipated level of thermal noise.  \nFigure 9 Transfer function (magnitude) from longitudinal force to longitudinal position of the top mass of an ITM suspension.  \n<!-- image -->', '4.5 Seismic isolation': 'The  general  arrangement  of  the  seismic  isolation  system  and  its  relationship  to  the vacuum system and the suspension systems is illustrated in Figure 10, where a cut-away view of one of the test mass vacuum chambers is also shown.  \nFigure 10 An Input Test Mass (ITM) vacuum chamber.  \n<!-- image -->  \n4.5.1 Requirements. The motion of the detector components, especially the interferometer optics,  must  be  limited  to  very  small  amplitudes.  The  conceptual approach for seismic isolation is to provide multiple stages of isolation, as depicted in Figure 11. The stages topologically closest to the ground are referred to as the seismic isolation system; they provide coarse alignment, and employ both active and passive isolation to deal with the highest amplitude of motion. An optics table provides the interface between the seismic isolation system and the subsequent suspension system. The optics tables in the smaller (HAM) vacuum chambers are 1.9 m by 1.7 m; the downward-facing optics tables in the larger  (BSC)  vacuum  chambers  are  1.9  m  diameter.  The  limits  to  optics  table  motion (Table  7)  are  derived  from  the  allowed  motion  for  the  interferometer  optics  using  the passive isolation performance of the suspension systems.  \nFigure 11 Seismic isolation for the test mass optic.  \n<!-- image -->  \nTable 7 Seismic isolation performance requirements for the BSC chamber, 3 stage systems.  \n4.5.2 Design description. The first measure taken to reduce ground motion was to site the observatories  in  seismically  quiet  locations  [36].  The  observatory  facilities  were  then designed to limit vibration source amplitudes (e.g., the chiller plant for the HVAC system is remote from the experimental hall). Additional isolation from the already seismically quiet ground motion is provided by the seismic isolation and suspension subsystems.  \nAll  in-vacuum interferometer  elements  are  mounted  on  seismically  isolated  optics tables  (with  the  exception  of  some  stray  light  control  elements).  The  typical  seismic isolation system consists of two or three stages of isolation (Figure 11). The first stage is accomplished  with  the  Hydraulic  External  Pre-Isolator  (HEPI)  system,  external  to  the vacuum  system.  The  next  one  or  two  stages  are  referred  to  as  the  Internal  Seismic Isolation  (ISI)  system  and  are  contained  within  the  vacuum  system.  The  test  mass, beamsplitter  and  transmission  monitor  suspensions  are  supported  by  inverted  optics tables  which  have  two  in-vacuum  stages,  housed  in  the  BSC  chambers.  All  other interferometer elements are supported by upright optics tables connected to one-stage ISI systems, housed in smaller (HAM) vacuum chambers.  \nThe  in-vacuum  payload  is  supported  by  a  structure  that  penetrates  the  vacuum chamber at four locations, through welded bellows. Each of these four points is supported by a HEPI assembly; each HEPI system supports a total isolated mass of 6400 kg. HEPI employs  custom  designed,  laminar  flow,  quiet  hydraulic  actuators  (8  per  vacuum chamber)  in  a  low  frequency  (0.1Ñ10  Hz),  6  degree-of-freedom  active  isolation  and alignment system. The actuators employ servo-valves in a hydraulic Wheatstone bridge configuration to control deflection of a diaphragm by differential pressure. For sensors, HEPI uses a blend of geophones and inductive position sensors. In addition,  a ground seismometer  provides  a  signal  for  feed-forward  correction.  The  HEPI  system  was deployed for the initial LIGO L1 interferometer [37] and remains essentially the same for Advanced LIGO.  \nThe  ISI  [38]  consists  of  three  stages  (each  a  stiff  mechanical  structure)  that  are suspended and sprung in sequence: stage 0 is the support structure connected to the HEPI frame; stage 1 is suspended and sprung from stage 0; stage 2 is suspended and sprung  \nfrom stage 1. The elastic, structural modes of stages 1 and 2 are designed to be > 150 Hz in order to keep them high above the upper unity gain frequency (~40 Hz) of the control system.  The  stage  2  structure  includes  the  optics  table  upon  which  payload  elements, such as the suspensions, are attached. Each suspended stage is supported at 3 points by a rod with flexural pivot ends, which are in turn supported by cantilevered blade springs. The springs provide vertical isolation and the flexure rods provide horizontal isolation. They are both made of high strength maraging steel in order to reduce noise resulting from discrete dislocation movement events associated with creep under load. The springs and flexures allow control in all 6 rigid body degrees-of-freedom of each stage, through the use of electromagnetic force actuation between the stages. Passive isolation from base (stage  0)  motion  is  achieved  at  frequencies  above  the  rigid  body  frequencies  of  these stages.  \nStage 1 of the ISI is instrumented with 6 capacitive position sensors (MicroSense), 3 three-axis  seismometers  (Nanometric  Trillium  T240)  and  6  geophones  (Sercel  L4C). Stage 2 is instrumented with 6 capacitive position sensors (MicroSense) and 6 geophones (Geotech GS13). The single-axis sensors are equally divided into horizontal and vertical directions.  All  of  the  inertial  sensors  are  sealed  in  vacuum-tight  canisters.  The  12 electromagnetic actuators (6 between stages 0-1 and 6 between stages 1-2) are equally split  between vertical and horizontal orientations,  and are a custom, ultra-high vacuum compatible design.  \nThe capacitive position sensor signals provide positioning capability, and are lowpass filtered in the isolation band. For stage 1 control, the T240 and L4C seismometer signals  are  blended  together  to  provide  very  low  noise  and  broadband  inertial  sensing; they  are  high-pass  filtered  to  remove  sensor  noise  and  other  spurious  low  frequency signals, such as tilt for the horizontal sensors. The T240 signals are also used for feedforward  to  the  stage  2  controller.  Before  filtering,  the  sensors  are  transformed  into  a Cartesian basis by matrix  multiplication  in  the  multi-input,  multi-output  digital  control system.  \n4.5.3 Performance. An  example  of  the  isolation  performance  achieved  to  date  for  the three-stage seismic isolation system is shown in Figure 12.  \nFigure 12 Example of the BSC ISI optics table isolation performance (from LHO). The blue  curve  shows  the  horizontal  ground  motion  adjacent  to  the  vacuum  chamber.  The gold curve shows the goal performance. The red curve is an in-loop measurement of the optics table longitudinal motion, using the stage 2 inertial sensors. At the mid-frequencies, these inertial sensor signals are pulled below their intrinsic noise floor by the feedback loop.  Below  ~30  mHz,  the  horizontal  inertial  sensors  are  likely  contaminated  by  tilt coupling.  \n<!-- image -->', '4.6 Thermal compensation': 'Absorption of the Gaussian-profiled laser beam in the core optics causes a non-uniform temperature  increase  leading  to  wavefront  aberration  through  the  thermo-optic  and thermo-elastic effects (elasto-optic effects are negligible). While thermal aberrations will occur in all the optics to some extent, only the test mass optics are anticipated to require active compensation.  \nThe projected thermal effects, without compensation, are indicated in Table 8. The only place of significant power absorption is at the test mass high-reflectivity surfaces, and the largest optical distortion is the resulting thermal lensing in the test mass substrate. The  ITM  thermal  lensing  affects  primarily  the  RF  sideband  mode  in  the  recycling cavities; the carrier mode is enforced by the arm cavities and is much less perturbed by the ITM lensing. The test mass surface distortion due to thermo-elastic expansion is about 10x smaller than the substrate lensing distortion, but at high power it becomes significant. Uncompensated,  the  surface  distortion  would  increase  the  ITM  and  ETM  radii  of curvature by a few tens of meters, which would reduce the beam size on each test mass  \nby  about  10%.  This  would  increase  coating  thermal  noise,  and  reduce  the  coupling efficiency between the arm cavity and recycling cavity modes.  \nTable 8 Absorbed power and corresponding thermal distortion at full power: 750 kW in each arm cavity, 5.2 kW in the PRC. Assumes absorption of 0.5 ppm at each HR surface. The distortion values are peak-to-valley over the beam diameter (1/ e 2 ).  The undistorted sagitta of a test mass is 725/850 nm (ITM/ETM).  \n4.6.1 Requirements. The TCS is required to:  \n- ∞ adjust the arm cavity spot size by adding up to 30 micro-diopters of power to all test mass HR surfaces,\n- ∞ compensate thermal aberrations in the recycling cavities sufficiently to maintain adequate RF sideband power buildup,\n- ∞ maintain recycling cavity and arm cavity mode overlap to within 95%, and\n- ∞ maintain  the  contrast  defect  ratio  by  limiting  the  additional  DC  power  at  the output mode cleaner (OMC) to within 1 mW  \nThe TCS capability to alter the test mass radius-of-curvature can also be used to adjust the  transverse  optical  mode  spacing  and  potentially  control  optical-acoustic  parametric instabilities at high optical power.  \n4.6.2 Design description. The  TCS consists of three major elements (see Figure 13): a radiative  ring  heater  (RH),  a  CO2  laser  projector  (CO2P)  and  a  Hartmann  wavefront sensor (HWS). The RH is used to correct surface deformation of the ITM and ETM, and to  partially  correct  the  ITM  substrate  thermal  lens.  The  CO2P  is  used  to  compensate residual ITM substrate distortions not corrected by the RH. The HWS is used to measure the test mass thermal aberrations.  \nThe basic intent of the combination of the RH and CO2P is to add heat to form the conjugate aberration to the thermal lens formed by the main beam heating. Whereas the RH power stability is good enough to permit direct actuation on the test mass, the CO2P actuates on the compensation plate to limit the effects of CO2 laser noise.  \nThe RH assembly is comprised of nichrome heater wire wound around two semicircular glass rod formers, which are housed within a reflective shield; the inner radius of the assembly is 5 mm larger than the test mass radius. The nichrome wire spacing along the  glass  former  is  variable  in  order  to  partially  compensate  for  boundary  condition effects and achieve better uniformity. The RH is mounted around and radiates onto the test mass barrel. It is positioned near the test mass anti-reflection face so that the thermal flexure  of  the  optic  produces  a  concavity  of  the  high-reflectivity  face,  correcting  the  \nconvex  deformation  caused  by  the  main  beam  heating.  The  thermal  flexure  is  very closely approximated by a spherical curvature at the high-reflectivity face. In addition, the thermal lensing produced by the RH partially compensates the lensing produced by the main beam. The effectiveness of the corrections can be expressed by considering a TEM00 mode probe beam that passes through or reflects from the optics; the correction factor  is  defined  as  the  power  scattered  out  of  the  TEM00  mode by the distorted optic, relative to the scattered power for the compensated optic. The RH provides a correction factor of about 10 for both types of test mass distortion (surface and substrate).  \nThe  CO2P  is  configured  to  make  static  pattern  corrections  via  both  central  and annular projected heating patterns. These two patterns are created using masks that are inserted into the beam using flipper mirrors. The annular pattern augments and refines the RH correction, providing another factor of 10 or more correction of the substrate lensing. The  central  pattern  can  be  used  to  maintain  central  heating  upon  lock  loss,  for  faster return  to  operation;  it  can  also  be  used  to  correct  non-thermal  power  terms  due  to substrate  inhomogeneity.  The  power  is  adjusted  with  a  polarizer  and  rotatable ½ -waveplate;  power  fluctuations  are  stabilized  using  an  AOM.  The  CO2P  is  designed  to deliver at least 15W to the compensation plate.  \nFigure 13 Schematic layout of the Thermal Compensation System for the X-arm. A similar  configuration  is  implemented  on  the  Y-arm,  with  the  SLED  probe  beam instead transmitting through the BS. Each of the masks can be independently flipped in or out of the beam path.  \n<!-- image -->  \nThe  HWS  is  used  to  measure  the  thermal  distortions,  both  before  and  after compensation. The HWS can measure thermal wavefront distortions with a sensitivity of < 1.4 nm and a spatial resolution of ≤ 1 cm, both over a 200 mm diameter at the ITM. In the vertex, the HWS uses super-luminescent LEDs (SLED) for probe beams. Independent probe beam paths for the X and Y-arms of the Michelson are achieved through choice of SLED wavelength, given the spectral properties of the beam splitter coating: 800 nm is used for the X-arm and 833 nm for the Y-arm (5 mW for both). Cross-talk between the X  \nand Y paths is less than 1 part in 100. Both probe beams make use of the beam expansion telescope integral to the signal recycling cavity (SR2 & SR3) to achieve a large profile at the BS, CP and ITM. The HWS for the ETM uses the ALS green laser beam as a probe.', '4.7 Scattered light control': 'A significant  fraction  of  the  input  laser  light  ends  up  outside  the  interferometer  mode through scattering or reflections from the various optics.  This light will hit and scatter from surfaces that are typically not as well mechanically isolated as the suspended optics, picking up large phase fluctuations relative to the main interferometer light. Thus even very small levels of scattered light can be a noise source if it rejoins the interferometer mode. Scattered light phase noise is proportional to the electric field amplitude, and for small surface motion proportional to the amplitude of motion. For large motion amplitude, fringe wrapping occurs, resulting in upconversion [39].  \nThe severity of a potential light scattering surface depends upon the location within the  interferometer.  Light  scattered  into  a  single  arm  cavity,  or  into  the  anti-symmetric port, directly contributes to an apparent differential signal. Light scattered into the power recycling cavity, on the other hand, is less impactful due to the common mode rejection of the arm cavities.  \nThe basic design approach for stray light control [40] is to (a) capture all first-order ghost beams in beam dumps, (b) baffle all views of the vacuum envelope (which is not isolated from ground motion), (c) provide baffles and apertures with low light scattering surface properties (low bidirectional reflectance distribution function (BRDF) surfaces), (d) provide baffle geometries which trap specular reflections into multiple reflections, (e) provide surfaces with some amount of absorption, and (f) vibration isolate the baffles. Surface treatments are restricted due to the need for ultra-high vacuum compatibility. The larger baffles and apertures are oxidized, polished stainless steel surfaces. The depth of the oxidized layer must be carefully controlled to maintain a well-bonded oxide layer and prevent a frangible layer. Smaller baffles and beam dumps are made of black glass. High power, in-vacuum, beam dumps are comprised of polished, chemical vapour deposited silicon carbide.  \nThe  locations  of  the  primary  baffles  are  shown  in Error!  Reference  source  not found. . An example of one of the baffle configurations is the Arm Cavity Baffle (ACB). This baffle has a ÒWÓ cross-section with an aperture slightly larger than the test mass diameter. A version of this baffle is placed in the arm cavity in front of each test mass optic. The small angle scatter from the far test mass (4 km away) is caught on the beam tube side of the ACB, and forced into multiple reflections in the acute angle ÔcavitiesÕ formed by the baffle surfaces. Large angle scatter from the adjacent test mass is caught on the other side of this suspended baffle. The ACB is mounted with a single pendulum suspension (1.6 Hz), with a cantilevered spring for vertical isolation (2 Hz).  \nLight  scattered  off  the  test  masses  at  even  smaller  angles  is  caught  by  the approximately  two  hundred  baffles  mounted  along  the  beamtube.  These  baffles  were installed  for  initial  LIGO,  but  were  designed  to  be  effective  for  later  generations  of interferometers.  \nFigure 14 Locations of the primary scattered light baffles.  \n<!-- image -->', '4.8 Global sensing and control': 'Using  primarily  interferometrically  generated  error  signals,  active  feedback  is  used  to keep  the  interferometer  at  the  proper  operating  point.  This  entails  keeping  the  four interferometer  cavities  on  resonance  (two  arm  cavities,  power-  and  signal-recycling cavity),  and  the  Michelson  at  the  dark  fringe  (or  at  a  controlled  offset  from  there).  In addition,  global  controls  are  required  to  keep  the  whole  interferometer  at  the  proper angular alignment.  \nThe optical sensing for both the length and alignment degrees-of-freedom is derived from photodetectors located at five output ports of the interferometer:  \n- ∞ Reflection port ( REFL ): the light reflected from the power recycling mirror; typically ~10% of the beam is detected\n- ∞ Power  recycling  cavity  pick-off  ( POP ):  the  beam  transmitted  by  PR2 coming from the beamsplitter; typically ~10% of the beam is detected\n- ∞ Anti-symmetric  port  ( AS ):  the  beam  exiting  the  signal  recycling  mirror; typically 99% of this beam is directed to the DC readout detectors, and 1% is directed to alignment and auxiliary detectors\n- ∞ ETM transmissions ( TRX & TRY ): beams transmitted by the two end test masses; typically a few percent of each beam is detected  \n4.8.1 Length sensing and control. The length sensing scheme is similar to  that  used  in initial LIGO [41], extended to sense the length of the new signal recycling cavity. As per standard  practice,  the  arm  cavity  lengths  are  treated  in  the  basis  of  common  and differential modes: the former is the average arm length, equivalent to the laser frequency, and  the  latter  is  the  arm  length  difference,  which  is  also  the  gravitational  wave  signal mode.  \nTwo sets of RF modulation sidebands are applied to the input laser field: one at 9 MHz and one at 45 MHz. Both pairs of RF sidebands are resonant in the power-recycling cavity, but not in the arm cavities. The Michelson contains the usual Schnupp asymmetry so that RF sideband power is transmitted to the AS port even when the carrier is at the dark fringe. In this case, we choose the asymmetry to couple the majority of the 45 MHz sideband  power  into  the  signal  recycling  cavity.  This  can  be  achieved  either  with  a relatively small (several cm) or relatively large (tens of cm) asymmetry, but the former is preferred because it suppresses the 9 MHz power in the SRC, leading to better separation of error signals for the two recycling cavities. With our Schnupp asymmetry of 8 cm, and a SRM transmission of 35%, nearly all of the 45 MHz sideband power is transmitted to the AS output, while only about 0.3% of the 9 MHz power arrives there.  \nFigure 15 Length sensing and control scheme for Advanced LIGO. Though not shown, the Michelson signal is also fed back to the PRM and SRM, so that the BS actuation affects only the Michelson degree-of-freedom.  \n<!-- image -->  \nFigure  15  summarizes  the  sensing  and  control  scheme  for  the  length  degrees-offreedom. Except for the DC readout of the GW channel, the length signals are derived from photodetectors at the REFL and POP ports, by demodulating their outputs at one or more of the RF modulation frequencies. The feedback controls are implemented digitally, with  a  real-time  sampling  rate  of  16,384  samples/sec.  The  arm  common  mode  loop actuates on the laser frequency so that it follows the highly stable common arm length. The servo includes an analogue feedback path to achieve high bandwidth. The design of this complex common mode servo follows that of initial LIGO [1].  \nAll of the photodetectors used for the length sensing during low-noise operation are located in vacuum chambers, mounted on seismically isolated platforms. This is done to reduce  spurious  noise  effects  in  the  signal  detection,  such  as  from  vibrations  of  the detectors,  acoustic  modulation  of  paths  in  air,  or  from  particulates  falling  through  the beams.  \nFor  the  auxiliary  degrees-of-freedom  (DoF)  Ð  all  those  other  than  the  arm  cavity differential mode Ð the control loop design involves a trade-off between having adequate loop  gain  to  avoid  non-linear  effects,  and  limiting  the  coupling  of  noise  into  the  GW channel. These auxiliary DoF couple weakly to the GW channel, at a level of order 10 -2 or smaller (meters/meter). However, the shot-noise limited sensing of these channels is 35  orders  of  magnitude  worseÑin  terms  of  equivalent  displacementÑthan  the  GW channel. Thus if the sensing noise of the auxiliary channels is impressed onto these DoF through  their  feedback  loops,  it  can  easily  spoil  the  GW  sensitivity.  This  noise mechanism is mitigated partially through the design of the auxiliary DoF servo loops: the loop bandwidths are kept low, and low-pass filters with cut-offs just above the unity gain frequencies  are  employed.  In  addition, noise  correction paths  are  implemented:  the auxiliary loop control signals are appropriately scaled and filtered, then added to the GW channel control signal to remove their coupling (feed-forward noise suppression). These correction paths reduce the auxiliary DoF noise infiltration by 30-40 dB.  \n4.8.2  Alignment  sensing  and  control. The  residual  angular  motion  of  the  arm  cavity mirrors must be 1 nrad-rms or less to adequately suppress alignment noise effects [42]. This  is  2-3  orders  of  magnitude  smaller  than  their  locally-controlled  angular  motion. Somewhat less stringent angular stability requirements apply to the other interferometer optics.  The  alignment  sensing  and  control  scheme  designed  to  provide  this  level  of stability  is  an  extension  of  the  Initial  LIGO  design  [43].  The  same  phase  modulationdemodulation techniques used for the length sensing are used with quadrant photodiodes to produce an alignment wavefront sensor (WFS). A WFS produces an alignment signal via the interference between the fundamental TEM00 Hermite-Gaussian field component and  the  TEM01/TEM10  field  components  generated  by  misalignments.  Several  new aspects of the alignment control design must be considered for Advanced LIGO:  \n- ∞ High  circulating  power  in  the  arms  produces  significant  radiation  pressure torques on the cavity mirrors\n- ∞ Additional  degrees-of-freedom:  signal  recycling  introduces  a  new  mirror  that must be aligned; the folded recycling cavities introduce another four mirrors\n- ∞ Alignment control noise must be filtered out starting at a much lower frequency  \nThe  radiation  pressure  effects  are  typically  described  in  terms  of  a soft and hard alignment mode, depending on whether the optical torque subtracts from or adds to the mechanical stiffness of the suspension [44]. This is illustrated in Figure 16 for a single cavity.  In  Advanced  LIGO,  the  radiation  pressure  torque  becomes  greater  than  the suspension mechanical torque at arm cavity powers above 700 kW. Above this, the soft mode becomes dynamically unstable,  and  must  be  actively  stabilized.  As  the  unstable eigenfrequency stays low even at full power (less than 0.3 Hz), it is straightforward to stabilize even with low bandwidth.  \nFigure 16 Representation of the hard and soft modes of cavity mirror alignment.  \n<!-- image -->  \nThe alignment WFS are located at the REFL and AS interferometer ports; two WFS are installed at different beam line positions at each port, such that they are separated in Gouy phase by 90 degrees. This allows combinations of WFS signals to be formed to reconstruct  any  Gouy  phase.  In  addition  to  the  WFS,  several  quadrant  photodiodes (QPDs) provide relative beam position information. The TRX, TRY and POP ports each have two QPDs, with each pair separated by 90 degrees Gouy phase. Lastly, the AS port contains a single QPD (detecting a small fraction of the AS beam). As with the length sensors, all of the alignment sensors that are used in low-noise operation (both WFS and QPD) are located in vacuum chambers, mounted on seismically isolated platforms.  \nThe control scheme for the arm cavity mirrors and the beamsplitter is summarized in Table 9. The other optics can be controlled using various combinations of the other WFS and  QPD  signals;  these  loops  are  implemented  essentially  for  drift  control,  with bandwidths of 0.1 Hz or less.  \nTable 9. Alignment control scheme for the arm cavity mirror (test masses) and the beamsplitter.  \n4.8.3 Output mode cleaner and DC readout. The output mode cleaner (OMC) is designed to filter out all RF sideband and higher-order spatial mode light at the AS port, so that the main  photodetectors  receive  only  light  that  carries  the  gravitational  wave  signal.  The OMC is a bowtie cavity with a moderate finesse (400); this is a trade-off between having a  narrow  bandwidth  to  filter  out  RF  components,  and  maintaining  a  high  transmission efficiency  (>  95%).  The  OMC higher-order mode spacing is fine-tuned (via the cavity length) to avoid overlap with higher-order modes likely to exit the interferometer AS port. The nominal OMC round trip length is 1.13 m.  \nCavity input/output  \nFigure 17 Layout of the OMC on the fused silica breadboard (dimensions 45cm x 15cm x 4.1cm).  \n<!-- image -->  \nAs shown in Figure 17, the OMC cavity optics and the output photodiodes are all bonded to a single breadboard of fused silica. This minimizes relative motion between the OMC  output  beam  and  the  diodes,  which  can  otherwise  be  a  source  of  noise.  The breadboard also includes two QPDs for aid in alignment, and multiple beam dumps for scattered light. Two of the OMC mirrors are mounted on PZT actuators for length control of the cavity. The OMC cavity is locked to the AS port beam with a dither scheme: one of the PZTs applies a small modulation to the cavity length at a frequency of several kHz; the  output  detectors  are  demodulated  at  the  dither  frequency,  and  the  resulting  error signal  is  fed  back  to  the  other  PZT  to  maintain  resonance.  For  vibration  isolation,  the whole  breadboard  is  mounted  in  a  two-stage  suspension  that  has  active  damping  and pointing capability. The OMC suspension is mounted in a HAM vacuum chamber on a HAM seismic isolation platform.  \nThe AS port beam is directed into the OMC by three steering optics. These optics provide  mode-matching  to  the  OMC,  and  they  are  mounted  in  active  single-stage suspensions  for  vibration  isolation  and  pointing  control.  There  are  several  possible schemes for alignment optimization and control of the beam into the OMC [45]. A simple method  is  to  dither  the  pointing  direction  of  the  AS  port  beam  using  the  suspended steering optics, and demodulate the OMC transmitted signal at the dither frequencies.  \n4.8.4  Arm length stabilization and lock acquisition. Lock  acquisition  is  the  process  of bringing the interferometer to its  operating  point,  with  all  the  cavities  resonant  so  that power  buildup  is  at  a  maximum.  Advanced  LIGO  implements  a  new  lock  acquisition scheme that incorporates two significant features:  \n- ∞ An arm length stabilization system [46] is used to control the microscopic length of each arm cavity, independently of the other degrees-of-freedom\n- ∞ The  vertex  dual-recycled  Michelson  interferometer  is  initially  locked  with  the third  harmonic  technique  [47]  (3f-technique),  providing  more  robust  control during the acquisition process  \nThe idea of the arm length stabilization  system  (ALS)  is  to  lock  each  arm  cavity individually using a laser mounted behind each end test mass. The arm cavities are then held away from resonance for the main laser light by offsetting the frequency of the end station  ALS  lasers,  relative  to  the  main  laser  frequency.  The  ALS  lasers  are  doubled Nd:YAG lasers, operating at 532 nm to distinguish them from the main laser light; they also have a 1064 nm output which is used to phase (frequency offset) lock them to the main laser light. The test masses have dichroic coatings designed to create a relatively low finesse cavity for 532 nm, with reasonable transmission of 532 nm light to the vertex beamsplitter.  \nIn the vertex, one of the ALS beams is interfered with a doubled sample of the main laser light, and the two ALS beams are interfered with each other (see Figure 18). The former produces a common mode signal that is used to control the frequency of the main laser.  The  latter  produces  a  differential  mode  signal  that  is  used  to  stabilize  the differential arm length.  \nFigure 18 Simplified schematic of the arm length stabilization system.  \n<!-- image -->  \nThe acquisition process is as follows [48]: Each ALS laser is locked to its arm cavity at  532 nm. The ALS common and differential mode loops are then engaged, using the vertex 532 nm heterodyne signals. The common mode frequency difference is set so that the main 1064 nm laser light is about 500 Hz away from resonance in the arm cavities. The  vertex  dual-recycled  Michelson  is  then  locked  using  the  3f-technique.  Next,  the common mode frequency offset is gradually reduced to zero to bring the interferometer to the operating point; this step is the most critical and in fact involves several transitions that  are  fully  described  in  reference  [48].  At  the  operating  point,  all  sensor  signals  are switched over to the low-noise, 1064 nm signals described in section 4.8.1.', '4.9 Calibration': 'The  output  signal  of  the  LIGO  detector  is  a  calibrated  time  series  of  ÒexternalÓ differential  length  variation  between  two  arm  cavities,  reconstructed  from  control  and error  point  signals  of  the  differential  arm  length  servo  by  applying  an  appropriate response function.  \nErrors  in  the  interferometer  response  function  degrade  the  ability  to  detect gravitational waves and the ability to measure source properties of detected signals [49]. Calibration accuracy is naturally more important for source parameter extraction than for detection.  We  have  set  the  calibration  accuracy  requirements  at  5%  in  amplitude  and 16µsec  in  timing,  over  2 σ confidence  levels.  This  is  consistent  with  requirements  for detection of strong binary black-hole signals [49].  \nFigure 19 Schematic of the photon calibration system.  \n<!-- image -->  \nTRANSMITTER  \nThree  different  calibration  methods  are  employed  to  allow  cross-checks  on accuracy: (a) free-swinging Michelson [50]; (b) frequency modulation [51]; (c) photon calibrator [52]. In the free-swinging Michelson method the interferometer laser light is used as the length reference to calibrate Michelson interference fringes as the test masses either  move  freely  or  are  forced  through  several  microns  of  motion.  This  method calibrates  ETM actuation with drive amplitude on the order of 10 -12 m.  The  frequency modulation  method  is  used  with  a  single  resonant  arm  cavity.  In  this  configuration,  a known modulation of the laser frequency calibrates the cavity sensing signal in terms of equivalent length modulation. A simultaneous drive of the ETM actuator (10 -14 m) at a slightly different frequency is then used to derive its actuation calibration.  \nThe photon calibration method uses an auxiliary, power-modulated laser to create displacements via photon recoil off the surface of the ETM (Figure 19). Two beams are used, offset symmetrically from the mirror center. The offset moves elastic deformation caused by the photon pressure away from the location of the main interferometer beam, and the two-beam geometry avoids imposing torque. The laser power is measured with a temperature stabilized InGaAs photodetector mounted on an integrating sphere, which is calibrated  against  a  NIST-calibrated  standard.  The  lasers  are  2  W  continuous-wave, 1047nm  Nd:YLF  lasers.  An  AOM  enables  power  modulation,  up  to  a  peak-to-peak sinusoidal modulation of 1 W, producing an ETM displacement of 10 -16 m-rms at 100 Hz.', '4.10 Physical environmental monitoring': 'To complete each LIGO detector, the interferometers described so far are supplemented with  a  set  of  sensors  to  monitor  the  local  environment  (Figure  20).  Seismometers  and accelerometers measure vibrations of the ground and various interferometer components; microphones monitor acoustic noise at critical locations; magnetometers monitor fields that could couple to the test masses or electronics; and radio receivers monitor RF power around  the  modulation  frequencies.  This  is  an  expanded  version  of  the  environmental monitoring  system  employed  in  initial  LIGO  [53].  These  sensors  are  used  to  detect environmental disturbances that can couple to the gravitational wave channel.  \nFigure 20 Physical environmental monitoring sensors at LLO. The test masses are in the vacuum chambers BSC1/3 (ITMs) and BSC4/5 (ETMs), and the 50/50 beamsplitter is in BSC1.  \n<!-- image -->', '4.11 Controls and data acquisition': 'Many of the subsystems employ real-time digital controls in their functioning; data from other subsystems and channels must be acquired in real-time for archiving and analysis.  \nA  custom  data  acquisition  architecture,  diagrammed  in  Figure  21,  is  implemented  to serve these needs.  \nFigure 21 Schematic of the data acquisition architecture.  \n<!-- image -->  \nInterferometer sensor and actuator signals flow through custom input-output chassis (IOC). Each IOC houses: a 17 slot PCI Express (PCIe) backplane; a timing module that provides  accurate  triggering  at  65536  Hz  and  is  synchronized  with  the  interferometer timing distribution system; a commercial fibre optic PCIe uplink to a real-time control computer. The PCIe slots are populated specifically for each IOC, but primarily contain commercial multi-channel, simultaneous sampling 16-bit analogue-to-digital and 16 and 18-bit  digital-to-analogue  converters  (ADCs  and  DACs).  Custom  anti-alias  and  antiimage filters interface between the ADCs and DACs and the analogue signals. The IOCs and  filters  are  located  in  rooms  separate  from  the  vacuum  chamber  areas  to  mitigate electronic and acoustic interference with sensitive interferometer components.  \nThe real-time control computers are located yet further from the interferometer, in a separate computer room, and are linked via fibre. The computers are commercial, multicore rack mount units, specially selected for compatibility with real-time operation: there must be no uncontrollable system interrupts, and they must be capable of supporting the required number of PCIe modules.  \nThe  system  is  designed  to  support  servo  loop  rates  of  up  to  65536  Hz,  which requires real-time execution to be precise and repeatable to within a few microseconds, and synchronized across the site. To attain this performance, the GPL Linux operating system  is  used  on  the  control  computers,  but  with  a  LIGO  custom  kernel  patch.  This patch allows the isolation of a given CPU core from the Linux system for exclusive use by a real-time control program.  \nSpecific subsystem data acquisition and control programs are created with the aid of a real-time code generator (RCG). The RCG provides a set of custom software modules, as well as support of many MATLAB Simulink parts. Using Simulink as the GUI, code is developed as a graphical model that describes the desired execution sequence. Standard scripts then produce executable software from the model.  \nA key RCG component is the IIR (infinite-impulse response) filter module, which is used to define control transfer functions and channel calibrations. A given control model may contain a few hundred of these modules, each module containing up to 10 secondorder section filters. The system supports reloading of filter coefficients during runtime, so that new filters can be implemented on the fly.  \nReal-time communications between RCG models is provided on several levels: via shared memory for applications running on the same computer; via a PCIe network for computers  located  within  300m  of  each  other;  via  a  reflected  memory  network  for computers 4km apart. One core on each CPU is reserved for a special model known as the I/O processor (IOP). The IOP handles the interfacing to the I/O hardware modules, and  synchronizes  the  user  code  execution  with  the  interferometer  timing  system.  The interferometer timing system [54] distributes a 65536 Hz clock signal to all of the IOCs; this clock is synchronized to Global Positioning System time. Timing is also distributed to  the  front-end  computers,  to  provide  time-stamps  for  real-time  communications between RCG models.  \nThe  control  system  also  uses  the  Experimental  Physics  and  Industrial  Control System (EPICS) software to provide communications between real-time systems and user interfaces. Though not shown in Figure 21, much of the slow controls hardware (switch settings,  slow  readbacks,  etc.)  is  managed  using  an  EtherCAT  (Ethernet  for  Control Automation Technology) system.  \nA custom hierarchical state machine, known as Guardian, manages the global state of  the  interferometers.  Written  in  Python,  Guardian  consists  of  a  distributed  set  of automaton nodes, each handling automation for a distinct sub-domain of the instrument. Each node is loaded with a directed state graph that describes the dynamics of its subdomain. A master manager node at the top of the hierarchy communicates with multiple sub-manager nodes; these in turn communicate with device level nodes at the bottom of the hierarchy, which directly control the instrument through EPICS. Guardian provides automation of interferometer lock acquisition, as well as the subsequent transitioning to low-noise operation.', '5. Outlook': 'Both Advanced LIGO interferometers are currently in the commissioning phase, in which the  lock  acquisition  scheme  is  implemented  and  the  strain  sensitivity  is  progressively improved.  When  the  sensitivity  reaches  an  astrophysically  significant  level,  the instruments  will  be  operated  in  observing  runs:  months-  to  years-long  periods  of  \ncontinuous  and  coincident  data  collection.  The  first  Advanced  LIGO  observing  run  is planned to begin in 2015, with a duration of 3 months and a BNS detection range of 40Ñ 80  Mpc.  Subsequent  observing  runs  will  have  increasing  sensitivity  and  duration.  We anticipate a 6 month run in 2016-2017 with a BNS detection range of 80Ñ120 Mpc, and a 9 month run in 2017-2018 at 120Ñ170 Mpc. The full sensitivity corresponding to a 200 Mpc BNS range should be achieved by 2019.', 'Acknowledgements': "The authors  gratefully  acknowledge  the  support  of  the  United  States  National  Science Foundation for the construction and operation of the LIGO Laboratory and the Science and Technology Facilities Council of the United Kingdom, the Max-Planck-Society, and the State of Niedersachsen/Germany for support of the construction and operation of the GEO600 detector. The authors also gratefully acknowledge the support of the research by these  agencies  and  by  the  Australian  Research  Council,  the  International  Science Linkages  program  of  the  Commonwealth  of  Australia,  the  Council  of  Scientific  and Industrial  Research  of  India,  the  Istituto  Nazionale  di  Fisica  Nucleare  of  Italy,  the Spanish Ministerio de Econom'a y Competitividad, the Conselleria d'Economia, Hisenda i  Innovaci- of the Govern de les Illes Balears, the Royal Society, the Scottish Funding Council, the Scottish Universities Physics Alliance, The National Aeronautics and Space Administration, OTKA of Hungary, the National Research Foundation of Korea, Industry Canada and the Province of Ontario through the Ministry of Economic Development and Innovation,  the  National  Science  and  Engineering  Research  Council  Canada,  the Carnegie  Trust,  the  Leverhulme  Trust,  the  David  and  Lucile  Packard  Foundation,  the Research  Corporation,  and  the  Alfred  P.  Sloan  Foundation.  This  article  has  LIGO document number LIGO-P1400177.", 'References': '- [1] Abbott B et al 2009 Rep. Prog. Phys. 72 076901\n- [2] Fricke T et al 2012 Class. Quantum Grav. 29 065005\n- [3] The LIGO Scientific Collaboration & the Virgo Collaboration 2009 Nature 460 990 Aasi J et al (The LIGO Scientific Collaboration and the Virgo Collaboration) 2014 ApJ 785 119\n- Abadie J et al (LIGO Scientific Collaboration, Virgo Collaboration) 2012 Phys Rev D 85 082002\n- Abadie J et al (LIGO Scientific Collaboration, Virgo Collaboration) 2012 Phys Rev D 85 122007\n- [4] Abadie J et al 2010 Class. Quantum Grav. 27 173001\n- [5] Veitch J, Mandel I, Aylott B, Farr B, Raymond V, Rodriguez C, van der Sluys M, Kalogera V and Vecchio A 2012 Phys. Rev. D 85 104045\n- [6] Meers B J 1988 Phys. Rev. D 38 2317\n- [7] Sidles J and Sigg D 2006 Phys. Lett. A 354 167\n- [8] Arain M A and Mueller G 2008 Optics Express 16 10018\n- [9] Buonanno A, Chen Y and Mavalvala N 2003 Phys. Rev. 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