The strain seen by an interferometric GW detector depends on the orientation of the detector with respect to the source as well as the polarization of the incoming GWs. The following equation projects the effect of the different polarizations onto the plane of the detector:
h(t+t0) =F+(θ, φ, ψ, t+t0)h+(ι,Σ, t+tc) +F×(θ, φ, ψ, t+t0)h×(ι,Σ, t+tc), (3.2)
Table 3.1: A non-comprehensive list of various auxiliary channels recorded by components in the LIGO de- tectors
Channel name Description
LSC-{MICH,PRC,DARM,CARM}CTRL 16384-Hz channels recording the information used to control the Michelson, power-recycling cavity, and differential and common arm length degrees of freedom.
LSC-DARM ERR A 16384-Hz channel recording the error signal for the con-
trol loop associated with the GW signal and described in Sec- tion 3.3.
LSC-REFL{I,Q} 8192- (in-phase) and 4096- (quad-phase) Hz channels moni-
toring the light coming back through the symmetric port, mea- sured by RF photodiodes in the Faraday isolator. See Fig- ure 3.10.
ASC-{E,I}TM{X,Y} {P,Y} 512-Hz angular torque feedback control signals for pitch and yaw of the X and Y ETMs and ITMs.
ASC-QPD{X,Y} {P,Y} 256-Hz channels measuring the beam position on the X and Y
ETMs.
ASC-WFS{1,2,3,4} {Q,I} {P,Y} 512-Hz channels measuring the in-phase and quadrature read- out of the alignment of the beam with respect to detector’s cav- ities. How the WFSs align to the different optical cavities is beyond the scope of this thesis.
OMC-QPD{1,2,3,4} {P,Y,SUM}OUT DAQ 4096-Hz (for QPD{1,2}and 2048-Hz (for QPD{3,4}) chan- nels measuring the pitch, yaw, and sum motion of the OMC mirrors. The pitch, yaw, and sum can be derived from the four quadrants of the photodiode: PITCH = (UL+UR)-(LL+LR), YAW = (UL+LL)-(UR+LR), SUM = (UL+UR+LL+LR);
where the quadrants are labeled by upper, lower, left, and right.
PEM-E{X,Y}SEIS{X,Y,Z} 256-Hz channels recording seismic activity in the X,Y, and Z directions at the X and Y end stations.
PEM-LVEA MAG{X,Y,Z} 2048-Hz channels recording magnetic fields in the X, Y, and Z directions in the laser and vacuum enclosure area at the vertex of the interferometer.
PEM-RADIO LVEA 2048-Hz channels recording information from a radio receiver
in the laser and vacuum enclosure area at the vertex of the in- terferometer.
PEM-{PSL1,BSC1,BSC3,HAM3,HAM6,LVEA,ISCT}MIC 2048-Hz channels recording audio noise in various places around the detector; see Figure 3.7 for their locations, but the areas on the detector are labeled in Figure 3.10.
SEI-{ITMX,ITMY,ETMX,ETMY,BS,RM} {X,Y,Z} 256-Hz channels recording seismic activity in the X, Y, and Z directions from seismometers near various optics inside the vacuum system .
SEI-OUT{X,Y} 256-Hz channels recording the output of the control system for
active seismic isolation in the X and Y direction.
SUS-{ITMX,ITMY,ETMX,ETMY,BS,RM}SUS{PITCH,YAW}IN 64-Hz channels recording the pitch and yaw of various optics.
SUS-{ITMX,ITMY,ETMX,ETMY,BS,RM}OPLEV{P,Y}ERROR 512-Hz channels containing the error signal for the SUS con- trol system for the pitch and yaw of various optics.
SUS-{ITMX,ITMY,ETMX,ETMY} {LL,LR,UL,UR}COIL OUTPUT 16 Hz channels containing the values of the currents in the coils used to control mirror positions.
Environmental Influences on LIGO Detectors in S6
425
Fig. 2. The Physical Environmental Monitoring system layout at the LIGO Livingston detector during S6. The setup for LIGO Hanford was very similar. Shaded regions indicate the vacuum enclosure. Circles and rectangles indicate vacuum chambers where mirrors were suspended. Optical tables were surrounded by acoustic enclosures but were not in vacuum.
Type Sensor Operating Frequency
seismometer Guralp
�R0.1-20 Hz
accelerometer Wilcoxon
�R731-207 1-900 Hz microphone Br ¨uel&Kjaer
�R4130 15-900 Hz magnetometer Bartington
�R03CES100 0-900 Hz
radio station AOR
�RAR5000A tunable
Table 1. The more important PEM sensor types and the frequency ranges in which they are used. The frequency range is a combination of sensor calibration range from the manufacturer and the sampling rate at which they are recorded.
Figure 3.7: A diagram depicting the locations of physical environmental sensor locations at L1. Figure courtesy of Annamaria Effler.
whereF+ andF× are the antenna pattern factors of a specific detector. They depend on time since the detectors are on the Earth, which is rotating with respect to celestial coordinates. t0is the average time the coalescing signal reaches the rotating detector andtcis the time the system coalesces at the center of the Earth (a fiducial location common to all detectors, makingt0−tc the propagation time from the detector to the center of the Earth.Σcontains all the other parameters in the waveform (see, for example, Equation (2.16)).
In order to define the angles, we must set up three coordinate systems — see Figure 3.11. The inclination angleι is the polar angle between the source frame’s z-axis (for CBCs, this is the direction of the orbital angular momentum) and the detector’s z’-axis (roughly, the local zenith). The polarization angleψ is the azimuthal angle from the detector’s x’-axis to the GW’s x”-axis. (Note that the terminology is a bit confusing here — the inclination angle determines the polarization content of the GW, while the polarization angle determines the angle between the stretch-squeeze in theh+wave and the axes of the arms of the detector).
θis the polar angle between the detector’s z’-axis and the GW’s z”-axis (the direction of propagation of the GW). φis the azimuthal angle between the x’-axis and the projection of the z”-axis onto the x’-y’ plane.
Figure 3.8: A representation of the seismic isolation stack for one of the suspended optics. Inside the dashed line is the vacuum system. The isolation stack provides passive isolation and the sensor and actuator are used to provide active seismic isolation in the x- and y-directions [9].
Figure 3.9: A representation of the output mode cleaner optical setup [10].
Using these definitions, the antenna pattern factors can be expressed as [42]:
F+= 1
2(1 + cos2θ) cos 2ϕcos 2ψ−cosθsin 2ϕsin 2ψ (3.3) and
F×= 1
2(1 + cos2θ) cos 2ϕsin 2ψ+ cosθsin 2ϕcos 2ψ. (3.4) We can average over all polarization angles, since these should be independent of the direction of arrival,
WFS 3 WFS 4 REFL 1
REFL 2 REFL CAM MCWFS 1MCWFS 2MC REFL CAM
WFS 2 WFS 1
ASPD 5
POX SPOB
POB AS CAM
IFI SM MMT1
MMT3 IMC1
IMC3
IMC2 MMT2
PRM
BS
ITMX ETMX
ITMY ETMY QPDY
TRANS PD Y
TRANS PD X QPDX
QPD4 QPD3 QPD2
OFI
QPD1 TT1
TT0
TT2 DCPD1DCPD2
OMC TRANS CAM
HAM 1 HAM 2 HAM 3
HAM 4
TRGR PD
HAM 6 BSC 1
BSC 2 BSC 3 BSC 4
BSC 5
IOT 1 ISCT 1
ISCT 4 4 km 4 km
Jeffrey S. Kissel LIGO-G0900777-v5
Approx. Radii of Curvature (m) MC2 17 MMT1 7 MMT2 3 MMT3 25 RM (HR) 16000 ITMs (HR) 15000 ETMs 9000 TT1 5 M2 2 M4 2 (Unspecified optics are flat)
M1
M2 M3
M4 Approx. Distances (m)
MMT1 to MMT2 14 MMT2 to MMT3 14 MMT3 to RM 16 RM to BS 4 BS to ITMs 5 ITMs to ETMs 4000 BS to TT0 24 TT0 to TT1 1 TT1 to TT2 2 TT2 to OMC 0.3
L1's Enhanced LIGO Optical Layout
Optics (Fused Silica) Laser Light (! = 1064e-9 m)
RF Photo Diode DC Photo Diode Faraday Isolator
IR Camera
RF Wave Front Sensor DC Quadrant Photodiode Shutter
High-power Beam Dump
Important Notes
- THIS DRAWING IS NOT TO SCALE, and HAM5 is not shown because it contains no optics in enhanced LIGO.
- Several important optics (specifically lenses on ISCT tables) have been left out of this diagram for simplicity.
- The optical layout of the ISCT Tables frequently changes and thus it is possible (if not probable) that their layout is only roughly correct.
- The quoted radii of curvature and distances are merely for rough scaling and are not to the accuracy needed for anything more precise than a ballpark calculation.
Light from PSL
Relevant Acronymns
HAM - Horizontal Access Module PRM (or RM) - Power Recycling Mirror BSC - Beam Splitter Chamber BS - Beam Splitter
PSL - Pre-Stablized Laser ITM - Input Test Mass SM - Steering Mirror ETM - End Test Mass IMC (or MC) - Input Mode Cleaner BRT - Beam Reducing Telescope MMT - Mode Matching Telescope WFS - Wave Front Sensor IFI - Input Faraday Isolator AS - Anti-Symmetric port REFL - Reflected Light TRANS - Transmitted Light IOT - Input Optics Table TT - Tip Tilt (Telescope) ISCT - Interferometer Sensing and Control Table OMC - Output Mode Cleaner (S)PO(B,X) - (Sideband) Pick Off (Beamsplitter, itmX) QPD - Quad Photo Diode
BRT2 BRT1
Figure 3.10: A diagram depicting the locations of various optical components and the auxiliary channels recording information from/about them. Figure courtesy of Jeff Kissel.
and calculate the mean square response of the detector as
F2= Z
F+2dψ= 1
4(1 + cos2θ)2cos22ϕ+ cos2θsin22ϕ (3.5)
=F+2(θ, ϕ, ψ= 0) +F×2(θ, ϕ, ψ= 0), (3.6) which is visualized in Figure 3.12.