ITMXPRM
3.4 Power-Recycled Fabry-Pérot Michelson Interferometer (PRFPMI) This configuration is simpler to lock and control, (because there is one less lengthThis configuration is simpler to lock and control, (because there is one less length
3.4.8 Angular sensing and control (ASC)
The high circulating laser power in the IFO’s Fabry-Pérot arm cavities couple the motion of the two constituent mirrors due to radiation pressure. In particular, the angular models of the ITM and ETM, which in the absence of radiation pressure are defined purely by the mechanical susceptibility of the pendulums they are suspended on, get modified and coupled. For sufficiently high powers, one of these coupled eigenmodes of the cavity become open-loop unstable (see for example Equations 5-16 and 5-17 of [46]), necessitating a feedback loop to maintain a locked IFO.
0°
45°
90°
135°
180°
225°
270° 315°
2 4 6 8
REFL11
0°
45°
90°
135°
180°
225°
270° 315°
2 4 6 8
REFL55
0°
45°
90°
135°
180°
225°
270° 315°
2 4 6 8
REFL33
0°
45°
90°
135°
180°
225°
270° 315°
2 4 6 8
REFL165
0°
45°
90°
135°
180°
225°
270° 315°
2 4 6 8
AS55
PD Wht Gain [dB] [ ] Z [ ] VVRFIF
REFL11 18 -162 400 0.55
REFL55 18 -16 420 4.88
REFL33 30 10 2000 0.27
REFL165 24 -59 1000 0.31
AS55 0 -122 300 5.35
DoF Actuator DC gain [m/ct] fexc [Hz]
MICH BS 9.48e-09 311.1
PRCL PRM 1.078e-08 313.31
CARM MC2 1.404e-08 309.21
DARM ETMX 1.23e-09 307.88
Radial axes are log10(mag).
Units are [W/m] (0.85A/W for InGaAs).
Uncertainties multiplied by 10.
PD IPD Q MICH
PRCL CARM
DARM
Figure 3.21: Sensing matrix in PRFPMI lock. This measurement is from a 5- minute stretch of data, segmented into 10-second long sections for some statistical averaging. Shaded ellipses around the tips of the stems are indicative of the statistical uncertainty from the 30 samples. Two demodulated quadratures per photodiode are indicated - their naming is arbitrary, but the convention is to orient (i.e. define) the quadratures, by adjusting a digital demodulation phase, such that "Common"
interferometer DoFs like CARM and PRCL produce a response in the "I" quadrature, while "Differential" DoFs like MICH and DARM produce a response in the "Q"
quadrature. The reflected beam from the IFO isnotequally split among the REFL photodiodes, which has to be taken into account when comparing the measurement to numerical simulations.
For the geometry of the 40m arm cavity, this critical power level is ≈ 3.5 kW12. While there is some uncertainty, it is estimated that the circulating power in the arm cavities is limited to≈ 2−2.5 kW13 due to the excess losses in the PRC. Therefore,
12This effect applies to the IMC as well - for the cavity geometry, with the input and output couplers being flat and the folding mirror having an RoC of≈18.4 m, the critical circulating power is estimated to be≈11.2 kW. Since the power gain of the cavity is≈500, angular instabilities are not expected for input powers less than 20 W into the IMC
13Interestingly, this makes the power-to-mass ratio at the 40m, with 250 g mirrors, comparable to that in the aLIGO interferometers at Hanford and Livingston, with≈200 kW circulating in the arm cavities whose mirrors weigh 40 kg. However, the classical noise levels at the 40m are also much higher than at the LIGO sites, making it much more difficult to probe optomechanical effects and noise evasion schemes, like in [47].
the IFO is not yet in the regime of dynamical angular instability, though planned upgrades for the Ponderomotive Squeezing measurement experiment will certainly push it over the threshold. Even so, implementing feedback loops to stabilize the angular positions of the various optics allows higher and more stable power buildup in the IFO (see after "H" in Figure3.12), which in turn improves DARM sensitivity.
For the inital phase of work presented in this chapter, a very rudimentary ASC scheme was implemented. Error signals were derived from single QPDs monitoring the transmitted beam from each arm cavity, and after an appropriate basis change to go from the X-arm and Y-arm basis to the "Common" and "Differential" basis and filtering, the control signal was fed back to the ETMs. The ITMs had their angular positions controlled by a different strategy - their Oplev loops were DC-coupled, so the spot positions on the Oplev QPDs were deemed a good enough reference.
This scheme is almost certainly sub-optimal - where possible, we should always be using interferometric signals in favor of local sensors like the Oplev. However, this feedback scheme allowed the interferometer to remain locked for a few tens of minutes at a time, which was deemed sufficient. Neither the cross-couplings between the Oplev based and Transmon QPD based ASC servos, nor the coupling to the DARM error point due to A2L, were characterized. The feedback loops had a bandwidth of≈10 Hz - with a low-frequency boost implemented, the loop shape was able to effectively suppress angular fluctuations in the 0.5−3 Hz band, which makes the dominant contribution to RMS angular motion. Angular fluctuations in the PRC also degrade the power buildup in the arm cavities. As mentioned in Section 3.2.2, seismometer-based feedforward control was able to stabilize the buildup in the PRC. These loops were left engaged during the PRFPMI lock. A single QPD is also available at the POP port of the IFO. However, it is not a good candidate sensor to stabilize PRC angular motion with a feedback loop, as the ITM and ETM produce much larger signals in the POP QPD. Thesimulated sensitivity of the available angular sensors at the 40m to motion of various suspended optics is summarized in Figure3.22. These could be validated against measurements using the same technique as in Section3.4.7- efforts to do so were hampered by lock losses when the measuring excitations were injected. While this could have indicated some instabilities in the ASC loops implemented, a more detailed characterization of the ASC system was deferred for future work.
The preferred technique of stabilizing angular motion in a locked interferometer is to use Wavefront Sensors (WFS). These detect angular misalignment by measuring
10−3 10−1 101 103 105 107
Mag[W/N/m]
POP QPD
PRM PR2HR PR3HR
ITM ETM
TR QPD
10−1 100 101 102
Frequency [Hz]
-180 -135 -90 -45 0 45 90 135 180
Phase[deg]
10−1 100 101 102
Frequency [Hz]
Figure 3.22: Sensing responses of the available angular sensors to torques on various suspended optics. Although only a single column is included for the "TR QPD", it is understood that there is an individual TR QPD monitoring the transmission of eacharm cavity.
(on a QPD) the beat between the TEM00 spatial mode of an LO field either at the carrier frequency or one of the PM sideband frequencies f1,2, and TEM01or TEM10 spatial modes at the other frequency, which get generated due to misalignment [48]. Note that the error signal generated from a WFS QPD is at an RF frequency offset from the carrier, unlike the signal generated on a DC QPD, and therefore, must be electrically demodulated like PDH error signals to pick out the quadrature signal that has maximum sensitivity to the angular motions we are trying to sense.
Polluting noise sources such as laser RIN or electronics noise are typically much lower at RF frequencies than at DC, making WFS a lower noise sensor than their DC QPD counterparts. However, they are also much more complex systems, consuming significant commissioning time to implement correctly. For the data presented in this chapter, there was no WFS available to sense fields from the IFO. A single WFS has recently been installed at the AS port of the IFO, and has been verified to work correctly from an electrical standpoint. However, it has still not been used for any angular stabilization of the interferometer.