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
3.4.4 DARM loop characterization
The DARM feedback loop is responsible for suppressing differential changes in the lengths of the two arm cavities, due to environmental disturbances, to a level well below the DARM linewidth, which is ≈ 1.2 nm for the 40m in the PRFPMI configuration11. If theresidual (i.e. under closed loop feedback control ) DARM motion were significantly larger than the DARM linewidth, then the PDH error signal response at the AS55 photodiode will no longer remain linear, and hence,
10The CARM linewidth is strongly dependent on the losses in the interferometer. The quoted number is assuming an average round-trip arm cavity loss of 50 ppm and≈2% losses in the PRC (on accounted of the flipped folding mirrors, see AppendixD.2). Once new optics are installed in the interferometer vertex to solve the geometric instability problems (see AppendixD.3), the CARM linewidth is expected to decrease to≈15 pm.
11In the dual-recycled configuration, the linewidth is≈45 nm in the Resonant Sideband Extrac- tion tuning of the SRC, and ≈ 36 pm in the Signal Recycled tuning of the SRC. For measuring Ponderomotive squeezing, the SRC tuning will bevery close toSignal Recycled, which will have to be taken into account when designing the DARM control loop for that configuration.
LSC signal conditioning
5.1 V/V REFL11 PD
TIA
Demodulator + IF amplifier
AA ADC DAA CM_SLOW CARM_B
MC2 CARM Violins DAI
DAC MC2 AI
dewhite MC2
suspension +0 dB Analog whitening
board
+4 dB CM board IN1 gain
Boost AO path HPF
CM_SLOW (TP2A)
+0 dB CM board
AO gain
IMC error point [m/V]
[m/V]
[W/m]
CM_SLOW
CDS system CM board
A2D, D2A
MC2 coil drive
TP1A EXC A
IN1 EXC IN2
Figure 3.13: Common mode servo topology. The REFL11 photodiode senses fluctuations in CARM. This error signal is then split into two feedback paths. One uses the suspended MC2 mirror as a frequency actuator - it modifies the length of the IMC cavity, and the high bandwidth (≈100 kHz UGF) IMC servo then ensures that the PSL frequency is modified to keep the beam resonant in the IMC, and hence, matched to CARM. The bandwidth of this path is ≈ 150 Hz, limited by delays in the digital feedback system and the mechanical susceptibility of the suspended MC2 mirror. The second path modifies the error point of the IMC servo, thereby modifying the PSL frequency (with the total RMS frequency actuation being much less than the IMC linewidth of ≈ 7.6 kHz). This path allows higher bandwidth control - the transfer function from modifying the IMC servo error point to the laser frequency is flat up to≈30 kHz.
the interferometer cannot be kept at its operating point using the linear feedback loops available. This requirement can be satisfied by a purely digital feedback loop - unlike the CARM loop, parallel low and high bandwidth feedback paths are not required. As with all of the interferometer feedback loops, implementing them as digital filters (as opposed to analog electronic filters) means that the frequency response of the servo filter can be easily changed simply by recompiling a piece of C-code (as opposed to having to change various analog electronic components).
As was the case with the CARM loop, the DARM loop was characterized using techniques described in AppendixB.2. The results are summarized in Figure3.16.
The measured DARM loop had a bandwidth of ≈ 150 Hz and a phase margin of
≈30◦. This loop design allowed the interferometer to remain locked for several tens of minutes at a time, permitting other characterization activities to be carried out,
-100 -50 0 50 100 150 200
Magnitude[dB] Slow path
Fast path
100 101 102 103 104 105
Frequency [Hz]
-180 -135135180-90-4545900
Phase[deg]
(a)
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Magnitude[dB] Before handoff
IN2 ramped Pre-boost Final
100 101 102 103 104 105
Frequency [Hz]
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Phase[deg]
(b)
Figure 3.14: Models of the CARM feedback loop. Figure3.14(a)shows the transfer functions of the two paths - the "Slow path" involves the digital feedback system and uses the IMC length as a frequency actuator. Due to delays and the mechanical susceptibility of the suspended optic, this loop is limited to a bandwidth of≈ 100 Hz.
The "Fast path" actuates on the PSL frequency by modifying the IMC servo’s error point - this path allows higher bandwidth, with the overall loop UGF being≈ 12 kHz.
In the lock acquisition process, the CARM loop is continually modified, first to facilitate smooth transition between ALS and RF control paths, and finally, to have very large DC gain for effective suppression of laser frequency noise. This evolution is shown in Figure3.14(b).
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Magnitude [dB]
ModelMeasurement100 101 102 103 104 105
Frequency [Hz]
-180 -135 -90 -450 45 90 135 180
Phase [deg]
(a)
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Magnitude [dB]
ModelMeasurement100 101 102 103 104 105
Frequency [Hz]
-180 -135 -90 -45 0 45 90 135 180
Phase [deg]
(b)
Figure 3.15: Measurements of the CARM feedback loop. For the overall OLTF shown in Figure3.15(a), a signal is injected at "EXC A" and the loop OLTF is given by the ratio TP1ATP2A. In Figure3.15(b)a signal is injected at "EXC" in the CDS system and the crossover transfer function is read out as IN1IN2 (see Figure3.13for the signal injection and readback points). The measurement cannot be done over the full range of modelled frequencies for the reasons described in AppendixB.2. Nevertheless, the overall gain and delay of the model can be fit to the measurement.
but was not optimized to yield the best possible noise performance - to improve the sensitivity to DARM displacement, the frequency response of this loop will likely have to be modified. In Figure3.16(a), the overallmodelled gain scaling and time delay in the loop are left as free parameters, which are then fit to match the measured data. The measurement does not extend over the full frequency range plotted for the reasons described in AppendixB.2. Nevertheless, the model and measurement do agree in the region where they overlap, giving confidence in the accuracy of the model.