As part of Wednesday's commissioning excercises, we looked at the coupling of input jitter into DARM.
I injected band-limited white noise into IM3 pitch (and then IM3 yaw) until I saw a rise in the noise floor of DARM.
We can use the IM4 QPD as an estimate of the amount of jitter on the interferometer's S port. On the AS port side, we can use the OMC QPDs as an estimate of the AS port jitter, and DCPD sum indicates the amount of S port jitter coupling into DARM.
One thing of note is that the jitter coupling from IM3 to DARM is mostly linear, and more or less flat from 30 to 200 Hz:
- For the pitch excitation, at 100 Hz the IM4 pitch ASD was 3.1×10−7 ct/rtHz, the measured TF was 1.0 mA/ct, and the observed IM3-induced DARM noise was sqrt[3.72 − 1.72]×10−7 mA/rtHz = 3.3×10−7 mA/rtHz. Numbers hang together.
- For the yaw excitation, at 100 Hz the IM4 yaw ASD was 1.6×10−7 ct/rtHz, the measured TF was 5 mA/ct, and the observed IM3-induced DARM noise was sqrt[8.22 − 1.72]×10−7 mA/rtHz = 8.0×10−7 mA/rtHz. Numbers hang together.
The upper limit on IM3 jitter that one can place using the IM4 QPD seems to be weak. At 40 Hz, projecting the quiescent level of the IM4 yaw signal to the DCPD sum suggests a jitter noise of 2×10−7 mA/rtHz, but this is obviously not supported by the (essentially zero) coherence between IM4 yaw and DCPD sum during low-noise lock. Of course, this does not rule out a nonlinear coupling.
As for AS port jitter, the coupling is seen more strongly in OMC QPD B than OMC QPD A.
The test excitation for yaw was 6 ct/Hz1/2 at 100 Hz.
We can propagate this to suspension angle as follows:
- Euler to OSEM matrix is (0.25 / L) ct/ct, where L is the lever arm that the coils act over.
- DAC gain is 20 V / 218 ct.
- Factor of 4×L (four coils providing torque, L is again the lever arm of the coils).
- Driver transimpedance of 1.0×10−3 A/V.
- Coil actuation strength of 0.016 N/V.
- This gives TF of 1.2×10−9 (N m)/ct.
- From the suspension model, the compliance at 100 Hz is 0.010 rad/(N m).
This gives 73 prad/Hz1/2 of yaw excitation at 100 Hz, which implies a DCPD coupling of 550 RIN/rad at 100 Hz.
Repeating the same computation for pitch [where the excitation was about 10 ct/Hz1/2 at 100 Hz, and the compliance at 100 Hz is 0.012 rad/(N m)] gives a pitch excitation of 140 prad/Hz1/2, which implies a DCPD coupling of 130 RIN/rad at 100 Hz. So the IM3 yaw coupling into DARM is a factor of 4 or so higher than the IM3 pitch coupling.
These excitations amount to >100 µV/Hz1/2 out of the DAC. Unless the IMs' electronics chains have an outrageous amount of input-referred noise, it seems unlikely that electronics-induced IM jitter is anywhere close to the DARM noise floor. Additionally, the seismically-induced motion of IM3 must be very low: projections of the HAM2 table motion suggest an IM3 suspension point motion of 10 prad/Hz1/2, and this motion will be filtered by the mechanical response of the suspensions before reaching the optics.
