Jitter (alog 30237): 10-6/√Hz (level) to n x 10-4/√Hz (peaks)
IMC suppression (alog 30124): ~1⁄200
⇒ at IFO: 5 x 10-9/√Hz to n⁄2 x 10-6/√Hz
Fixed misalignment of RF sidebands: Δα < 0.3
DC power in reflection with unlocked ifo at 50W: REFLDCunlocked ~ 300 mW
Error offset in REFL = jitter * REFLDCunlocked * Δα
⇒ 5 x 10-9/√Hz * 0.3 W * 0.1 ~ 1.5 x 10-10 W/√Hz (low)
⇒ n⁄2 x 10-6/√Hz * 0.3 W * 0.3 ~ n⁄2 x 10-7/√Hz (high)
Frequency noise coupling into DARM (alog 29893):
⇒10-10 m/W at 1kHz (approx. f-slope)
at 1kHz: 10-20 m to 10-17 m
at 300 Hz: n x 10-18 m (high) with periscope peak n ~ 4.
This seems at least a plausible coupling mechanism to explain our excess jitter noise.
Some additional comments:
This calculation estimates the jitter noise at the input to the ifo by forward propagating the measured jitter into the IMC. It then assumes a jitter coupling in reflection that mixes the carrier jitter with a RF sideband TEM10 mode due to misalignment. The corresponding RF signal would be an error point offset in the frequency suppression servo, so it would be added to the frequency noise. Finally, we are using the frequency noise to OMC DCPD coupling function to estimate how much would show up in DARM.
If this is the main jitter coupling path, it will show up in POP9I as long as it is above the shot noise. Indeed, alog 30610 shows the POP9I inferred frequency noise (out-of-loop) more than an order of magnitude above the one inferred from REFL9I (in-loop) at 100Hz. It isn't large enough to explain the noise visible in DARM. However, it is not far below the expected level for 50W shot noise.