Some days ago, I had tried to measure the SRCL->MICH and PRCL->MICH cross couplings using broadband noise injected between 120-180 Hz, a frequency band chosen arbitrarily, in hindsight, I could have done a more broadband test. I've spent some time including the infrastructure to calculate "White-Noise TFs" in the noise budgeting code, where a transfer function is estimated by injecting a "broadband" excitation into a channel of interest, and looking at the resulting response in MICH. I figured this would be useful to estimate other couplings as well, e.g. laser intensity nosie, oscillator noise etc.
I estimate the transfer function of the coupling using the relation (MICH is the median ASD of the MICH error signal in the below expression, and similarly for PRCL)

Attachments #1 and #2 show the spectra of the MICH, PRCL and SRCL signals during 'quiet' times and during the injection, while Attachment #3 shows the calculated coupling TFs using the above relation. These are significantly different (more than 10dB lower) than the numbers I reported in elog 13367, where the measurement was made using swept sine. As can be seen in the attached plots, the injected broadband excitation is visible above the nominal noise level, and I calculated the white noise TFs using ~5mins of data which should be plenty, so I'm not sure atm what to make of the answers from swept-sine and broadband injections being so different.
Attachment #4 shows the noise budget from the October 8 DRMI lock with the updated SRCL->MICH and PRCL->MICH couplings (assumed flat, extrapolated from Attachment #2 in the 120-180Hz band). If these updated coupling numbers are to be believed, then there is still some unexplained noise around 100Hz before we hit the PD dark noise. To be investigated. But if Attachment #4 is to be believed, it is not surprising that there isn't significant coherence between SRCL/PRCL and MICH around 100Hz.
Nov 8 1600: Updating NB to inculde estimated Oplev A2L.
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AUX coupling
This is the other find.
- While chatting with Gabriele, he suggested measuring the SRCL->MICH and PRCL->MICH cross couplings.
- I injected a signal in SRCL servo EXC channel, and adjusted amplitude till coherence in MICH_IN1 was good.
- The actual TF measured was MICH_IN1 / SRCL_IN1 (so units of cts/ct).
- My multiplying the in-lock PRCL and SRCL IN1 signals by these coupling coefficients (assumed flat in frequency for now, note that measurement was only made between 100Hz and 1kHz), I get the trace labelled "AUX coupling" in Attachment #1 (this is the quadrature sum for SRCL and PRCL couplings).
- Also repeated for PRCL -> MICH coupling in the same way.
- Measurements of these TFs and coherence are shown in Attachment #5 (again png screenshot because of DTT).
- However, there is no significant coherence in MICH/SRCL or MICH/PRCL in this frequency range.
This seems to be limiting us from saturating the dark noise once the coil de-whitening is engaged. But lack of coherence means the mechanism is not re-injection of SRCL/PRCL sensing noise? Need to think about what this means / how we can mitigate it.
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