Summary:

I spent this weekend doing a more careful investigation of the DRMI noise. I think I have some new information/insights. Attachment #1 is the noise budget (png attached because pdf takes forever to upload, probably some ImageMagick problem. The last attachment is a tarball of the PDF). Long elog, so here are the Highlights:

1. Coil de-whitening does result in small improvement in noise in the 60-200Hz band.
2. Above 200Hz, we seem to be limited by "Dark" noise. More on this below.
3. The coupling from SRCL->MICH is the other limiting noise in the 60-200Hz band now.

Sensing Matrix Measurement:

• I rotated the AS55 demod phase from -42 degrees to -82 degrees, the idea being to get more of the MICH error signal in AS55_Q.
• Consequently, the MICH servo gain has been lowered from -0.035 to -0.021. Settings have been updated in the snap file used by the locking script.  
• Seems to have worked.
• Attachment #2 is the measured sensing elements.
• One major source of uncertainty in these sensing element numbers is the actuator gains for PRM, SRM and BS. The coil driver electronics for the latter two have been modified recently, and for them, I am using numbers from this elog scaled by the expected factor as a result of removing the x3 gain in the de-whitening boards for SRM and BS.

MICH OLTF

• Measurement was done in lock using the usual IN1/IN2 method.
• Model made by loading the FOTON filters + assumed models for the BS pendulum and AA/AI filters in Matlab, and fitting to an overall gain + delay.
• Attachment #3 shows the agreement between measurement and model.
• The model was exported and used to invert in-loop signals to their out-of-loop counterparts in the noise budget.

DAC Noise

• I had claimed that turning on the coil de-whitening did not improve the MICH noise.
• This was not exactly true - I had only compared MICH noise with the BS de-whitening turned ON/OFF, while the ITM de-whitening was always on.
• Turns out that there is in fact a small improvement - see Attachment #4 (DTT crashes everytime I try to print a pdf, so png screenshot will have to do for now).
• I have also changed the way in which DAC noise is plotted in the Noise Budget code:
  • I used to directly convert the measured voltage noise (multiplied by appropriate scalar to account for quadrature sum of 4 coils each in 3 optics) to displacement noise using the sensing measurement cts/m values.
  • Now I convert the measured voltage noise first to current noise (knowing the series resistance), then to force noise (using the number 0.016 N/A per coil), then to displacement noise (assuming a mirror mas of 250g).
  • Quadrature sum is again taken for 4 coils on 3 optics.
• I've also added the option to plot the DAC noise with the de-whitening filter TF applied (taking care that the maximum of filtered DAC noise / coil driver electronics noise is used at each frequency).
• So the major source of uncertainty in the calculated DAC noise is the assumed actuator gain of 0.016 N/A.

The DAC noise is not limiting us anywhere when the coil de-whitening is switched on.

Dark Noise

I think this is the major find.

• The dark noise spectrum is measured with:
  • the PSL shutter closed
  • the AS55 I and Q analog whitening filters (and corresponding digital de-whitening filters) engaged, to mimic the operating conditions under which the in-lock error signal is acquired.
• Comparing the blue and black traces, it is clear that turning on the analog whitening is having some effect on the dark noise.
• However, the analog whitening filters should suppress the ADC noise by ~30dB @ 100Hz - so assuming 1uV/rtHz, this would be ~30nV/rtHz @100Hz.
• But the measured noise seems to be ~5x higher, with 4*10^-4 cts/rtHz translating to roughly 120nV/rtHz.
• The photodiode dark noise is only 15nV/rtHz according to the wiki. Where is this measured?

So I don't understand the measured Dark Noise level, and it is limiting us at frequencies > 200Hz. Some busted electronics in the input signal chain? Or can the LSC demod daughter board gain of ~5 explain the observed noise?

Shot noise

• The DC power on AS55 photodiode was measured to be ~13mW with the SRM misaligned.
• This corresponds to ~100cts peak amplitude on the ASDC channel (derived from AS55 photodiode).
• In the DRMI lock, the ASDC level is ~200cts.
• I used these numbers, and equation 2.17 in Tobin's thesis, to calculate this curve.

Edit 1730 9 Oct: I had missed out the factor of 5 gain in the demod board in calculating the shot noise curve. Attachment #7 shows the corrected shot noise level. Explicitly:

, where is to convert shot noise in W to displacement units.

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.

OL A2L coupling

• I didn't measure these
• These couplings would have changed because I modified the Oplev loop shapes to allow engaging of coil de-whitening filters.
• But anyways, their effect will only be below 100Hz because I made the roll-offs steeper.

Still to measure (but not likely to be limiting us anywhere in the current state):

• Laser intensity noise -> MICH coupling (using AOM).
• Laser frequency noise -> MICH coupling (using CM board IN2).
• Oscillator noise (amplitude + phase) -> MICH coupling (using AM/FM input of Marconi).

I've also made several changes to the NB code - will push to git once I finish cleaning stuff up, but it is now much faster to make these plots and see what's what.