Summary:

I've been looking into the cross-coupling from the SRCL loop control point to the Michelson error point.

[Attachment #1] - Swept sine measurement of transfer function from SRCL_OUT_DQ to MICH_IN1_DQ. Details below.

[Attachment #2] - Attempt to measure time variation of coupling from SRCL control point to MICH error point. Details below.

[Attachment #3] - Histogram of the data in Attachment #2.

[Attachment #4] - Spectrogram of the duration in which data in #2 and #3 were collected, to investigate the occurrance of fast glitches.

Hypothesis: (so that people can correct me where I'm wrong - 40m tests are on DRMI so "MICH" in this discussion would be "DARM" when considering the sites)

• SRM motion creates noise in MICH.
• The SRM motion may be naively decomposed into two contributions -
  • Category #1: "sensing noise induced" motion, which comes about because of the SRCL control loop moving the SRM due to shot noise (or any other sensing noise) of the SRCL PDH photodiode, and
  • Category #2: all other SRM motion.
• We'd like to cancel the former contribution from DARM.
• The idea is to measure the transfer function from SRCL control point to the MICH error point. Knowing this, we can design a filter so that the SRCL control signal is filtered and summed in at the MICH error point to null the SRCL coupling to MICH.
• Caveats/questions:
  • Introducing this extra loop actually increases the coupling of the "all other" category of SRM motion to MICH. But the hypothesis is that the MICH noise at low frequencies, which is where this increased coupling is expected to matter, will be dominated by seismic/other noise contributions, and so we are not actually degrading the MICH sensitivity.
  • Knowing the nosie-budget for MICH and SRCL, can we AC couple the feedforward loop such that we are only doing stuff at frequencies where Category #1 is the dominant SRCL noise?

Measurement details and next steps:

Attachment #1

• This measurement was done using DTT swept sine.
• Plotted TF is from SRCL_OUT to MICH_IN, so the SRCL loop shape shouldn't matter.
• I expect the pendulum TF of the SRM to describe this shape - I've overlaid a 1/f^2 shape, it's not quite a fit, and I think the phase profile is due to a delay, but I didn't fit this.
• I had to average at each datapoint for ~10 seconds to get coherence >0.9.
• The whole measurement takes a few minutes.

Attachments #2 and #3

• With the DRMI locked, I drove a sine wave at 83.13 Hz at the SRCL error point using awggui.
• I ramped up the amplitude till I could see this line with an SNR of ~10 in the MICH error signal.
• Then I downloaded ~10mins of data, demodulated it digitally, and low-passed the mixer output.
• I had to use a pretty low corner frequency (0.1 Hz, second order butterworth) on the LPF, as otherwise, the data was too noisy.
• Even so, the observed variation seems too large - can the coupling really change by x100?
• The scatter is huge - part of the problem is that there are numerous glitches while the DRMI is locked.
• As discussed at the meeting today, I'll try another approach of doing multiple swept-sines and using Craig's TFplotter utility to see what scatter that yields.

Attachments #2

• Spectrogram generated with 1 second time strides, for the duration in which the 83 Hz line was driven.
• There are a couple of large fast glitches visible.