I decided to analyze the data I took in December more carefully to see if there are any clues about the weird LSC sensing.

Attachment #1 shows the measurement setup.

• The PSL shutter was closed. All feedback to both lasers was disconnected during the measurement. I also disabled the input switch to the FSS Box - so the two laser beams being interfered shouldn't have any modulations on them other than the free running NPRO noise and the main IFO modulations.
• Everything is done in fiber as I had the beams already coupled into collimators and this avoided having to optimize any mode matching on the beat photodiode.
• The pickoff of the PSL is from the collimator placed after the triply resonant EOM that was installed for the air BHD experiment.
• The other beam is the EX laser beam, arriving at the PSL table via the 40m long fiber from the end (this is the usual beam used for ALS).
• I didn't characterize precisely the PLL loop shape. But basically, I wasn't able to increase the SR560 gain any more without breaking the PLL lock. Past experience suggests that the UGF is ~20 kHz, and I was able to get several averages on the AG4395 without the lock being disturbed.

Attachment #2 shows the measured spectrum with the PSL and EX laser frequency offset locked via PLL.

• The various peaks are identified.
• There are several peaks which I cannot explain - any hypothesis for what these might be? Some kind of Sorensen pollution? They aren't any multiples of any of the standard RF sources. They are also rather prominent (and stationary during the measurement time, which I think rules out the cause being some leakage light from the EY beam, which I had also left connected to the BeatMouth during the measurement).
• In the previous such characterization done by Koji, such spurious extra peaks aren't seen.
• Also, I can't really explain why some multiples of the main modulation are missing (could also be that my peak finding missed the tiny peaks)?
• The measuremet setup is very similar to what he had - important differences are 
  • Much of the optical path was fiber coupled.
  • Beat photodiode is NF1611, which is higher BW than the PDA10CF.
  • The second laser source was the Innolight EX NPRO as opposed to the Lightwave that was used.
  • The RF source has been modified, so relative phasing between 11 MHz and 55 MHz is different.

Fitting the measured sideband powers (up to n=7, taking the average of the measured upper and lower sideband powers to compute a least squares fit if both are measured, else just that of the one sideband measured) agains those expected from a model, I get the following best fit parameters:

To be explicit, the residual at each datapoint was calculated as

.

The numbers compare favourably with what Koji reported I think - the modulation depths are slightly increased, consistent with the RF power out of the RF box being slightly increased after I removed various attenuators etc. Note the large uncertainty on the relative phase between the two modulations - I think this is because there are relatively few sidebands (one example is n=3) which has a functional dependence that informs on phi - most of the others do not directly give us any information about this parameter (since we are just measuring powers, not the actual phase of the electric field). 

Attachment #3 shows a plot of the measured modulation profile, along with the expected heights plugging the best fit parameters into the model. The size of the datapoint markers is illustrative only - the dependence on the model parameters is complicated and the full covariance would need to be taken into account to put error bars on those markers, which I didn't do. 

Attachment #4 shows a time domain measurement of the relative phasing between the 11 MHz and 55 MHz signals at the EOM drive outputs on the RF source box. I fit a model there and get a value for the relative phase that is totally inconsistent from what I get with this fit.