Summary: I've an estimate of the squeezing angle fluctations caused by phase noise at the OMC DCPDs from the interferometer control sidebands(~6mrad rms), which is far too small (~6mrad) to explain our apparently high level of phase noise infered from squeezing and anti-squeezing measurements (on the order of 100mrad).  There are several assumptions that go into this, but for reasonable values of the sideband imbalance, sideband power at the AS port or contrast defect won't result in 100mrad phase noise.  However, if the power at the AS port is mostly in a higher order mode for the sidebands, and that higher order mode has a larger transmission through the OMC than what I have used, we could potentially generate much higher levels of RF phase noise.  At LHO we have seen evidence of a 9th order 9MHz mode being transmitted through the OMC, so it may be worth using the information from a OMC scan with Koji's model of OMC transmission for higher order modes to check how much sideband higher order mode we could have at the AS port.

Details:

Power percentages at AS port: 19.4% carrier, 74.3% 45 MHz, 6.3% 9 MHz alog 48595  The 9MHz power for L1 could be much smaller, we don't understand the 9MHz power levels in H1.

OMC transmission: Finesse 390 FSR 264.8MHz (T1000276).  Power transmission of 00 mode for 9 MHz 3.53e-4; power transmission for 45 MHz 2.08e-5

Power on DCPDs: 

• total power on DCPDs is 23.3mW (20mA, responsitivity of 0.858A/W), assume this is nearly all carrier. 
• 45 MHz power is 1.86uW
• 9MHz power is 2.67uW
• Here I am acting as though all of the power is in the 00 mode, although as we have seen there is a higher order mode for 9MHz which also has a high transmission for the H1 OMC and could contribute.

Contrast defect:

• Most recent measurement was by Craig at 2W input power was 8ppm of input power (46142).  If we scale this with input power, we would predict 0.15mW of contrast defect light on the DCPDs at 37W input power, although the power recycling gain drops as we go to 37W input power and the contrast probably gets worse due to point absorbers. 
• Evan Hall's 2016 measurement 30573 was made with 50W input power, which would have been fairly similar to our current circulating power with the reduced recycling gain at the time.  With different fitting methods he and Gabriele found 1.8 to 5 mW contrast defect light, so one order of magnitude larger than Craig's measurement. The current situation might be better than this since the point absorber on ITMX is no longer bothering us.
• There's about an order of magnitude difference between these two estimates, but I will use the numbers measured at higher power since that seems like the most simliar situation.  I do think that there is a more recent measurement of contrast defect at high power, I will update this entry if needed.

Sideband imbalance:

• We would ideally use OMC scans to estimate the sideband imbalance for the 00 modes, as well as any other modes that are large enough after filtering through the OMC to have an impact.  We do have OSA scans that give us some estimate of the sideband imbalance with all the modes included: 44582  By eye, there is about a 20% difference in power between the upper and lower sidebands of 45MHz, and about a 60% difference for 9MHz.

The rms phase noise due to contrast defect light is given by eqn 5.60 here the phase noise due to sideband imbalance is given by 5.62, although there is a factor of 2 in 5.62 that I don't understand (think could be wrong) and am leaving out here. With the assumptions above I estimate:

The quadrature sum of these contributions is 6 mrad, which is enough to have an impact on our total budgeted phase noise, but not nearly enough to help explain the large excess of aparent phase noise based on measured squeezing and anti-squeezing.