Summary of discussion between Koji and gautam on 14 Oct:

1. Koji questioned the accuracy of the "open loop" ASD shown here. While it may not be entirely accurate to compute the free-running (homodyne) phase noise simply by taking the arctangent of the I and Q signals (because the magnitude of the signal is also changing), gautam claims the estimate is probably still close to the true homodyne phase, especially since the ratio of the "in-loop" and free-running ASDs gives something that closely approximates the magnitude of the supposed OLG of the system.
2. Koji suggested the following tests:
   • Investigate the relative stability of the two RF signal generators involved in this system. Since the 44 MHz electrical LO signal (for demodulation) is generated by a separate IFR from the one used to imprint 11 MHz and 55 MHz phase modulation sidebands on the main PSL beam, we want to investigate what the drift is.
   • Try implementing an analog feedback loop using LB1005 - the idea being we should be able to implement higher bandwidth control, for better suppression of the high frequency noise (which looking at the ASD is not only due to seismic phase modulation of the IFO output field). Maybe some combination of this and the Marconi investigation would suggest why we have these forests of lines in the ASDs of the error signal?
   • Turn off the HEPAs on the PSL enclosure completely as a test, to see if that improves (i) phase noise due to air currents and (ii) mechanical pickup on the fiber producing  phase noise.

I tried all of these last night / overnight, here are my findings.

Analog locking of the homodyne phase:

See Attachment #1. 

• RF44_I was used as the error signal.
• The "C1:OMC-ZETA_IMON_OUT" channel is actually looking at the error signal monitor from the LB1005, and is uncalibrated in this plot.
• The "monitor" port on the demodulator board provides a convenient location for us to route the demodulated signal to an LB1005 box, while simultaneously digitizing both demodulated quadratures.
• Empirically, I found settings that could engage the lock. I also found that I couldn't increase the gain much more without destroying the lock. 
• The time domain signals look much "cleaner" in this analog feedback loop than when I achieved similar stabilization using the digital system. But I will quantify this more when I post some spectra of the in loop error signals.
• I will do some more characterization (loop TF measurement, error point spectrum in lock etc), but in summary, it looks like we still only have ~100 Hz UGF. So something in the loop is limiting the bandwidth. What could it be?
• The main problem is that the LB1005 isn't well suited to remote enabling/disabling of the lock, so this isn't such a great system.

Relative stability of two IFR2023s synchronized to the same FS725 Rb standard:

The electrical LO signal for demodulation of the 44 MHz photocurrent is provided by an IFR2023 signal generator. To maintain a fixed phase relation between this signal, and the phase modulation sidebands imprinted on the interferometer light via a separate IFO2023 signal generator, I synchronize both to the same Rb timing standard (a 10 MHz signal from the FS725 is sent to the rear panel frequency standard input on the IFR). We don't have a direct 44 MHz electrical signal available from the main IFO Marconi at the LSC rack (or anywhere else for that matter). So I decided to do this test at 55 MHz. 

• RF input of the demodulator was driven by 5*11.066209 MHz pickoff from the LSC rack.
• LO input of the demodulator was driven by 5*11.066209 MHz signal from the IFR2023 used for the RF44 demodulation setup.
• The outputs were monitored overnight. The RF44_Q channel had a DC level of nearly 0. So this channel is nearly a linear sensor of the phase noise between LO and RF signals.
• To convert ADC counts to radians, I offset the LO Marconi frequency by 100 Hz, and saw that the two quadratures showed pk-pk variation of ~24000cts. So, at the zero crossing, the conversion is 1/(24000/2) rad/ct ~83urad/ct.
• The result is shown in Attachment #2. The "measurement noise" trace corresponds to the RF. input of the demodulator being terminated to ground with a 50 ohm terminator.
• For comparison, I also overlay the phase noise estimate of an individual IFR from Rana. In his investigation, the claim is that the PLL that locks the IFR to the Rb timing standard has ~1kHz UGF, but if my measurement is correct, the relative stability between the two signal generators synchronized to the same timing standard already. degrades at ~1 Hz. Could be just a cts/rad calibration error I guess.
• In any case, we are far from saturating this limit in the homodyne phase lock.
• There are several sharp lines in this measurement too - but I don't know what exactly the source is. Of course the two marconis are plugged into separate power strips, so that may explain the 60 Hz lines and harmonics, but what about those that aren't a multiple of 60 Hz?

A look at the time domain signal:

With the Michelson locked on the dark fringe, the RF44 I and Q signals in the time domain are shown in Attachment #3 for a 1 minute stretch.

• The RF44 signal level bottoms out at ~40 cts. Okay, so this is the offset.
• However, the maximum value of the RF44 signal amplitude seems to be modulated in time. How can we explain this?