Well, I was here until just about sunrise this morning trying to get my head around how the error signal should change with the optical gain (among many other things---I am not that dense). After a while I realized that increasing the optical gain should have no effect on the error signal; therefore, dividing the error spectrum by the increased optical gain results in a cavity noise spectrum that is lower by exactly the same amount.
Between my last post and last night, I realized that somehow I had nudged the PD---it wasn't properly fastened to the table---and so I didn't have the full REFL power on the diode. Whoops. I now need -12 dB of attenuation between the PD and the mixer to keep the loop stable with 100 mW input power, and I have removed the Cougar, so there's an additional 10 dB. (Actually, though I did remove the Cougar from PD S/N 01, I have replaced that PD altogether with PD S/N 02---which never had a Cougar in the first place---because I have taken a reliable transfer function of it and am confident with its tuning. I will make a post dedicated to that shortly.) What this means is that we now have ~10 dB higher optical gain than we did in that post, which is good. I am going to get a good measurement of the OG once the gyro is finished being built for the spillover estimate.
One of the things that was puzzling me last night was why, if I had increased the optical gain, was there no more improvement in the low-frequency noise? I have no plot for this, but I expected to see more low-f improvement like I did in the linked post when I added gain up front and attenuated the electrical signal by the same amount. This didn't happen, and it was frustrating. Today, Alastair pumped the chamber down, so I thought I would remeasure the error signal spectrum to see any changes. The results are good(!):
The noise at low frequencies (which seems to have come from the air) is lower, and so is the noise in the high audio band, which might have come from acoustic buffeting of the cavity optics). This shows that I didn't see any further improvement in the low-frequency region because I had already reduced the effect of electronics noise below the level of environmental noise. I am interested to see if this new low-frequency level is once again the PD noise or instead the lower environmental noise level in vacuum. The former will be limited by the amount of optical gain we can put up front; the latter we can reduce by increasing our OL gain at the servo (but, of course, we can only improve it to the point that it is lower than the PD noise).
Since the breadboard version of the PDH2 has turned out to be a real pain in the ass, I think I will opt for Frank's idea which is to simply modify the #1437 FrankenPDH box further to include a switch that disengages the low-frequency-gain-limiting resistor of the traditionally non-switchable stage. This will give us an extra factor of 1/f below 50 Hz so that we truly have 1/f2, and it should be enough to reduce common-mode environmental noise to below our other noise sources at this stage.