Summary:

I measured the transfer function of the AO path, and think that there are some features indicative of a problem somewhere in the IMC locking loop.

Details:

Regardless of the locking scheme used, high bandwidth control of the laser frequency relies on the fact that the laser frequency is slaved to the IMC cavity length with nearly zero error below ~50 kHz (assuming the IMC loop has a UGF > 100 kHz). In my single arm experiments, I didn't know what to make of the ripples that became apparent in the measured OLTF as the AO gain was ramped up.

Tonight, I measured the TF of the "AO path", which modifies the error point of the IMC, thereby changing the laser frequency. 

• An SR785 was used to make the measurement.
• The signal was injected at the "EXC B" input on the CM board.
• The CM_SLOW path was disabled, AO gain = 0dB, IMC IN2 gain = 0dB.
• Between "EXC B" and the IMC error point (which I measured at TP1A on the IMC board), we expect that there are 2 poles at ~ 6 Hz, and one pole at ~ 11 Hz.

Attachment #1 shows the result of the measurement. 

• This measurement should be the "Closed Loop Gain" [= 1/(1+L) where L is the open loop gain] of the IMC locking loop. For comparison, I've overlaid the inferred CLG from a measurement of the IMC OLG I made in Jun 2019. The magnitude lines up quite well, but the phase does not 🤔 
• Above 10 kHz, the measurement is as I expect it to be.
• However, between 1 kHz and 10 kHz, I see some periodic features every 1 kHz, which I don't understand. In the IMC OLTF, these would be sharp dips in the OLTF gain.
• I was careful not to overdrive the servo, so I believe these features are not a measurement artefact.
• Combing through past elogs, I couldn't really find any measurements of the IMC OLTF in the 1 kHz - 10 kHz band.
• I decided to measure the spectrum of the IMC error point (with no excitation input), to see if that offered any additional insight. Attachment #2 shows the result - again, periodic features at ~ 1 kHz intervals.

I didn't use POX / POY as a sensor to confirm that this is real frequency noise, I will do so tomorrow. But it may be that realizing a stable crossover is difficult with so many features in the AO path.

Previous thread with a somewhat detailed characterization of the IMC loop electronics.