As part of trying to determine whether we require the AO path for lock acquisition, or if we can survive on just digital loops, I looked at the noise suppression that we can get with a digital loop.

I took a spectrum of POX, and calibrated it using a line driving ETMX to match the ALSX_FINE_PHASE_OUT_HZ channel, and then I converted green Hz to meters. 

I then undid the LSC loop that was engaged at the time (XARM FMs 1,2,3,4,5,8 and the pendulum plant), to infer the free running arm motion. 

I also applied the ALS filters (CARM FMs 1,2,3,5,6) and the pendulum plant to the free running noise to infer what we expect we could do with the current digital CARM filters assuming we were not sensor noise limited.

In the figure, we see that the free running arm displacement is inferred to be about 0.4 micrometers RMS.  The in-loop POX signal is 0.4 picometers RMS, which (although it's in-loop, so we're not really that quiet) is already better than 1/10th the coupled cavity linewidth.  Also, the CARM filters that we use for the ALS lock, and also the sqrtInvTrans lock are able to get us down to about 1 pm RMS, although that is not including sensor noise issues. 

For reference, here are the open loop gains for the LSC filters+pendulum and ALS filters+pendulum that we're currently using.  The overall gain of these loops have been set so the UGF is 150Hz.

It seems to me that as long as our sensors are good enough, we should be able to keep the arm motion down to less than 1/10th or 1/20th the coupled cavity linewidth with only the digital system.  So, we should think about working on that rather than focusing on engaging the AO path for a while.