Summary:

Currently, I am unable to engage the coil-dewhitening filters without destroying cavity locks. One reason why this is so is because the present Oplev servos have a roll-off at high frequencies that is not steep enough - engaging the digital whitening + analog de-whitening just causes the DAC output to saturate. Today, Rana and I discussed some ideas about how to approach this problem. This elog collects these thoughts. As I flesh out these ideas, I will update them in a more complete writeup in T1700363 (placeholder for now). Past relevant elogs: 5376, 9680. 

1. Why do we need optical levers?
   • ​​To stabilize the low-frequency seismic driven angular motion of the optics.
2.  In what frequency range can we / do we need to stabilize the angular motion of the optics? How much error signal suppression do we need in the control band? How much is achievable given the current Oplev setup?
   • ​​To answer these questions, we need to build a detailed Oplev noise budget.
   • Ultimately, the Oplev error signal is sensing the differential motion between the suspended optic and the incident laser beam.
   • What frequency range does laser beam jitter dominate the actual optic motion? What about mechanical drifts of the optical tables the HeNes sit on? And for many of the vertex optics, the Oplev beam has multiple bounces on steering mirrors on the stack. What is the contribution of the stack motion to the error signal?
   • The answers to the above will tell us what lower and upper UGFs we should and can pick. It will also be instructive to investigate if we can come up with a telescope design near the Oplev QPD that significantly reduces beam jitter effects (see elog 10732). Also, can we launch/extract the beam into/from the vacuum chamber in such a way that we aren't so susceptible to motion of the stack?
3. What are some noises that have to be measured and quantified?
   • Seismic noise
   • ​​Shot noise
   • Electronics noise of the QPD readout chain
   • HeNe intensity noise (does this matter since we are normalizing by QPD sum?)
   • HeNe beam pointing / jitter noise (How? N-corner hat method?)
   • Stack motion contribution to the Oplev error signal
4. How do we design the Oplev controller?
   • ​​The main problem is to frame the right cost function for this problem. Once this cost function is made, we can use MATLAB's PSO tool (which is what was used for the PR3 coating design optimization, and also successfully for this kind of loop shaping problems by Rana for aLIGO) to find a minimum by moving the controller poles and zeros around within bounds we define.

5. What terms should enter the cost function?

   • ​​In addition to those listed in elog 5376
   • We need the >10Hz roll-off to be steep enough that turning on the digital whitening will not significantly increase the DAC output RMS or drive it to saturation.
   • We'd like for the controller to be insensitive to 5% (?) errors in the assumed optical plant and noise models i.e. the closed loop shouldn't become unstable if we made a small error in some assumed parameters.
   • Some penalty for using excessive numbers of poles/zeros? Penalty for having too many high-frequency features.
6. Other things to verify / look into
   • ​​Verify if the counts -> urad calibration is still valid for all the Oplevs. We have the arm-cavity power quadratic dependance method, and the geometry method to do this.
   •  Check if the Oplev error signals are normalized by the quadrant sum.
   • How important is it to balance the individual quadrant gains?
   • Check with Koji / Rich about new QPDs. If we can get some, perhaps we can use these in the setup that Steve is going to prepare, as part of the temperature vs HeNe noise invenstigations.

Before the CDS went down, I had taken error signal spectra for the ITMs. I will update this elog tomorrow with these measurements, as well as some noise estimates, to get started.