Last week, while I had the PRMI locked on REFL33, I did some poking around with mirror excitation to RFPD quadrature transfer functions. I got some indication of weird things with sensing MICH with the 3F REFL signals, but it should be explored more before taken as a real thing. I just figured I would show what I saw. 

With that disclaimer out of the way, here's what I did:

• Locked PRMI on PRCL:REFL33_I and MICH:REFL33_Q, as detailed in my earlier ELOG
• Created PRCL and MICH excitations at two different frequencies, notched said frequencies out of the control filters
• Took transfer functions from mirror LSC output signals to 33 I, 33 Q, 165 I, 165 Q in DTT
• For each DOF, look at the measured transfer functions only at the excitation frequency. (Assuming good coherence, which was there)

The basic idea was, some PRCL motion (for instance), has a transfer function to both the I and Q quadratures at a given PD. As the PRCL excitation sine wave goes through one cycle, the REFL signals at the excitation frequency go through some coherent cycle. Thus, the excitation traces out some trajectory in the I vs. Q plane. I believe this is analogous to the typical "radar plot" that we make for sensing matrix elements. 

However, the straight line that we normally plot in the radar plots assumes a certain phase relationship between the DOF-> I and DOF->Q transfer functions that results in a straight line. Here are the trajectories I actually measured, normalized by the excitation amplitudes.

The plotted traces are (x,y) = (H_prcl->I * prcl, H_prcl->Q * prcl) and  (x,y) = (H_mich->I * mich, H_mich->Q * mich) where H_prcl->I is the measured complex transfer function from prcl to REFL I, for instance, and prcl and mich are the excitation signals, normalized to unit amplitude.

PRCL looks like a nice straight line in both of these, and pretty well phased, but not only is MICH not very orthogonal to PRCL, there is quite a bit of ellipticity present, which means we can't fully decouple the two DOFs, even if they were nominally orthogonal. 

I'm not sure what may cause this. To back up this measurement/interpretation, I tried to take measurements of these transfer functions across different excitation frequencies via swept sine DTT, but seismic activity kept me from staying locked long enough...