J. Kissel

In trying to understand what Elenna has discovered in LHO:65495, where she showed -- through a multi-channel coherence wiener filter projection -- that PR3 V and HAM1 X/RY are dominating the REFL WFS performance. 

Since I have a tough time grokking the physical mechanism when looking at a multi-channel coherent projection, I figured I'd start back at what I do understand -- how the ground couples to the suspension point of PR3. Much like in LHO:64466 where I highlight the difference between 
    - FC1's HAM7 ISI with ST0 FF L4Cs and lower noise "fine" Vertical CPS ("BEST SO FAR")
    - SRM's HAM5 ISI with ST0 L4C feed-forward and higher noise "coarse" Vertical CPS, and ("GOOD")
I use this aLOG to highlight 
    - PR3's HAM2 ISI that has no ST0 FF L4Cs and higher noise "coarse" Vertical CPS.

I'm using the exact same time -- 2022-Aug-11 18:00 UTC -- in order to make a fair comparison between all three chambers. I am using the HAM2 GND T240 rather than the HAM5 GND T240, however, as my reference for ground motion.

As with my LHO:64466 and Elenna's LHO:65495, there are 1000 plots to show so I try to take them in bite size chunks. In the main entry here I talk about PR3 longitudinal and pitch. In the subsequent comments I'll show Vertical (whose SUS POINT motion we know is *not* coherent), then Yaw, then the less interesting T and R, and close out with showing the raw cartesian ISI displacement to eventually make a model of the HAM2 ISI performance a la CSWG:11236, that I can then use to update the total noise budget of the PR3 (HLTS) optic much like I've been doing for the HSTSs a la LHO:65317.

So, first, PR3's L and P.
    :: 2022-08-12_H1SUSPR3_Suspoint_L_ASD.png shows the ISI cartesian contributions to PR3 longitudinal. As with SRM, but worse, PR3's 0.5 Hz to 20 Hz longitudinal motion is entirely dominated by ISI CART_RX, which is limited by the coarse CPS noise. This has been known for quite some time; it's the whole reason why the we pushed to get the HAM ISIs upgraded to use the lower noise "fine" CPS. But, I'm not used to looking at HAM2 / HAM3 chambers, where there's no ST0 L4C feed-forward either. Quite a stark contrast! The HEPI pier resonance structure between 10-20 Hz is a bit louder, and more broad than how it appears from HAM5 in SRM's SUS Point L ASD.

    :: 2022-08-12_H1SUSPR3_Suspoint_P_ASD.png shows the sus point pitch ASD dominated by HAM2 ISI RY, which you can compare against SRM's sus point pitch ASD dominated by HAM5 ISI RX. Here, I think there might be room for improvement on the HAM2 RY blend filters, since the tables are symmetric in X & Y (and thus RX and RY), and RX DOF from HAM5 ISI appears to show better performance in the 0.5 to 5 Hz region.

These ASDs alone doesn't really answer any questions I had from Elenna's WFS budget, but I wanted to start investigating coupling paths -- especially for the 10-20 Hz region. As in -- we see that there's multi-channel coherence between the HAM1 Table Top L4Cs. But the mystery is why when Jim's tried feed-foward from HAM1 Table Top L4Cs to CHARD P, he does NOT have success. So ... is there a another coupling path that has similar coherence to the REFL WFS that moves both the HAM1 TT L4Cs and the HAM2 ISI in this frequency region?
 
So I thought -- the HAM1 L4Cs contribution to the REFL WFS is predominantly from the X and RY DOFs -- and the "let's fix it with L4C FF" mentality is motivated by the thought that the REFL WFS sensors themselves are moving differentially w.r.t. to the REFL laser beam thus creating "sensor noise," i.e. a coupling path that is

   GND X >> HAM1 Table X and RY >> WFS Sensors >> Confusing CHARD

But those X and RY DOFs are the same longitudinal direction as the longitudinal direction HAM2 for PR3. And if that motion is between 10-20 Hz, I wondered, has the coherent path between that's instead

   GND X >> HAM2 ISI RY >> PR3 suspoint L >> PR3 Optic P >> Confusing CHARD

GND X (or Y, or Z) are coherent through both paths, then we might have more success feeding forward to PR3 than to the REFL WFS or the CHARD error signal.

So, I'm not sure if I'm convinced that I've discovered that that is what's happening to REFL WFS, but I attach supporting plots to see if it helps motivate the story. 

Here're those calibrated transfer functions, and I've cast them into meters of GND to meters of RY *contribution* to Sus Point L and P via the projection matrix lever arm shown in the legends of the above ASDs.
    :: 2022-08-12_H1GNDHAM2_XY_to_H1SUSPR3_Suspoint_L_TF.png indeed shows a (m/m) transmission from GND X to HAM2 ISI RY's contribution to L that takes the same shape as the total GND X to PR3 Sus Point L for *some* of the 10-20 Hz hump -- between 13-14 Hz. 

    :: 2022-08-12_H1GNDHAM2_XY_to_H1SUSPR3_Suspoint_P_TF.png shows the same GND X to HAM2 ISI RY, but instead shows its contribution to PR3's Sus Point P in (rad / m). Here, and I'm not sure I get why, but the contribution's coherence in the 10-20 Hz region matches the shape of the transfer function of the higher frequency part of the hump, spanning ~15 - 25 Hz.

    :: 2022-08-12_H1GNDHAM2_Z_to_H1SUSPR3_Suspoint_L_TF.png shows the (m/m) transmission of GND Z to HAM2 ISI's RY contribution to PR3 Sus Point L. While there is a striking about of coherence -- the magnitude of the transfer function is at least smaller than the GND X to ISI RY. 

    :: 2022-08-12_H1GNDHAM2_Z_to_H1SUSPR3_Suspoint_P_TF.png shows the (rad/m) transmission of GND Z to HAm2 ISI's RY contribution to PR3 Sus Point P. Like GND X, the GND Z contribution to PR3 Sus Point P takes a different shape than it's contribution to Sus Point L, but still strikingly coherent.

The message from these transfer function sets -- this is why we need multi-channel coherent projections -- GND X, GND Y, and GND Z are all finding coherent coupling paths to HAM2 ISI RY in this 10-20 Hz region. 
Further, although the transfer function magnitude for GND Z is smaller than for GND X by a factor of ~10x, the *amplitude* of the GND Z motion in the 10-20 Hz region is a factor of ~10x larger [I'll show this when I show the Sus-Point V results in the comments below], resulting in similar levels of RY -- and thus PR3 sus point L -- from each DOF.

On to the next DOFs.