J. Kissel (inspired the work of A. Pele and E. Hall, and working with C. Cahillane, E. Capote, J. Warner, B. Ratto, J. Driggers)

As we 
   - continue to poke around the CHARD noise budget (see e.g. LHO:62976), 
   - consider implementing HAM1 TT L4C feedforward schemes like what has demonstrated to be successful at LLO (see e.g. LLO:51552 with a filtered HAM1 TT L4C Z fed directly to CHARD_A input), as just shown in Jim's LHO:63108
   - contemplate the impacts of the vertical mode of RMs (see, e.g. LHO:62994) 
   - in case we want to short the blades as L1 has done (see, e.g. LLO:59949)

I wanted to see if I could tell a story of the coupling mechanism of HAM1 to CHARD is via coherent, passive, transfer functions while the IFO is fully locked with all ASC loops (and their corresponding DC centering loops) engaged.

Attached are plots of what I've learned, described below. Admittedly, I've only had the steam to look at the X direction of L4Cs, length and pitch of the RMs, and REFL WFS A, but I think there's a clear story there.
   (1) Attachment 1: 
       (A) Left column of plots -- Both RM's L are very coherent with the TT L4C X. This should not be terribly surprising at all, given that the RMs L direction is very much aligned to the HAM1 / IFO's X axis (see D1000313). What's interesting / confusing is that RM1 (which is further away from the only horizontal L4C in the chamber, that which is also aligned with the X direction) is so very much *more* coherent with the X than RM2.
       (B) Right column of plots -- The DC pointing on REFL WFS A are coherent with both RM's L. But, it's interestingly complicated -- they're coherent in different frequency regions. This may be due to the "DC Centering" servos, DOF's called DC1 and DC2, where REFL WFS A DC serves as the error signal for DC1, and DC1 uses both RM1 and RM2 for control *in pitch* though, *not in L*. The DC1 P open loop gain transfer function has a unity gain frequency of around 6 Hz. I don't know what the UGF of the DC2 P loop, or the DC1 or DC2 Y loops are. Jenne says "we've vacillated between having high UGFs (~5 Hz, above the RM SUS resonances) for the DC centering and low UGFs (~100 mHz below the SUS resonances), over the years." 

So yeah, not enough information and understanding, but here is a clear, linear, coherent coupling path between X of the table, and DC Pitch pointing on REFL A.

   (2) Attachment 2: 
       (A) Left column of plots -- Both RM's P are "only mildly" coherent with TT L4CX, and it's right around the 6 Hz vertical mode frequency.
       (B) Right column of plots -- REFL WFS A DC is coherent with with both RM's P. Here, not only is the 6 Hz region coherent, but also, the lower frequency region as well, between 100 mHz and 1 Hz. Here, because the DC1 and DC2 loops are using the RMs in P, I would expect coherence. But, with a 5 Hz UGF, I'm surprise to see so *little* coherence.

   (3) Attachment 3: 
       (A) Left column of plots -- REFLWFS_A_RF9_I and REFLWFS_A_RF45_I are coherent with the REFL WFS A DC.
       Recall that RF9_I and RF45_I are the beam on REFL WFS A, demodulated at the IFO's "radio frequency" RF sideband frequencies, 9 and 45 MHz and the signal is DC the audio frequency pointing of the beam on the WFS collection of PDs. 
       Ideally, the RF signals would *only* contain information about the motion of the IFO's cavities; 
           - the input pointing to the PRM (aka INP1), 
           - the power recycling cavity waist tilt (PRC2), and 
           - the common hard arm cavity waist tilt (CHARD) 
       where that motion is imprinted as an audio frequency "sideband" (but really a full amplitude spectral density of cavity motion) on the optical interference between the carrier frequency and these radio frequency side bands, and "rectified" to audio frequency (the lowest frequency of the cavity motion audio ASD brought to 0 Hz instead rather than audio frequency + 9 MHz or audio + 45 MHz). However, seemlingly (because there is coherence), it *also* contains some direct transmission of beam pointing on to the WFS.
       (B) Right column of plots -- REFL A RF9 and RF45 are coherent with HAM1 TT L4Cs directly -- BUT only at the 6 Hz RM vertical resonance. So, even though there's lots of interesting coherence along the physical way, every displacement by the RM's vertical mode gets mixed and confused and washed out, by the time it "makes it" to the RF signals.

With these plots and internal dialog, I convince myself that there's a direct, linearly coherent, *physical* coupling path from HAM1 Table Top motion, to RMs, to DC Pointing on the REFL WFS, to the RF9 and R45 demod signals. And it's these demod signals that are used as the error signals for CHARD, INP1, and PRC2. (Well, they are *now* -- there was a long while there where we were using POP WFS for PRC2 and INP1 for reasons, but Jenne *just today* reverted to the nominal sensing scheme defined in the aLIGO ASC design, T0900511).

In doing so -- that convinces me that the "blind wiener method" (I'll call it) where you just pick a random sensor as a witness (HAM1 TT L4C Z) that's most coherent with a target (CHARD), and build a "feed forward" sensor correction filter -- like Arnaud and Jim have done -- is perhaps *not* the most sensible or effective way to kill all the non-cavity HAM1 seismic signal in CHARD. I think it may be more sensible to use (or at least interesting to compare) the following options:
     - run a feed forward directly to the RM actuators, 
     - "sensor correction" for the DC pointing control loops by subtracting the HAM1 TT signal out of the REFL WFS DC error signal, or
     - "sensor correction" for the RF channels of the REFL WFS -- to remove the HAM1 from *all* the INP1, PRC2, and CHARD loops, rather than just the CHARD loop
and to do this with *multiple* degrees of freedom of witness X, Z, RX, and RY TT L4C, rather than just Z.

In the fullness of time, me, or someone else will hopefully show the same story for the Z L4Cs.