Using PRX, I remeasured the relative actuation strengths of the BS and PRM to see if the PRM correction coefficient we're using is good.
My result is that we should be using MICH -> -0.2655 x PRM + 0.5*BS.
This is very close to our current value of -0.2625 x PRM, so I don't think it will really change anything.
The reason that the BS needs to be compensated is that it really just changes the PRM->ITMX distance, lx, while leaving the PRM-ITMY distance, ly, alone. I confirmed this by locking PRY and seeing no effect on the error signal, no matter how hard I drove the BS.
I then locked PRX, and drove an 804Hz oscillation on the BS and PRM in turn, and averaged the resultant peak heights. I then tried to cancel the signal by sending the excitation with opposite signs to each mirror, according to their relative meaured strength.
In this way, I was able to get 23dB of cancellation by driving 1.0 x PRM - 0.9416 * BS.
Now, in the PRMI case, we don't want to fully decouple like this, because this kind of cancellation just leaves lx invarient, when really, we want MICH to move (lx-ly) and PRCL to move (lx+ly). So, we use half of the PRM cancellation to cancel half of the lx motion, and introduce that half motion to ly, making a good MICH signal. Thus, the right ratio is 0.5*(1.0/0.9416) = 0.531. Then, since we use BS x 0.5, we divide by two again to get 0.2655. Et voila.