Kiwamu, Stefan

We drove the IM4 in PIT and YAW, and measured the beam jitter to OMC_DCPD_RIN transfer function. We calibrated the drive signal in Relateve Beam Jitter (RBJ), so we can directly compare it with measured beam jitters at other places (for calibration, see below).

We found a transfer function from IM4 RBJ to DCPD_RIN of about 2e-2 RIN/RBJ for yaw, and 3e-3 RIN/RBJ for pitch. When then tried to minimize the couipling by putting offests into the INP1 ASC loop that controls IM4.
For YAW, we found a minimum (with sign change) for -1300cts OFFSET, resulting in about the same transfer function as for the undisturbed PIT.
For PIT, the improvement was minimal, and we didn't find a minimum. But the best coupling was achieved at +1800cts PIT OFFSET.

With those offsets the recycling gain dropped a bit, but there still was a net range improvement.

Calibration:
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DCPD_SUM: The channel is in mA. The attached txt file includes the closed loop correction, as well as the factor 1/20mA, casting the channel into RIN.

H1:SUS-IM4_M1_OPTICALIGN_P_OUT: The channel should be calibrated in urad at DC, and the PIT pendulum frequency is 1Hz. Also H1:SUS-IM4_M1_OPTICALIGN_P_GAIN is 0.212. Thus, the calibration in rad is 1e-6/0.212 = 4.72e-6 rad/ct + 2 poles at 1Hz

H1:SUS-IM4_M1_OPTICALIGN_Y_OUT: The channel should be calibrated in urad at DC, and the YAW pendulum frequency is 0.727Hz. Also H1:SUS-IM4_M1_OPTICALIGN_Y_GAIN is 0.388. Thus, the calibration in rad is 1e-6/0.388 = 2.58e-6 rad/ct + 2 poles at 0.727Hz

Calibration in Relative Beam Jitter (RBJ):

The field overlap between two Gaussian beams with k=2*pi/lambda, w the beam spot size, and Theta the angle between the beams is
  ovl =exp(-(k*w*Theta/2)^2/2 )
Thus, the mode-mismatch M=1-|ovl|^2 = (k*w*Theta/2)^2 = (Theta/Theta_w)^2
where Theta_w =lambda/(pi*w).

From T1200470 and the attached wCalc.m file, we find the beam spot on IM4 to be 2.12mm. Thus Theta_w for IM4 is 160urad.

Finally, there is a factor of two between the beam deflection angle Thata and the mirror angle Phi: Theta=2*Phi.
Thus, we have to divide the calibration for H1:SUS-IM4_M1_OPTICALIGN_P_OUT and H1:SUS-IM4_M1_OPTICALIGN_Y_OUT by 80urad to ger relative beam jitter (RBJ):

H1:SUS-IM4_M1_OPTICALIGN_P_OUT: 0.0590 RBJ/ct
H1:SUS-IM4_M1_OPTICALIGN_Y_OUT: 0.0323 RBJ/ct