I measured the TF from SLOW_DAQ to MIXER_DAQ of IMC servo. The result is attached.
The configuration of the measurement is as follows:
IN1 gain = -21 dB
PSL output power: 5.2 W
IMC_REFL: maximized with 5.2 W PSL output
actuator: only PZT
The calibrated optical gain is
60 dB / (-21 dB) / (3 MHz/V) = 71 dB V/MHz
Combined with the TF measurement reported in klog13027 , the optical gain of CARM can be calculated.
In a nutshell, the CARM optical gain C can be calculated as C = Cmc*Tc, where Cmc is the optical gain of MC and Tc is the TF from the IMC AO path input to the CARM error signal.
Cmc = 71dB = 3550 [V/MHz]
Tc = 80dB*(1e3/f) = 1e7/f [cnts/V]
Therefore, the CARM optical gain is: C = 3.6e10/f [cnts/MHz]
The injected signal (s1) into the MC AO path is attenuated by 1/(1+Gmc), where Gmc is the OPLG of MC.
Gmc = Cmc*L*Smc, where L is the frequency actuation efficiency (3MHz/V) and Smc is the TF of the MC servo board.
The actual frequency change of the laser df is: df = L*Smc*s1/(1+Gmc) = s1/Cmc within the control bandwidth of MC (Gmc >> 1).
The CARM error signal s2 is: s2 = C*df = C*s1/Cmc.
Therefore, Tc =s2/s1 = C/Cmc => C = Cmc*Tc.
Correction to the result.
When Tc was measured, the anti-whitening filter was not engaged. This filter has a flat gain of -20dB above 100Hz. So, Tc is actually 20dB larger than the measured value.
That is, Tc = 100dB@1kHz.
With this correction, the optical gain of CARM is C = 3.6e5/f [cnts/Hz]
I put a DTT template to show the calibrated CARM signal in Hz/rtHz and m/rtHz (using dL = df*L/f) in the following place:
/users/Commissioning/data/CARM/2020/0219/Calibrated_CARM.xml
Now, K1:LSC-CARM_RESIDUAL_OUT is a calibrated CARM error signal.
Depending on the filter enabled in the K1:LSC-CARM_RESIDUAL filter bank, the unit can be either Hz or m.
