Combined with the TF measurement reported in klog13027 , the optical gain of CARM can be calculated.

Bottom line

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]

Why C = Cmc*Tc ?

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.