Measurement with FPMI

i)By locking the FPMI with AS55Q and arms using POX,POY we measured  the OLTF on AS55Q, the response from BS actuation to error signal on AS55Q  for H_mich. The fitted,  measured OLTF and the residual function is in attachment1. I fitted two parameters and they are time-delay and the gain. The time delay is -275 usec. The time delay in three different control are almost same. The response from BS to AS55Q is in attachment 2.

With these two measuremets, I calclated the H_mich in FPMI. This H_mich should be different from simple MI because the cavity  refrectivity is different from the front mirror. Acrually it changed and the value was
Hmich = 4.4026e7

ii) I excited the ETMX and ETMY and measure the response from actuation to the error signal of MICH on AS55Q. The response is in attachment 3 and 4. from these result I calculated the H_L-l by using the formula as I mentioned. The value was
H_Lx-l = 175.7650 (XARM)
H_Ly-l = 169.8451 (YARM)

iii) I measured the error signal of MICH and XARM and YARM and with measured H_L-l, I estimated the FPMI noise caused by ARM locking. You can see in the higher frequency region than 10 Hz is dominated by noise caused by ARM control in-loop noises. 150 Hz and 220Hz are the UGF of each arms, so the two peaks are caused by arm control. You can see the small difference between FPMI noise and  noise from arms. There are two possibilities, one is that these measurement is not same time measurement so they should have small difference. and  other possibility is the error of the caliculation. But I think it doesn't look so bad estimation.

Next step

We will do same measurement with lock the arms the ALS system on tomorrow. Then we will check the PDH servo or other noise source and investigate the ALS system