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Entry  Wed Sep 25 23:15:11 2013, Masayuki, Summary, Green Locking, FPMI noise caused by ARM locking fpmibd.pdf
    Reply  Wed Sep 25 23:59:29 2013, Masayuki, Summary, Green Locking, FPMI noise caused by ARM locking XARM_OLTF.pdfYARM_OLTF.pdfXARM_ITMXresponse.pngYARM_ITMYresponse.pngfree_running.pdf
       Reply  Thu Sep 26 01:49:28 2013, Masayuki, Summary, Green Locking, FPMI noise caused by ARM locking MICH_OLTF.pdfBS-RS55Q.pngETMX-RS55.pngETMY-RS55.pngplot.pdf
       Reply  Thu Sep 26 23:02:40 2013, rana, Update, LSC, FPMI noise caused by ARM locking Xarm_sweep_130926.pdflsc.pdferr.png
          Reply  Fri Sep 27 00:48:53 2013, Masayuki, Update, LSC, FPMI noise caused by ARM locking phase_badget.pngFPMI_noises.png
Message ID: 9161     Entry time: Wed Sep 25 23:15:11 2013     Reply to this: 9162
Author: Masayuki 
Type: Summary 
Category: Green Locking 
Subject: FPMI noise caused by ARM locking 
I measured some error signal, OLTFs and responses for FPMI noise estimation. Especially we are interested in the noise from in-loop noise of ALS Green PDH control. The strategy and
1) Purpose
 Estimation of the FPMI phase shift noise caused by in-loop noise of Green PDH control. 
2) What we should figure out
 For that estimation we have to figure out the transfer function from the cavity length change to the phase shift which is measured by MICH.
3) Strategy
 I attached the block diagram of  our interferometer. Our goal is to find the transfer function H_L-l and to calibrate the out of loop noise of interferometer with that TF and error signal of the PDH control.
 H,A and F mean the sensitivity, actuator response and servo filter for each control loop. L_xarm is the disturbance of the cavity length and l- is the differencial motion of the interferometer
We can get this H_L-l from measurement of the response from calibrated ETM actuation to the MICH error signal. You can get the formula for calculating H_L-l with simple calculation and that is
             1 + G_mich       1 + G_xarm      V_mi  
H_L-l = ---------------  -----------------  ------------
              H_mich             A_etmx         V_excetm
where the each G is OLTF and V_mi/Vexcetm is the response from the ETM actuation to the MICH error signal.
And then  the FPMI noise in the unit of meter / rHz is
N_fpmi = l_dis + ------------ Vx
This second term is what we are interested in.
To estimate these noises
i) We can calibrate the actuators of  ITMX, ITMY and BS with using the MICH as sensor. So we can calibrate the arm error signals by  excitation of arm length using ITMs actuator.
ii) If we know the TFs of arms, we can calibrate the ETMX and ETMY actuators.
iii) We should know the response from ETMX or ETMY actuating to error signal of mich.
iv) Also we should calibrate the error signal of MICH in FPMI locking(H_mich). We can do that by exciting the BS.

Then we can estimate the noises.

In next entry, I will write about measurement.


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