[Masayuki, Manasa]

Estimation of free-running MICH displacement noise:

Method 1. Assuming AS55_Q_err to be a linear sensor, as shown in (1) of figure below, free-running MICH noise (V_d) can be estimated by measuring V_err and the OLTF G. H can be estimated by using method explained in elog

 Method 2. Considering that the AS55_Q signal might be distorted or saturated, method 1 may not be precise. In method 2, we will use the ASDC as the sensor (S' in (3)) instead and lock MICH using ASDC in mid-fringe to calibrate the ITM actuators.

Figure:1

Schematic:

What we did:

1. Estimate H' from free-running ASDC signal (bright to dark fringe).
2. With MICH locked on ASDC, give an excitation signal to C1:LSC-SUS_XXXX_EXC (XXXX could be ITMX or ITMY) and measure R'. [(3) of schematic]
3. Measure OLTF of MICH locked on ASDC (hence estimate L). [(3) of schematic]
4. With MICH locked on AS55_Q, give an excitation signal to C1:LSC-SUS_XXXX_EXC (XXXX could be ITMX or ITMY) and measure R1. [(2) of the schematic] 

Results/Plots: 

Figure:2

OLTF of MICH locked on ASDC

Figure2:

Actuator excitation to MICH transfer function (MICH locked using ASDC) 

* y axis (no units)

Figure 3:
Actuator excitation to MICH transfer function (MICH locked using AS55Q)

* y axis (no units)

Figure 4:
Free-running MICH noise

Discussion: 

1. By using the second sensor, we also eliminate the effect of the MICH servo loop locked on AS55_Q (Estimated V_d does not depend on G but only on G').

2. The free-running MICH noise is still suppressed at 1Hz. This should be coming from the effect of the UGF of the loop at ~10Hz and the vicinity to the pendulum frequency at 1Hz.

Edit/Masayuki// This noise curve is not collect, especially in low frequency region. We used the measured OLTF for compensating the free running noise, but that is not collect in low frequency region. So we should model the OLTF and fit that into the measured OLTF. We will fix this soon.