(Jax, Keita)
Yesterday morning we measured the sensing matrix for the ALS WFS. We did this by Injecting 30000cts at 5Hz into H1:SUS-L2_(I/E)TMX_L2_TEST_(P/Y)_EXC, then measuring the transfer function between H1:ALS-X_WFS_(A/B)_I_(PIT/YAW)_OUT and H1:SUS-(I/E)TMX_L3_OPLEV_(PIT/YAW)_OUT.
In cavity basis:
Pitch Sensing Matrix: (WFS ct/uRad)
| Hard | Soft | |
| A | -24871 | -44392 |
| B | -10475 | 52694 |
Pitch Input Matrix: (uRad/WFS ct)
| Hard | Soft | |
| A | -2.967e-5 | -2.5e-5 |
| B | -5.899e-6 | -1.401e-5 |
Pitch Output Matrix:
| 0.707 | 0.707 |
| -0.707 | 0.707 |
Yaw Sensing Matrix: (WFS ct/uRad)
| Hard | Soft | |
| A | 38421 | 67629 |
| B | -18263 | -25945 |
Yaw Input Matrix: (uRad/WFS ct)
| Hard | Soft | |
| A | -1.088e-4 | -2.838e-4 |
| B | 7.665e-5 | 1.612e-4 |
Yaw Output Matrix:
| 0.707 | 0.707 |
| 0.707 | -0.707 |
Raw data:
Useful information for determining sign conventions from raw data:
1. ETM/ITM Yaw is defined with positive as a counter-clockwise rotation of the optic around the z-axis.
2. ETM/ITM pitch is defined as positive pitch "down", but ITM oplev is set such that an increase in pitch gives a decrease in oplev measurement.
ETM Yaw:
| WFS | dB Magnitude | Phase |
| A | 86.3 | 126 |
| B | 74.7 | -46.1 |
ETM Pitch:
| WFS | dB Magnitude | Phase |
| A | 93.79 | 123.2 |
| B | 89.5 | -57.8 |
ITM Yaw:
| WFS | dB Magnitude | Phase |
| A | 97.5 | -62.58 |
| B | 89.9 | 122.24 |
ITM Pitch:
| WFS | dB Magnitude | Phase |
| A | 82.8 | 115.7 |
| B | 93.0 | -60.7 |
Edited the main alog to make some of the definitions more clear and add the calculated output matrices.
The input/output matrices have been added to the computer system:
H1:ALS-X_WFS_INPIT_MTRX_...
H1:ALS-X_WFS_INYAW_MTRX_...
H1:ASC-OUTMATRIX_P_...
H1:ASC-OUTMATRIX_Y_...
Written by Yuta
From the measured WFS sensing matrix, the estimated Gouy phase difference between WFSA and WFSB is 66 +/- 4 deg for pitch and 24 +/- 5 deg for yaw.
I think this is a reasonable measurement. See also alog #10056.
[Method]
Theoretical WFS sensing matrix can be written as;
DIFF COMM
WFSA P*(a*sin(etaA)-b*cos(etaA)) P*(c*sin(etaA)-d*cos(etaA))
WFSB P*(a*sin(etaB)-b*cos(etaB)) P*(c*sin(etaB)-d*cos(etaB))
a,b,c,d can be calculated by the cavity geometrical parameters(length, RoCs). So, from the sensing matrix measurement, P, etaA, etaB can be estimated by the fitting.
Here, I used the least squares method (scipy.optimize.leastsq) to estimate etaA and etaB, and the measurement error is assumed to be 10% for all the sensing matrix element.
[Result]
Attached. Curves show theoretical WFS signal dependence on the Gouy phase. DIFF and COMM is approximately HARD and SOFT mode of the caivty.
(Comment added: HARD/SOFT is opposite in the measurement?)