[Aidan, Alastair]
Per the discussion on the position dependent coupling of CO2 noise to DARM, we injected a 23.8Hz line into CO2Y yesterday (using a function generator) yielding a 1.5E-2 /sqrtHz line in RIN for that laser.
We turned the laser on to inject 100mW onto ITMY. A line appeared in DARM at 23.8Hz
We used PICO_G Motor 3 to steer the TCSY beam around on ITMY and observed the magnitude of the line in DARM. By eyeballing the live spectra, I could roughly maximize the line around PICO motor counts [-1E4, 3E4]. Then we swept the beam in the vertical direction on the mirror until the line disappeared in DARM. We reversed the direction of the sweep, moving the beam through maximum coupling through to minimum coupling again. We returned the beam to the rough position of maximum coupling and repeated the procedure in the horizontal direction.
The results were a bit noisy. We used the following channels to track the position of the PICO_G mirror and the line magnitude vs time.
- t0 = 1138508180
- t_end = 1138510325
- power to ITM:'H1:TCS-ITMY_CO2_LSRPWR_MTR_OUT16
- X-position: H1:SYS-MOTION_C_PICO_G_CURRENT_X_POSITION
- Y-position: H1:SYS-MOTION_C_PICO_G_CURRENT_Y_POSITION
- DARM spectrum: H1:CAL-DELTAL_CTRL_DQ
We left the mirror at position [-1E4, 3E4] last night.
Following the scanning, I analyzed the data this morning and found that the, despite being noisy, we could estimate the maximum coupling point as [-5E3, 3.1E4] with an uncertainty of approximately +/- 3000 counts. I moved the mirror to this position this morning.
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A word on the uncertainty:
- as previously established, the beam moves approximately 6E-6m on the test mass per count of the PICO mirror.
- The uncertainty of 3000 counts corresponds to approximately +/- 20 mm
- The single-pass thermal lens per Watt of CO2 laser central heating is around 39uD
We can estimate the maximum single-pass thermal tilt we should see because of the uncertainty in the alignment:
- defocus: S = 39uD/W
- wavefront, 1D: W = S/2 * x^2
- gradient: dW/dx = S*x
- centering uncertainty: sigma_xc
- maximum thermal tilt = S*sigma_xc ~ 40uD/W*20mm ~ 800nrad/W
If we operate the TCS in the range [0, 500mW], then we should anticipate up to 400nrad of thermal tilt induced in the IFO beam
