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takafumi.ushiba - 13:59 Friday 26 July 2024 (30580) Print this report
Comment to Consideration of OMC trans noise caused by OMC length noise transferred from the OMC chamber optics table (30498)

I crosschecked the OMC length noise from the measurement done on July 22.
Figure 1 shows the diaggui file, which I used for the calculation.

According to the OMC SUM during the measurement (fig2), OMC transmission power was about 29 mW, so I calibrated K1:OMC-TRANS_DC_SUM_OUT_DQ to RIN by dvided with 29.
According to klog30535 and klog50539, the calibration factors estimated from two different method were 5.1e9 and 6.4e9 cnt/m, respectively.
So, I used the averaged value, 5.75e9 cnt/m, for the calibration of error signals to displacement.
I also calibrated geophone signals and seismometner signals to displacement by devided with 2*pi*f (I could not confirm current calibration is um/s for both geophone and seismometer at OMC, so it might be wrong. If so, please let me know).

Around 92 Hz (injection frequency), RMS of OMC error signals were 2.2e-12 m.
According to the PZT actuator efficiency, 1.3e-10 m/cnt (klog30490), and cavity scan of OMC (fig3), FWHM in the unit of meter is 1.3e-10*5.5 = 7.2e-10 m.
So, RIN of OMC transmission generated by the displacement around 92 Hz can be estimated as 2*(2.2e-12/7.2e-10)**2~2e-5.
According to the direct measurment of RIN of OMC transmission, RMS of RIN around 184 Hz, which is double of the injection frequency, is about 1.9e-5 (fig5), which is almost consistent with the value estimated above.
So, the above estimation method from OMC error signals to RIN of OMC transmission seems to work well.

The transfer function from geophone to OMC error signals at 92 Hz is 0.0023, according to the measurement (fig6).
Now, let's say OMC vibration around 92 Hz without excitations is 1e-11 m/rtHz according to the measurement (fig7).
OMC length displacement can be estimated as 1e-11*0.0023=2.3e-14 m/rtHz
So, RIN of OMC transmission will be 2*(2.3e-14/7.2e-10)**2~2e-9, which is lower than shot noise limit of 15mW OMC transmission, 5e-9.

According to the TF measurement from geophone to OMC error signals (klog30521), the gain from geophone to OMC error signals at 92 Hz is larger than that at the other frequency, except for 82 Hz: this means RIN of OMC transmission would be lower than 2e-9 at the other frequencies.
So, it might be difficult to explain the OMC noise floor above 100 Hz only by optical table vibration on the OMC stack.

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