[Komori getting information from Tamaki, Ushiba, and Yokozawa]
The upper limits of pitch and vertical suspension thermal noises were estimated by fitting a thermal noise model to the DARM spectrum measured at 11 UTC on June 7th.
We are aware of the two resonant frequencies of the pitch and vertical modes of the blade spring and CuBe fiber, as documented in klog:25800 and klog:25830.
The Q-values were estimated by fitting to each resonance peak.
The coupling factor was estimated based on the CuBe resonance around 40 Hz, assuming that the CuBe peak is driven by thermal fluctuations.
An example of the fitting is shown in the first figure.
Due to the roll-off and notches in the MN damping filters, the CuBe resonances are not excited by actual motion or ADC noise but are excited by DAC noise (~1e-4 count/√Hz).
This DAC noise is comparable to (much smaller than) the thermal noise of the pitch (vertical) mode.
The thermal noise spectra from the pitch and vertical modes are shown in the second and third figures, respectively.
The fitting results are listed below.
The term "mis-centering" refers to the discrepancy in the beam spot from the mirror center, and VHC stands for vertical horizontal coupling.
| Pitch Q of blade | Pitch Q of CuBe | Miscentering [mm] | Vertical Q of blade | Vertical Q of CuBe | VHC | |
| ETMX | 2.9e3 | 4.1e3 | 10 | 9.1e3 | 2.2e3 | 0.13 |
| ETMY | 6.1e3 | 5.5e3 | 2.6 | 4.7e3 | 3.7e3 | 0.011 |
| ITMX | 8.0e3 | 2.3e3 | 11 | 6.5e3 | 5.5e3 | 0.051 |
| ITMY | 6.3e3 | 1.0e3 | 5.5 | 4.3e3 | 5.6e3 | 0.019 |
According to klog:25874, the mis-centering of ETMX in the pitch direction is 2.5 mm.
However, here it is overestimated to be 10 mm.
This discrepancy may be due to the pitch mode being primarily excited by comparable DAC noise.
Regarding vertical coupling, the estimated ETMX VHC value of 0.13 seems too large.
The VHC is determined by the relative angle between the IM (or MN) and the TM.
The oplev measurements indicate that the angle is not significant.
The reason for the vertical mode being excited by other noises is unknown.
I will upload the estimated spectra of the pitch and vertical suspension thermal noise to Pastavi.
It is important to note that this analysis provides only the upper limit, but in reality, the thermal noise is at least a few times smaller than the upper limit.
Lastly, the Q-value of the sapphire blade spring ranges from a few 10^3 to 10^4, which is lower than the design value but consistent with some previous measurements such as Tamaki-kun's master thesis.
This imposes stringent requirements on mis-centering and vertical horizontal coupling in the near future, making it challenging to achieve the design sensitivity.
