Figure 1 shows the spectrum for the 56MHz TEM00, both USB and LSB, normalized to be units of RIN, and with the contribution of shot noise and PD electronic noise quadratically subtracted. The spectrum looks the same for both sidebands, and there was no significant change during the 2.5 hours separating the repeated measurement of the USB, which is a sign that the alignment has not drifted in the meantime, the beam jitter peaks are small in all cases. The requirement (VIR-1225B-19) for the RAM servo is 2.5e-8 V/V/rtHz at 100Hz, which should correspond to RIN of the sideband of 5e-8 1/rtHz. So probably RAM is a significant part of that spectrum, but this would need to be checked further, as the RAM servo was better than the requirements from what I remember.

Figure 2 shows the coherence with B1s, it is substantial at ~30%. It means that the sidebands are a major contributor to the dark fringe fluctuations in the 100Hz and 500Hz. The coherence for the red trace is smaller as there is a loud glitch on B1s dominating the spectrum during that measurement. 

There is no broadband coherence of the sideband with h(t).

Figure 3 shows the series of measurements with the first measurement being the 56MHz USB, and the last measurement being also the 56MHz USB

Figure 4 shows the spectrum of the higher order modes from 2 to 10, with two measurements for the mode order 9 (vertical and horizontal peaks). The PD electronic noise is 1e-8 mW/rtHz, and for the peaks with low power, the spectrum at 1kHz is very close to that limit. There is about a factor 10 difference in power between the brightest mode (order 3) and the  dimmest (order 10). The B1 photodiodes have a lower dynamic (~5mW), which would be sufficient as the brightest mode has 1mW in this scan, and have a lower electronic noise at 6.5e-9, so that could be a simple solution to gain a factor sqrt(2) in SNR for these measurements.

Figure 5 shows the same normalized in units of RIN and with the shot noise and electronic noise quadratically subtracted. In these units the noise level is more similar between the modes, the beam jitter peak height varies by one order of magnitude between different modes. There could be a similar level (within a factor 2) of noise that has a power-law shape around 100Hz, with a slope between 1/f and 1/f^{2/3}. That level of noise is a factor 2 higher than what is measured with the 56MHz sideband, so it is not intrinsinc to the measurement process, but HOM may be more affected than a TEM00 mode by beam jitter.

Figure 6 shows that none of those mode is coherent with B1s down to 0.1% level, which is surprising. It tells us that the EDB OMC is adding new information that is not accessible using only B1s, but it is unclear what that information means. There is coherence in the 20-30Hz band where the SRCL and MICH lines are in LN2 and at ~156Hz where the mechanical mode of SIB1 is.

Figure 7 shows the coherence with h(t), there is no broadband coherence to the 0.1% measurement noise level.

Figure 8 and 9 shows mode 3 and 5 which have the powerlaw slope the most clear, as they have high power and low amplitude for the beam jitter peaks

Figure 10 and 11 shows mode 2 and 4 which have a significant lower noise than modes 3 and 5

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