Continued the study of the HOM noise in LN2. Went through all the modes from 1 to 9. 

The attached figure show the mode shape, and the corresponding spectrum, taken during the measurement. Started to take the pictures only starting from mode order 3.

The OMC error signal demodulation phase might be badly tuned, with most of the signal on the q quadrature, so it is better to reconstruct the error signal from the demodulated signals instead of using directly the EDB_OMC1_err channel. I noticed it only when looking at mode order 9.

The data collected below needs to be analyzed.

15:49 UTC (5min) - locked on carrier order 1 mode (mostly horizontal)
15:55 UTC (5min) - increased OMC modulation depth to 0.5V

16:08 UTC (5min) - locked on carrier order 2 mode (mostly vertical)
tried to improvement alignmetn to reduce the beam jitter peaks at a few hundred Hz. It did work, used only the first mirror. The power of the mode also increased slightly
16:19 UTC (5min) - locked on carrier order 2 mode (mostly vertical)
16:25 UTC (5min) - increased OMC modulation depth to 0.5V

locked on mode order 3 and made small vertical realignment to reduce beam jitter peaks
16:37 UTC (7min) - locked on carrier order 3 mode (6 petals), but then around 16:38:40 1 minute jumped to mostly vertical, with higher beam jitter peaks
16:45 UTC (5min) - increased OMC modulation depth to 0.5V

locked on mode order 4 and made small vertical realignment to reduce beam jitter peaks
16:57 UTC (6min) - locked on carrier order 4 mode (mostly horizontal
17:04 UTC (5min) - increased OMC modulation depth to 0.5V

locked on mode order 5 and made small vertical realignment to reduce beam jitter peaks
17:20 UTC (5min) - locked on carrier order 5 mode (5 horizontal lobes, two vertical)
17:26 UTC (5min) - increased OMC modulation depth to 0.5V

locked on mode order 6, beam jitter peaks are already relatively small
17:38 UTC (5min) - locked on carrier order 6 mode (mostly vertical)
at 17:43:05 the registered temperature of the EDB OMC jupmed by 5mK (it is out of loop), also B1s increased by a few percent (PD with turned of Vbias)
17:46 UTC (5min) - increased OMC modulation depth to 0.5V

locked on mode order 7, realigned slightly in horizontal and vertical, beam jitter peaks almost completely disappeared and power of mode increased by factor 2
18:03 UTC (5min) - locked on carrier order 7 mode (mostly vertical)
at 18:07:40 the registered temperature of the EDB OMC jupmed by 5mK (it is out of loop), also B1s increased by a few percent (PD with turned of Vbias)
18:11 UTC (4min) - increased OMC modulation depth to 0.5V

18:15 unlock due to WE DSP glitch, the work around implemented so far does not help

relocked in LN2, locked OMC on moder orde 8, aligned slightly to reduce beam jitter peak and increase power of mode
18:51 UTC (5min) - locked on carrier order 8 mode (a wide blob in both directions), forgot to reduce modulation depth, so it is at 0.5V
another alignment improvement
19:00 UTC (5min) - reduced OMC modulation depth to nominal

locked on mode order 9, realigned slightly in horizontal and vertical, to reduce beam jitter, peaks sometimes disappear, but go up and down in height
19:15 UTC (5min) - locked on carrier order 9 mode (mostly horizontal)
19:22 UTC (5min) - increased OMC modulation depth to 0.5V

relocked onto the vertical mode 9, not trying to realign it, as it is the smaller mode from which it easy to jump into the horizontal one
19:34 UTC (5min) - locked on carrier order 9 mode (mostly vertical)

locked on order 10 mode
19:52 UTC (5min) - mostly horizontal

going to order 2 mode again, when crossing all the sideband and
carrier TEM00 I have noticed the 56MHz TEM00 had low power, the 56MHz
order 1 modes had similar power as the 56MHz TEM00, and there was a
high power TEM00 in between, is it a carrier created from the HOM?

20:13 UTC (5min) - order 2 mode, vertical, has 5 times less power than at the beginning

20:27 UTC (5min) - unexpected TEM00, jitter peaks are relatively high, but I haven't realigned for this mode

Most likely the realignments to reduce the beam jitter peak have
actually completely misaligned the OMC, so it mixes all the modes
together, including all of the HOM into a TEM00.

Will need to repeat the whole experiment, but this time aligning only
once on the 56MHz, and not touching the alignment afterwards, even if
the spectra are spoiled by beam jitter
 

Figure 1 shows the spectrum of the order 2 mode for three different alignment: initial alignment, slight re-alignment to reduce the beam jitter peaks by factor 10, alignment after doing slight realingments on 9 different modes. That last curve has 5 times less power than the other two, as the alignment has drifted far after many realignments on very high order modes. 

Figure 2 shows the same data in terms of RIN, with the expected level of shot noise and PD electronic noise quadratically subtracted. There is an underlying broadband noise that has a slope somewhere between -1 and -0.66, it is present in all three cases, but is higher for the large misalignment (yellow line)

Figure 3 shows the sensing noise subtracted RIN for modes 1, 2, 3, 4 and 5, in that order. Modes order 1 and 3 are more strongly affected by beam jitter peaks. All the spectra hint at a broadband noise with a slope between -1 and -0.66.

Figure 4 shows that low level of noise with this setup can be achieved. It shows a spectrum of a single bounce beam from two months, lock on the 56MHz LSB done the previous day, and the order 1 mode and order 2 mode after realignment. The single bounce beam had noise a factor 4 lower at 100Hz, and had a similar power to the order 1 mode and order 2 mode. The 56MHz LSB had 5 times lower power, so more sensing noise,  it has a comparable RIN to the carrier HOM, but a different shape, more flatter.

Figure 5 shows modes 6, 7, 8, 9 horizontal, 9 vertical, 10 and mode 00 after the cumulative misalignment from many changes in alignments for each HOM. The three 20% higher spectra at 140Hz correspond to modes that had a mostly vertical shape (order 6, 7 and 9 vertical mode). 

As the realignment to minimize the beam jitter peaks actually degraded the alignment for the TEM00 mode by a factor few, the latter measurements correspond to observing  each time a different mix of higher order modes of the beam. As the EDB OMC decomposes the beam on a completely different basis in a misaligned state.

None of the modes was coherent with h(t).

/users/mwas/ISC/RINanalysis_20250624/analyseRIN.m