Figure 1. The B4 phase camera has an apparent offset in the sideband power measurement when no light and no reference beam is present on the phase camera. The offset is around 25e-6 in the not normalized channels. This offset has been present for at least the past three years, and has been relatively stable over that period.
Figure 2. That offset is comparable to the sideband power in single bounce, especially when the input power is low, as in this example with 11W of input power. The signal of the phase camera for the 6MHz increases only by a factor 2, in the single bounce configuration, compared to the dip in the middle which is at 25e-6 corresponding to no beam arriving on the phase camera.
If that is a real offset, then in single bounce the power of the sidebands is overestimated by a factor, and the sideband gain is under estimated by a factor 2. It would also affect the measurement of the sideband modulation depth that use single bounce beam data and the ratio between the sideband and the carrier power as measured by the phase camera.
Analyzing data from the reference period at 11W used in the O4 detector paper (VIR-0710G-24), on Dec 10, 2023. The 6MHz modulation depth without compenstating for the offset is 0.21, while by subtracting the offset it becomes 0.15. However, the modulation depth measured simultanously with the B1p camera is 0.19, much closer to the value without subtracting the offset, and the B1p camera is not affected by the offset issue because the power is much higher, so the offset is always negligible compared to the sideband power in single bounce.
Similarly the 56MHz sideband has modulation depth of 0.21 on B4 without correcting for the offset, and 0.14-0.16 after correcting for the offset, while on the B1p phase camer it is 0.19-0.20.
/users/mwas/PC/PC_modulation_depth/SB_mod_depth.m
Figure 3-5 The OMC was scanned a few days later on Dec 19. The carrier TEM00 power is 0.0272 and the 56MHz sideband power is 0.29e-3, which correspond to a modulation depth of sqrt(4*0.29e-3/0.0272) = 0.206, which agrees with the B4 phase camera measuremetn without offset correction.
It appears that the offset visible in the phase camera does not affect significantly the sideband power measurement despite the offset being equal to half of the sideband power measured value on a single bounce beam.
Looking at the phase camer code and raw data, this offset is likely the average value of numerical noise.
Figure 6 shows the raw phase camera data at a time when no beam is present, and it is clearly a digital noise with an integer number of counts between 0 and 3. Looking at the computation of the sideband power in /virgoApp/PyALP/v3r0/src/main.py, it is the average value of the square of that channel over one second.
Figure 7 for comparison shows the same raw data when the interferometer is full locked. This is only available in raw full data so we do not have recent data, but there were some times which have been archived. I did not search the archive extensively, but I do not expect we have archived single bounce raw full data. The power of the sideband in single bounce should be a factor 5e-2*0.5^2/20 smaller, where 5e-2 is the PR transmission, 0.5 the BS reflectivity and 20 the sideband gain, which means the amplitude as measured by the phase camera should be a factor 40 smaller in single bounce than with a full interferometer, corresponding to up to 15 counts. Given that the average is looking at the square of the PC raw channel, mostly the times when the value is large count in the average, and these will be less affected by a digital noise of a few counts around 15, especially if that noise becomes symmetrical once the signal is no longer at the zero rail of the digital output.
This might be an explanation why the offset is not affecting so much the measurement of the sideband power, but that depends on how that digital noise behaves when there is a small but not zero signal. It will be easier to confirm once we get back a single bounce beam to have access to PC raw data in single bounce.