[Alex]
Investigating if the Beam Jitter Coupling has Changed
Summary: The beam jitter coupling has become worse since July 2025, especially around 350 Hz. This seems to be a real change in the coupling and not just an increase in the amount of beam jitter. We're not sure why it has increased but it may have something to do with warming up the detector or reducing the power.
Background
A few weeks ago we (Carl and Alex) made measurements of the beam jitter coupling from 250-500 Hz we noticed that the beam jitter projections were very close to darm and even over-projected at some points. We were confident that the coupling function was reasonable accurate since we had a high SNR is our noise injections in the witness sensors and DARM. This was concerning we know that DARM was lower when the detetector was operating at 10W in July but the detector noise was also lower in the regions that we were projecting beam jitter.

We manually fitted the shot noise component to DARM in order to estimate the techincal noise in this region.

This also implied that the technical noise was much higher now than in July. This left us two posibilities: the beam jitter has increased or the detetector is now more sensitive to beam jitter.
Witness Sensors
I chose to look at the IMC-REFL_QPDA1_DC since we had engaged the whitening filters on the RF channels for the time period I was looking at, as far as I am aware has have been no changes to DC sensors since O4. The noise spectra of the sensors did not appear to show any major differences between July 2025 and Februrary 2026. The spectra in february do show an increase level of noise in in the peaks around 350Hz but the increase does not correspond with the same increase in DARM.

I then looked at the coherence of these sensors with DARM which showed that the coherence had increased significantly in this region.

This implies that the coupling function has changed so that the detector has become more sensitive to beam jitter. I then decided to try and estimate the coupling function in July and Compare it to now.
Coupling Function Estimates
Ideally to measure the coupling function we would perform a noise injection, however this is not possible since we are looking at past data. Instead I used the method given in Davis et al which describes on the ways that noise subtraction was done at LIGO Hanford. This uses the cross spectra density to estimate the transfer function from multiple witness sensors to DARM.
The cross spectral density is defined as:
where Y1 and Y2 are the fourier transforms of the time series. The coupling function for each witness sensor is then defined as:
where CF is the coupling function and 0 is the target channel for noise estimation/subtraction and indices > 0 represent different witness sensors. In the case of N=1 this reduces to:
which is the conventional definition of a transfer function. In our case we use a 2 channel estimation which witness sensor 1 being pitch and witness sensor 2 being yaw of the IMC-REFL QPDA1 DC.
I took 1000 averages from 02/07/25 01:25:00 UTC for the July measurement and 1000 averages from 24/02/26 14:53:00 UTC for the February measurement. This gave the following coupling function estimates:


and the corresponding jitter noise projections:


While there is obviously some overprojection these seem to match DARM reasonably well and show that the beam jitter noise has changed.
Causes and Solutions?
We don't know what has caused this but we know that the arm finesse has changed since the detector has warmed up so maybe the balance of the arms has also changed? As for a solution, not sure if what the solution is if we don't know the origin of the change, it's possible that going back to cryogenic temperatures and increasing the power again might reverse the change. It highlights the need for any noise subtration to be able to cope with changes in the coupling function over time.