We grabbed the measurement data that Oli generated on [LHO: 85288] which was taken using the calibrated OSEMINF gains that we obtained by driving the ISI an looking at the OSEM response at high frequencies [see LHO: 84367].

The TL;DR is that the calibration works:

• The diagonal elements of the measured and modeled plants now match.
• The measured TFs are a bit more symmetric.
• We see the expected reduction in cross-couplings to Roll and Pitch.

The .pdf attached can be found in

https://svn.ligo.caltech.edu/svn/sus/trunk/HLTS/H1/SR3/SAGM1/Results/2025-06-24_1900_H1SUSSR3_M1_ALL_TFs.pdf

We can see that the diagonal M1 to M1 modeled and measured transfer functions actually match one another much better than before (for an example uncalibrated plot, click here to see April 2025). This happens even though the calibration did not involve M1 to M1 transfer functions.

We can assess the impact that the calibration had on the M1 to M1 cross-couplings by plotting a normalized version of the cross-coupled transfer functions. For example, the Length-Pitch normalized transfer function will be (L2P)_norm=(L2P)/sqrt(P2P*L2L).

This way we can get rid of the overall scaling factors that come from the OSEM calibration and focus on the cross-coupling. The result is shown in the second attachment. The columns correspond to M1 drives, and the rows are OSEM displacements, all plots are dimensionless. The blue trace is after OSEM calibration, and red is before OSEM calibration, and from 2024/08/08 to avoid the gains that were in the yaw and pitch TEST drive paths in the more recent data [see LHO: 84259].

The cross-couplings of=n this last plot can be broken down into 4 general types of cross-couplings:

1) Things that don't change much (L2T, L2P, etc)- Nothing to say.

2) Cross couplings that improve quite a bit with the calibration. [V2R, V2P R2V, and R2P]. This were what we expected from the original calibration procedure. Especially cross-couplings involving the Roll degree of freedom were expected to improve.

3) Cross couplings that got a bit worse, but were expected [Y2R, Y2V, L2V, and L2R]. These are related to the fact that the average calibration for the LF and RT OSEMs is very different for the three osems atop the suspension T1, T2, and T3. The cross-coupling is not higher, it's just a normalization quirk.

4) Cross-coupling that got worse and was unexpected. Only P2R fits this category. The calibration should make the plant more symmetric, so it is at least good that P2R and R2P seem more similar now. Since the coupling that's changing is going to Roll, we believe this is actually more accurate to the underlying Pitch-Roll plant compared to the results from before.

The next steps for this work are to semi-automate the calibration process, and to methodically deploy the calibration to other suspensions now that the SatAmp work has been done.