Follow up to LHO alog 83200 and LHO alog 80863.
Brian and I thought of a better way of getting the M1 OSEMs in PR3 calibrated relative to the HAM2 GS13s: Use the ISI drives in L, T, V for frequencies above the suspension resonances to get an absolute calibration.
We can use the measurements Jeff took in LHO alog 80863 and project them in the OSEM basis, then use the translational (Longitudinal, Transverse, Vertical) drives to calibrate the OSEMs. Since the GS13s are calibrated to [m] all of the transfer functions (shown in the first attachment) are in [OSEM meters]/[GS13 meters]. At high frequencies (sufficiently above the resonances) the OSEMs should just be measuring (-1)*ISI motion, because the suspension is isolated. The calibration error will depend on how well we are able to drive L,T,V from the ISI without cross-coupling to any other DOF.
Figure 1 attached shows the 6x6 transfer matrix between the ISI drives and OSEMs (inputs are columns, and outputs are rows). We highlight the 6 translational transfer functions that can be used to calibrate the OSEMs in red. The drives seem decoupled enough to do the calibration (for example, we expect to see a length drive only in LF and RT, no motion anywhere else).
Figures 2,3, and 4 show a detail of the 6 transfer functions we will use for calibration, all of them should be scaled to 1 [OSEM m]/[GS13 m]. The scalings are:
T1 T2 T3 LF RT SD
1.544 0 0 0 0 0 T1
0 1.394 0 0 0 0 T2
0 0 1.273 0 0 0 T3
0 0 0 1.411 0 0 LF
0 0 0 0 1.588 0 RT
0 0 0 0 0 1.366 SD
Two things to note:
1) The relative calibrations are consistent with the ~15% mismatch that led to the V to R and the L to Y couplings that Brian and I observed in the comments of
LHO alog 83200.
2) The absolute calibrations being in the ballpark of 1.5 seem large, but they are close to the calibration factor in
plotHLTS_ISI_dtttfs_M1.m that transforms between [um/drive cts] to [m/N]. The transfer functions plotted always seem about a factor of 1.5 off from the MATLAB model. Maybe there's a connection that explains why the calibration factor seems so large.
Figure 5 shows all of the diagonal ISI to M1 transfer functions after applying the calibration factors. They all asymptote to 1 at high frequencies even though we only used L, T, and V for calibration. A good sign that we're on the right track.
Figure 6 shows the effect of the calibration on the M1 to M1 transfer matrix (inputs are columns, and outputs are rows). The solid Black trace is the corrected M1 to M1, the dashed lines show what it was before the sensor calibration. A few of the cross couplings become significantly better: [L-Y], [V-P-R] are the best performing.
I think this gets enough benefit for the ISI - SUS estimatior. It also might be worth trying this scheme in other suspensions where we would benefit from eliminating more cross terms in the OSEM transfer matrix.
