J. Kissel, K. Izumi, D. Tuyenbayev, S. Karki, C. Cahillane

We've completed all the to-do list items for comparing all three methods of measuring actuation strength (listed in LHO aLOG 21015). This means that the ER8 / O1 DARM model is virtually complete. Now we just need to compare the full model against measured DARM OLGTFs to confirm no remaining high-frequency systematics in either the actuation or sensing function, the we can declare victory on the frequency domain model side of things. Once victorious there, we
- Update the CAL-CS front-end model to match the low-frequency content of matlab model
- Update the GDS pipeline to matach the high-frequency content of the matlab model
- Generate an inverse actuation filter, and install it in the CAL-CS bank
We hope to complete these items within the next few days.

Results on the Actuation Strength of ETMY
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Though there still remain some unexplained systematics, we are confident enough in the PCAL results that we've chosen to use only the PCAL to determine the actuation strength to high precision. The other two methods, ALS DIFF and Free-Swinging Michelson, though less precise, confirm the accuracy within their statistical uncertainty (though rigorous, statistical comparison was not done). The results are as follows:

    'Optic'      'Weighted Mean'    '1-sigma Uncertainty'    '1-sigma Uncertainty'
    'Stage'      '[m/ct]'           '[m/ct]'                 '%'                  
    'ETMY L1'    '5.15e-11'         '2e-12'                  '3.9'                
    'ETMY L2'    '7.3e-13'          '5.6e-16'                '0.076'              
    'ETMY L3'    '1.11e-14'         '1.1e-17'                '0.096' 


Discussion Against ER7, Expectations, & Alternate Displays of Above
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ETMY L1 and L2 are 0.5% and 4.5% larger than what was used during ER7 (see LHO aLOG 18767), as expected because we do not expect this actuation strength to change. The larger percent change on L2 is almost certainly because we've greatly refined our knowledge of the actuation chain electronics. However, both numbers still remain very consistent with models of the transconductance of the coil drivers (the ER8 model uses the cannonical values from G1100968) and actuation stength of the A/BOSEM coil/magnet system (1.74 [N/A] and 0.0333 [N/A] are the fit values for the UIM and PUM used in this model, as opposed to the cannonical 1.694 and 0.0309 [N/A], originally from T1000164).

ETMY L3 is 45% stronger (or 82% depending on whether you choose preER7 or this measurement as the reference) from prior to ER7 (again, see LHo aLOG 18767), we believe simply because the test mass has been discharged. For those who like the numbers reported in more "fundamental" units, the ESD strength has changed from 7.96e-11 to 1.55e-10 [N/V^2].

ETMY L1's uncertainty is so much larger than L2 and L3 because a relatively huge, frequency-dependent systematic still remains in the data. Indeed, if we believe the measurements (and ALL methods show it) the UIM has a rather unsettling right-half-plane zero at around 100 [Hz].

These numbers, in the form of [N/ct], will be added to the CAL-CS model within the next day or so,
    'Optic'      'Weighted Mean'    '1-sigma Uncertainty'    '1-sigma Uncertainty'
    'Stage'      '[N/ct]'           '[N/ct]'                 '%'                  
    'ETMY L1'    '8.17e-08'         '3.2e-09'                '3.9'                
    'ETMY L2'    '6.82e-10'         '5.2e-13'                '0.076'              
    'ETMY L3'    '4.24e-12'         '4.1e-15'                '0.096'

Details & Plots
-----------------
I attached several sets of plots, one set comparing all three calibration methods against the model and each other for each stage of actuation (*_AllMethods.pdf) for all three days of measurement, and the other set comparing all three days of PCAL on one plot for each stage. It is to the latter combined data set that we fit the model and form the uncertainty estimations based on the residuals between that fit and the data. 

The model lives here:
/ligo/svncommon/CalSVN/aligocalibration/trunk/Runs/ER8/H1/Scripts/DARMOLGTFs/
H1DARMOLGTFmodel_ER8.m
with the paramater set
/ligo/svncommon/CalSVN/aligocalibration/trunk/Runs/ER8/H1/Scripts/DARMOLGTFs/
H1DARMparams_1124827626.m

The comparison script
/ligo/svncommon/CalSVN/aligocalibration/trunk/Runs/ER8/H1/Scripts/
compare_actcoeffs_ER8.m

uses Kiwamu's recently functionalized
/ligo/svncommon/CalSVN/aligocalibration/trunk/Runs/ER8/H1/Scripts/
PCAL/analyze_pcal.m
ALSDiff/Matlab/analyze_alsdiff.m
FreeSwingMich/analyze_mich_freeswinging.m

to "quickly" analysis all of last weeks data and to compare against the same model.

One can immediately see that the UIM is the outlier in terms of gross systematics here. I've been trying to chase down the high-frequency discrepanct for days, but in the interest of time, we must move on. Unfortunately, the pre-ER7 UIM measurements were only taken up to the 7 [Hz] upper-limit of FSM method, so we cannot say whether this feature has always been there. Thankfully, because the UIM is well-rolled-off by 100 [Hz] with the hiearchical control filters, even this nasty of a systematic should not impact the DARM calibration above 10 [Hz], given that the UIM / PUM cross-over frequency is roughly 2 [Hz] (we will confirm this more precisely with our model, but it has been confirmed via measurement in LHO aLOG 20941). 

We are using updated electronics chain information for the PUM and TST, based on Darkhan's and my work earlier last week (see LHO aLOGs  21232 and 21189), and this has cleaned up the results greatly from when the data was peviously, individually processed in LHO aLOGs 21049 and 21015.