Brett and Jeff

Summary:

I have managed to account for the missing 1.5 factor by adding in the pitch to cavity transfer functions. See the first attached figure. The black curve is the model of the SUS point longitudinal to cavity. The red curve is the same measurement of the SUS point witness sensor (H1:SUS-ETMY_M0_ISIWIT_L_DQ) to cavity (H1:ALS-Y_REFL_CTRL_OUT_DQ) transfer function measured in log 7214. Thus, the same factor of 1.5 exists between these curves. It turns out that the cavity also has a lot of coherence in the same frequency band from the SUS point pitch witness sensor (H1:SUS-ETMY_M0_ISIWIT_P_DQ). So, I followed the assumption that I could account for the missing factor by simply measuring the pitch to cavity transfer function, converting it to length coordinates, and adding it to the longitudinal transfer function. The blue curve is this transfer function converted to length units. The conversion from rotation to length units was done using the measured transfer function from the pitch SUS point witness to the length SUS point witness. The magenta curve is the coherent sum of the two transfer functions. This magenta transfer function agrees much better with the model.


Details:

What I hadn't taken into account before is that the measured transfer functions between the ISI and cavity are passive. Thus, there are 6 simultaneous excitations influencing the cavity through ETMY which are the 6 DOFs of STG2 of the ETMY ISI. It turns out that 2 of these excitations are coherent to the cavity as well as themselves. The two are the ISI pitch witness and the ISI longitudinal witness. The argument justifying/explaining why one must sum the pitch and long witness to cavity transfer functions in order to agree with the modeled SUS point long to cavity transfer function is intended to be explained in detail in a future document. It will be summarized briefly here.

Since the witness long and pitch TFs have good coherence in a band around 1 Hz, (where the measurement needed help matching the model), the long and pitch displacement can be thought of as transformed versions of the same noise. Fundamentally, the noise must be thought of together as a single long-pitch source (analogous to how SUS long and pitch modes are really long-pitch modes), rather than thinking of them separately. The relation projecting the long-pitch seismic motion into long and pitch components is determined by the coherent transfer function between long and pitch. 

To get the right measurement to match the model, we must find the transfer function between the long-pitch seismic source and the cavity signal. Since none of our measurements directly measure this long-pitch source, we must effectively recreate is with the measured transfer functions from its components. Those transfer function components are then summed coherently as described in the summary above and in the attached plot.

It seems that during these measurements, the ETMY ISI was indeed only damped while the ITMY ISI was isolated. This is evident given the large discrepancy in measured ISI WIT L and P ASDs between the two ISIs. See the attached figure.

This data is collected in the DTT file 
/ligo/svncommon/SusSVN/sus/trunk/QUAD/H1/ETMY/Common/Data/2013-07-23_CavityASDMeasurements.xml
and exported in the file
/ligo/svncommon/SusSVN/sus/trunk/QUAD/H1/ETMY/Common/Data/2013-07-23_CavityASDMeasurements_Export

The exported data is exported in the following order:

1. H1:ALS-Y_REFL_CTRL_OUT_DQ
2.  H1:SUS-ETMY_M0_ISIWIT_L_DQ
3.  H1:SUS-ETMY_M0_ISIWIT_T_DQ
4.  H1:SUS-ETMY_M0_ISIWIT_V_DQ
5.  H1:SUS-ETMY_M0_ISIWIT_R_DQ
6.  H1:SUS-ETMY_M0_ISIWIT_P_DQ
7.  H1:SUS-ETMY_M0_ISIWIT_Y_DQ
8.  H1:SUS-ETMY_L3_OPLEV_PIT_OUT_DQ
9.  H1:SUS-ETMY_L3_OPLEV_YAW_OUT_DQ
10. H1:SUS-ETMY_MASTER_OUT_F1_DQ
11. H1:SUS-ETMY_MASTER_OUT_F2_DQ
12. H1:SUS-ETMY_MASTER_OUT_F3_DQ
13. H1:SUS-ETMY_MASTER_OUT_LF_DQ
14. H1:SUS-ETMY_MASTER_OUT_RT_DQ
15. H1:SUS-ETMY_MASTER_OUT_SD_DQ
16.   H1:SUS-ITMY_M0_ISIWIT_L_DQ
17.  H1:SUS-ITMY_M0_ISIWIT_T_DQ
18.   H1:SUS-ITMY_M0_ISIWIT_V_DQ
19.   H1:SUS-ITMY_M0_ISIWIT_R_DQ
20.   H1:SUS-ITMY_M0_ISIWIT_P_DQ
21.   H1:SUS-ITMY_M0_ISIWIT_Y_DQ
22.   H1:SUS-ITMY_L3_OPLEV_PIT_OUT_DQ
23.   H1:SUS-ITMY_L3_OPLEV_YAW_OUT_DQ
24. H1:SUS-ITMY_MASTER_OUT_F1_DQ
25. H1:SUS-ITMY_MASTER_OUT_F2_DQ
26. H1:SUS-ITMY_MASTER_OUT_F3_DQ
27. H1:SUS-ITMY_MASTER_OUT_LF_DQ
28. H1:SUS-ITMY_MASTER_OUT_RT_DQ
29. H1:SUS-ITMY_MASTER_OUT_SD_DQ

Note, the cavity signal H1:ALS-Y_REFL_CTRL_OUT_DQ is calibrated in Hz. The ISI witness signals are calibrated in nm. The calibration of the optical levers is unknown. The MASTER_OUTs calibration is also unknown to me.
The fist column of the exported data is the frequency vector. Each exported channel then follows in order, occupying the remaining columns. The transfer function export in 7214 above follows a similar pattern, except that each channel occupies two columns. The first is the real part of the transfer function data, the second is the complex part.

After doing some modeling in MATLAB, the analysis in 7236 stating that it is necessary to consider both the pitch and longitudinal seismic noise in the transfer function to the cavity looks to be incorrect. The transfer function between the longitudinal ISI witness sensor and the cavity motion should indeed replicate the quad MATLAB model transfer function between the suspension point and test mass L DOF. Thus, it appears there is a calibration error of 2 in measured transfer function.