M. Todd, S. Dwyer

I've been polishing up the analysis of models estimating the various couplings of TCS powers to substrate and surface defocus in the test masses. This can be used to test the validity of the HWS estimate of the absorption in the ITMs. For reference, assuming the HWS are correct in their calibration of what the substrate defocus is in the test masses [ITMY = 63.5uD, ITMX = 54.5uD], and that my model is right estimating the absorbed Watts of power from substrate defocus [250 uD/W], then we have rougly 254mW of absorbed power in ITMY and 216mW of absorbed power in ITMX. Naively this seems too much, but I wanted to see if this could be consistent with measurements of the arm cavity Gouy phase.

We have fully thermalized HOM spacing measurements from the OMC DCPDs which can be translated into absorbed power estimates if you know how the Ring Heaters and how they couple to defocus. Models have yielded great agreement with the measurements of this coupling (previous conventions were not consistent with proper radius of curvature relation to defocus, but a technical note should hopefully be linked soon). Then, if we use the absorption derived from the HWS estimates, with an arm power of 345kW (average of Sidles-Sigg mode inference and arm gain inference), as well as coupling factors from my modeling we would infer ETM absorptions: ETMX abs: 0.228ppm and ETMY abs: -0.255ppm. For comparison, the galaxy estimates are 0.21ppm and 0.20ppm, respectively. This indicates that the ITMX HWS may be fine, but that the ITMY HWS may be miscalibrated. 

If instead, we assume ETM absorptions reported by galaxy, then the HOM spacing measurements would suggest ITM absorptions: ITMX abs = 0.678ppm, ITMY abs = 0.321ppm, half of what the HWS on ITMY reports. Some evidence that may support this is turning the CO2s off separately after the IFO cools off, where ITMY HWS reports twice the defocus as ITMX HWS -- unless there is some gross misalignment of CO2X the values should not be very different given the same CO2 power. I do not have any models of this to corroborate this but it is interesting (the HWS SLED was just replaced for ITMX).

I am not well versed in HWS code and I'm not totally sure how these values of defocus are calculated from the deflection of each partitioned beam but these errors may be mis-identification of the position of the centroid. More thought is needed!

This is a table of parameters describing the various coupling factors from the modeling. Note that the values for the ring heaters are assuming perfectly efficient ring heaters, which have previously been estimated to have an efficiency of around 75%, though the cold IFO HOM spacing measured with the SQZ dataset suggests the ring heater efficiencies are actually much closer to 100%. 

This is a summary table using the above modeled parameters