Camilla, Mitchell, Cao (remote), Dan
Last night we did a cooldown measurement of the test masses and then estimated the absorption in the test masses, which assumed we know the arm power. Instead here I'll assume that we know the absorption which was measured to be 0.5ppm from the Galaxy pages for our test masses. This fit suggested 90mW absorbed which for 0.5ppm coating absorption is 180kW, which is way too low.
Our plot from this morning shows a somewhat good fit, but the temporal behaviour is obviously different and the spherical power flattens out in a way that the FEA models don't predict at later times. This temporal disagreement can also be seen in other results too such as in ring heater tests, (fig 5). I've always put this down to just the FEA models not being quite right, but after seeing the very astigmatic HWS dither magnification measurements today it seems that can also change the temporal response of the spherical power estimation from the HWS data.
From the test mass dither measurements we found it is about 30% for both ITMX and ITMY, each being astigmatic in the opposite direction. Another estimation of astigmatism can be made by assuming the ring heater tests should be cylindrically symmetric, a 10% or 3% astigmatism is found there which doesn't quite gel with the 30% from the dither measurements so not sure what to make of that at the moment.
The HWS code does not take into account astigmatic magnifications, so Cao and I made some changes and went back and reprocessed the data from last night. If I use these astigmatic dither measurements we see a much better fit. The model used is a COMSOL one from Aidan and finishes an hour in. It looks as if would continue matching well at longer times which the stigmatic HWS assumption does not.
This fit estimates that ITMY is absorbing 0.149W and ITMX is absorbing 0.283W (much higher due to the 3-4 point absorbers on it), ITMY doesn't have any point absorbers as far as we can tell, so assuming 0.5ppm of coating absorption from Galaxy: 0.149W/0.5ppm = 298kW of arm power. Which is unexpectedly in the right ballpark. Looking at E1700269, it states 0.5+-0.1 ppm but figure 1 says 0.465ppm (although outside the 120mm diameter?), 0.149/0.456 ~ 320kW...
The stigmatic setup predicts a lower 0.134/0.5ppm = 270kW of arm power from the poorer ITMY fit and about 240mW absorbed in ITMX.
There are clearly some large uncertainties in this analysis, especially with exactly how astigmatic the HWS really is, but it is suspiciously close to what we expect the arm power is from the PRG and arm gain method. Perhaps a more detailed Bayesian fit to get some better uncertainties would be interesting to try.
The code from this analysis lives in: /ligo/gitcommon/labutils/hws_absorption_fit/nov2022/fit_absorption_v2.py
After thinking about it, the dither calibration done in 6607 is not only a measure of the astigmatism, but an overall calibration of the HWS. It only makes sense to measure the astigmatism this way if we can assume that the HWS data is otherwise completely accurate.
I suspect that the HWS magnification is not actually astigmatic, especially given previous contradicting measurements. By assuming some effective astigmatism which we measured with the dither calibraiton, you essentially fix some other miscalibrations of the HWS.
This would explain why we see a better fit to the transient response here by assuming this effective astigmatism and fudging the HWS data to fit the OPLEV sensors.
Cao (remote), Dan: Better FEA model & no fudge factors => 160mW/0.5ppm = 320kW @ 50W of input power
The 30% astigmatism in the HWS system is hard to believe from the dither results. The various actuator tests and uniform absorption measurements are not 30% astigmatic. Why applying this astigmatic correction in the analysis ends up giving a resonable power estimation I'm not sure, perhaps Mitchell is correct above.
Cao generated a new transient FEA model that takes into account the radiative coupling between the CP and ITM better for self heating. Figures 1 and 2 here show how the contributions to the optical path depth change seen by the HWS changes radially and as a function of time. This FEA model assumes that the IFO was locked for about 10 hours before hand, so the CP has warmed up. The ITM OPD and surface cool down quickly (~1 hour), but the CP takes longer and leads to a different temporal response than what we were fitting for before.
Rather than fitting to "spherical power" (in the EPICs channel or re-processed) I fit the gradients generated by the theoretical FEA OPD against the measured ones, this is less susceptible to junk that comes out of the integrated OPD.
My full transient fitting code isn't working quite yet but if I take the measured HWS data 3 hours after the lockloss at 1353641304 and fit it to the 3 hour simulated I get a reasonable fit. This estimates ~0.16W of power being absorbed in the ITMY coating at the 10 hour lock point. Depending on what coating absorption you want to assume: 160mW/0.5ppm = 320kW @ 50W of input power. The uncertainty of the absorption is +-0.1ppm which gives a fairly wide error bar here, but on average 320kW agrees well with the PRG power estimation and we do not need any crazy 30% astigmatism fudge factors so I'm much more confident in this estimation from the HWS.
I assume the magnification is 17.5 in all this analysis.
Code is in /ligo/gitcommon/labutils/hws_absorption_fit/nov2022/cao_model_fit.py
