I started putting together some code to implement some ideas we discussed at the Tuesday meeting here. Pipeline isn't setup yet, but i think it's commented okay so if people want to play around with it, the code lives on the 40m gitlab.
__Model parameters:__
- T+ --- average transmission of MC1 and MC3.
- T- --- difference in transmission between MC1 and MC3 (this basis is used rather than T1 and T3, because the assumption is that since they were coated in the same coating run, the difference in transmission should be small, even if there is considerable uncertainty in the actual average transmission number.
- T2 --- MC2 transmission.
- Lrt --- Round trip loss in the cavity.
- "sigma" --- a nuisance parameter quantifying the error in the time domain ringdown data.
__Simulation:__
- Using these model parameters, calculate some simulated time-domain ringdowns. Optionally, add some noise (assumed Gaussian).
- Try and back out the true values of the model parameters using
**emcee** - priors were assumed to be *uniformly* distributed, with a +/- 20% uncertainty around the central value.
- For a first test, see if there is any improvement in the parameter estimation uncertainty using only transmission ringdown vs both transmission and reflection.
__Initial results and conclusions:__
**Attachment #1 **- Simulated time series used for this study. The "fit" trace is computed using the median values from the monte-carlo.
**Attachment #2 **- Corner plots showing the distribution of the estimated parameter values,* using only transmission ringdown*. The "true" values are indicated using the thick blue lines.
**Attachment #3 **- Corner plots showing the distribution of the estimated parameter values, *using both transmission and reflection ringdowns*.
- The overall approach seems to work okay. There seems to be only
*marginal* improvement in the uncertainty in estimated parameters using both ringdown signals, at least in the simulation.
- However, everything seems pretty sensitive to the way the likelihood and priors are coded up - need to explore this a bit more.
__Next steps:__
- Add more simulated measurements, see if we can constrain these parameters more tightly.
- Use linear error analysis to see if that tells us which measurements we should do, without having to go through the
**emcee**.
There still seems to be some data quality issues with the ringdown data I have, so I don't think we really gain anything from running this analysis on the data I have already collected - but in the future, we can do the ringdown with complete extinguishing of the input light, and repeat the analysis.
As for whether we should clean the IMC mirrors - I'm going to see how much power comes out at the REFL port (with PRM aligned) this afternoon, and compare to the input power. This technique suffers from uncertainty in the Faraday insertion loss, isolation and IMC parameters, but I am hoping we can at least set a bound on what the IMC loss is. |