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Entry  Wed Oct 15 20:10:29 2014, ericq, Update, LSC, Interim DARM Signal 7x
    Reply  Thu Oct 16 16:21:42 2014, ericq, Update, LSC, Interim DARM Signal dcDARMSweep-300.pdfdcDARMSweep-120.pdfdcDARMSweep-50.pdfdcDARMSweep-0.pdf
       Reply  Thu Oct 16 21:20:59 2014, rana, Update, LSC, misleading modelling 
          Reply  Fri Oct 17 03:05:00 2014, ericq, Update, LSC, DARM locked on DC Transmission difference TRdifflock.pngOct17lock.pdf
             Reply  Fri Oct 17 13:19:48 2014, Jenne, Update, LSC, POP22 ?!?! 
          Reply  Tue Oct 21 00:38:40 2014, ericq, Update, LSC, sweep + RMS as uncertainty dcCARMSweep_uncertainties.png
             Reply  Wed Oct 22 06:32:29 2014, rana, Update, LSC, sweep + RMS as uncertainty 
Message ID: 10627     Entry time: Tue Oct 21 00:38:40 2014     In reply to: 10619     Reply to this: 10631
Author: ericq 
Type: Update 
Category: LSC 
Subject: sweep + RMS as uncertainty 


BUT, what we really need (instead of just the DC sweeps) is the DC sweep with the uncertainty/noise displayed as a shaded area on the plot, as Nic did for us in the pre-CESAR modelling.

I've taken a first stab at this. Through various means, I've made an estimation of the total noise RMS of each error signal, and plotted a shaded region that shows the range of values the error signal is likely to take, when the IFO is statically sitting at one CARM offset. 

I have not included any effects that would change the RMS of these signals in a CARM-offset dependent way. Since this is just a rough first pass, I didn't want to get carried away just yet. 

For the transmission PDs, I measured the RMS on single arm lock. I also measured the incident power on the QPDs and thorlabs PDs for an estimate of shot noise, but this was ridiculously smaller than the in-loop RIN. I had originally though of just plotting sensing noise for the traces (i.e. dark+shot), because the amount of seismic and frequency noise in the in-loop signal obviously depends on the loop, but this gives a very misleading, tiny value. In reality we have RIN from the PRC due to seismic noise, angular motion of the optics, etc., which I have not quantified at this time. 

So: for this first, rough, pass, I am simply multiplying the single transmission noise RMSs by a factor of 10 for the coupled RMS. If nothing else, this makes the SqrtInv signal look plausible when we actually practically find it to be plausible. 

For the REFL PDs, I misaligned the ITMs for a prompt PRM reflection for a worst-case shot noise situation, and took the RMS of the spectra. (Also wrote down the dark RMSs, which are about a factor of 2 lower). I then also multiplied these by ten, to be consistent with the transmission PDs. In reality, the shot noise component will go down as we approach zero CARM offset, but if other effects dominate, that won't matter. 

Enough blathering, here's the plot:


Now, in addition to the region of linearity/validity of the different signals, we can hopefully see the amount of error relative to the desired CARM offset. (Or, at least, how that error qualitatively changes over the range of offsets)

This suggests that we MAY be able to hop over to a normalized RF signal; but this is a pretty big maybe. This signal has the response of the quotient of two nontrivial optical plants, which I have not yet given much thought to; it is probably the right time to do so...

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