The other day, I took spectra of the Yend transmission QPD dark noise for several different configurations of the transimpedance gain and the whitening gains. 

I also calculated with Optickle the expected sensitivity vs. CARM offset for the sqrtInv CARM sensor. 

I put these things together to get a plot of transmission QPD noise vs. CARM offset, for a chosen set of analog settings.

Measurement of Yend transmission QPD dark noise

Since EricQ had already checked out the whitening filters (see elog 9637 and elog 9642), I didn't check on them.  I just left them (the analog whitening, and the digital antiwhitening filters) on. 

First, I checked the noise vs. transimpedance gain. There are a few too many settings to put them all on one plot, so I have them sorted by the original transimpedance:  0.5 kOhms vs 5 kOhms.  It's a little tricky to see, but all of the spectra that begin with the 5k transimpedance have a little extra noise around 10 Hz, although I don't know why.  In the legend I have made note of what the settings were.  x1 x1 is my representation of the "inactive" setting.

I then looked at the noise with different whitening gain slider settings.  All but one of the traces are the 20 kOhm setting.  

These .xml files are in /users/jenne/Arms/TransQPDnoise_July2014/

Calculation of inverse sqrt transmission sensitivity

I used Optickle to give me the power transmitted through the ETMs.  I first find the transmission in the FPMI case.  I use that to normalize the full PRFPMI transmission, so that the output units are the same as our C1:LSC-TR[x,y]_OUT units. 

I take the square root of the transmitted power (sum of transmissions from each arm) at each CARM offset point, add 1e-3 as we do in the front end model to prevent divide-by-zero problems, and then take the inverse.

I find the slope by taking the difference in power between adjacent points, divided by the CARM offset difference between those points. 

In this plot, I have taken the absolute value of the sensitivity, just for kicks.  I also display an arbitrarily scaled version of the log of the transmitted power, so that we can see that the highest sensitivity is at half the maximum power.

 Calculate the QPD dark noise in terms of meters

Finally, I put it all together, and find the dark noise of the QPD in terms of meters.  Since the spectra were measured in units where the single-arm transmission is unity, the already match the units that I used to calculate the sqrtInv sensitivity. 

I take the spectra of the QPD dark noise for the 20 kOhm case, and multiply it by the sensitivity calibration number at several different CARM offsets.  As we expect, the noise is the best at half-max transmission, where the sensitivity is maximal.