Reports until 16:17, Monday 15 July 2019
H1 ISC
jenne.driggers@LIGO.ORG - posted 16:17, Monday 15 July 2019 - last comment - 14:59, Tuesday 16 July 2019(50550)
Q measurement of the 10.430 kHz mode

A while ago, I took some data for measuring the Q of the 10430.5 Hz mode (alog 50374).  However, the RMS monitor channel for this mode wasn't working, which doesn't make a lot of sense, since it really should just be taking the rms (in the front end system) of the same signal that is being used to ring up the mode.  So, I couldn't use pre-existing fitting scripts.  I have not yet investigated why the RMS monitor isn't outputting sensible data.

If I pull the H1:OMC-PI_DCPD_64KHZ_AHF_DQ channel and bandpass it (8th order butterworth with 2 Hz width), I clearly see the ringdown of this mode.  I start the bandpassing a few hundred seconds before the beginning of the ringdown, so that I don't have to worry about transient effects of the filter.  The bandpassed data is the blue trace in the attached plot.

To do the fit, I take a Hilbert Transform of the data (shifts the phase of the data by 90 degrees), so that I can get the magnitude of the ringdown envelope via: sqrt(data^2 + imag(hilbert(data))^2).  I decimate this resulting envelope from 64kHz to 1024Hz to make it a less crazy number of points.  I fit this envelope data (using data that starts 20 seconds after I stopped exciting up to 100 seconds before we began powering up) to a function of the form A*exp(B*t). 

In the attached plot, I show the original bandpassed data, as well as the fitted envelope.  Note that the result of the fit doesn't change appreciably if I restrict the data used to [20 sec, 1200 sec].

The fit results in a decay time tau of 259 seconds, which implies a Q of (pi * 10430.5Hz / tau) = 8.48e6 as the Q of the 10430.5 Hz mode.

The attached matlab .m file pulls the data, and does all of the analysis and plotting to get the tau number.

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jenne.driggers@LIGO.ORG - 14:59, Tuesday 16 July 2019 (50578)

I neglected to mention that this data was taken at 2W, so as not to risk it ringing up and causing a lockloss.