40m QIL Cryo_Lab CTN SUS_Lab TCS_Lab OMC_Lab CRIME_Lab FEA ENG_Labs OptContFac Mariner WBEEShop
 40m Log Not logged in
 Thu Nov 5 02:18:32 2015, gautam, Update, LSC, FSR and linewidth measurements with phase tracker Fri Nov 6 15:56:00 2015, gautam, Update, LSC, FSR and linewidth measurements with phase tracker Mon Nov 9 11:34:51 2015, yutaro, Update, LSC, FSR and linewidth measurements with phase tracker Mon Nov 9 14:24:36 2015, yutaro, Update, LSC, FSR and linewidth measurements with phase tracker Mon Nov 9 15:59:06 2015, ericq, Update, LSC, FSR and linewidth measurements with phase tracker Mon Nov 9 16:58:59 2015, gautam, Update, LSC, FSR and linewidth measurements with phase tracker Tue Nov 10 02:34:28 2015, gautam, Update, LSC, Updated interpretation of peaks Tue Nov 10 11:06:02 2015, yutaro, Update, LSC, Updated interpretation of peaks Tue Nov 10 11:40:03 2015, Koji, Update, LSC, Updated interpretation of peaks Tue Nov 10 16:34:00 2015, yutaro, Update, LSC, Updated interpretation of peaks Fri Nov 13 17:33:39 2015, gautam, Update, LSC, g-factor measurements Tue Nov 10 11:41:56 2015, Koji, Update, LSC, Updated interpretation of peaks Fri Nov 13 15:48:16 2015, gautam, Update, LSC, Phase tracker calibration using Rubidium standard 6x
Message ID: 11762     Entry time: Fri Nov 13 17:33:39 2015     In reply to: 11749
 Author: gautam Type: Update Category: LSC Subject: g-factor measurements
 Quote: ROC_ETMY = 59.3 +/- 0.1 m.

Summary:

I followed a slightly different fitting approach to Yutaro's in an attempt to determine the g-factor of the Y arm cavity (details of which are below), from which I determined the FSR to be 3.932 +/- 0.005 MHz (which would mean the cavity length is 38.12 +/- 0.05 m) and the RoC of ETMY to be 60.5 +/- 0.2 m. This is roughly consistent (within 2 error bars) of the ATF measurement of the RoC of ETMY quoted here.

Details:

I set up the problem as follows: we have a bunch of peaks that have been identified as TEM00, TEM10... etc, and from the fitting, we have a bunch of central frequencies for the Lorentzian shapes. The equation governing the spacing of the HOM's from the TEM00 peaks is:

$\Delta f_{HOM_{mn}} = \frac{FSR}{\pi} (m+n)cos^{-1}(\sqrt{g_1 \times g_2})$

The main differences in my approach are the following:

1. I attempt to simultaneously find the optimal value of FSR, g1 and g2, by leaving all these as free parameters and defining an objective function that is the norm of the difference between the observed and expected values of $\Delta f_{HOM_{mn}}$ (code in Attachment #1). I then use fminsearch in MATLAB to obtain the optimal set of parameters.
2. I do not assume that the "unknown" peak alluded to in my previous elog is a TEM40 resonance - so I just use the TEM10, TEM20 and TEM30 peaks. I did so because in my calculations, the separation of these peaks from the TEM00 modes are not consistent with (m+n) = 4 in the above equation. As an aside, if I do impose that the "unknown" peak is a TEM40 peak, I get an RoC of 59.6 +/- 0.3 m.

Notes:

1. The error in the optimal set of parameters is just the error in the central positions of the peaks, which is in turn due to (i) error in the calibration of the frequency axis and (ii) error in the fit to each peak. The second of these are negligible, the error in my fits are on the order of Hz, while the peaks themselves are of order MHz, meaning the fractional uncertainty is a few ppm - so (i) dominates.
2. I am not sure if leaving the FSR as a free parameter like this is the best idea (?) - the FSR and arm length I obtain is substantially different from those reported in elog 9804 - by almost 30cm! However: the RoC estimate does not change appreciably if I do the fitting in a 2 step process: first find the FSR by fitting a line to to the 3 TEM00 peaks (I get FSR = 3.970 +/- 0.017 MHz) and then using this value in the above equation. The fminsearch approach then gives me an RoC of 60.7 +/- 0.3 m

 Attachment 1: findGFactor.zip  1 kB
ELOG V3.1.3-