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 Thu Dec 1 20:20:15 2016, gautam, Update, IMC, IMC loss measurement plan Fri Dec 2 16:40:29 2016, gautam, Update, IMC, 24V fuse pulled out Mon Dec 5 01:58:16 2016, gautam, Update, IMC, IMC ringdowns Mon Dec 5 15:55:25 2016, gautam, Update, IMC, IMC ringdowns 7x Mon Dec 5 19:29:52 2016, gautam, Update, IMC, IMC ringdowns Tue Dec 6 00:43:41 2016, gautam, Update, IMC, more IMC ringdowns Wed Dec 7 11:52:48 2016, ericq, Update, IMC, Partial IMC ringdowns Thu Dec 8 19:01:21 2016, rana, Update, IMC, Partial IMC ringdowns Sun Dec 2 17:26:58 2018, gautam, Update, IMC, IMC ringdown fitting Fri Dec 7 12:51:06 2018, gautam, Update, IMC, IMC ringdown fitting
Message ID: 14328     Entry time: Sun Dec 2 17:26:58 2018     In reply to: 12667     Reply to this: 14334
 Author: gautam Type: Update Category: IMC Subject: IMC ringdown fitting

Recently we wondered at the meeting what the IMC round trip loss was. I had done several ringdowns in the winter of 2017, but because the incident light on the cavity wasn't being extinguished completely (the AOM 0th order beam is used), the full Isogaio et. al. analysis could not be applied (there were FSS induced features in the reflection ringdown signal). Nevertheless, I fitted the transmission ringdowns. They looked like clean exponentials, and judging by the reflection signals (see previous elogs in this thread), the first ~20us of data is a clean exponential, so I figured we may get some rough value of the loss by just fitting the transmission data.

The fitted storage time is $60.8 \pm 2.7 \mu s$.However, this number isn't commensurate with the 40m IMC spec of a critically coupled cavity with 2000ppm transmissivity for the input and output couplers.

Attachment #1: Expected storage time for a lossless cavity, with round-trip length ~27m. MC2 is assumed to be perfectly reflecting. The IMC length is known to better than 100 Hz uncertainty because the marconi RF modulation signal is set accordingly. For the 40m spec, I would expect storage times of ~40 usec, but I measure almost 30% longer, at ~60 usec.

Attachment #2: Fits and residuals from the 10 datasets I had collected. This isn't a super informative plot because there are 10 datasets and fits, but to eye, the fits are good, and the diagonal elements of the covariance matrix output by scipy's curve_fit back this up. The function used to fit the t > 0 portions of these signals (because the light was extinguished at t=0 by actuating on the AOM) is $\text{Transmission} = Ae^{-\frac{2t}{\tau_{\mathrm{storage}}}}$, where A and tau are the fitted parameters. In the residuals, the same artefacts visible in the reflection signal are seen.

Attachment #3: Scatter plot of the data. Width of circles are proportional to fit error on individual measurements (i just scaled the marker size arbitrarily to be able to visually see the difference in uncertainty, the width doesn't exactly indicate the error), while the dahsed lines are the global mean and +/- 1 sigma levels.

Attachment #4: Cavity pole measurement. Using this, I get an estimate of the loss that is a much more believable $300 \pm 20\, \mathrm{ppm}$.

 Attachment 1: tauTheoretical.pdf  18 kB
 Attachment 2: ringdownFit.pdf  76 kB
 Attachment 3: ringdownScatter.pdf  16 kB
 Attachment 4: cavPole.pdf  192 kB  Uploaded Mon Dec 2 15:42:52 2019
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