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Entry  Sun Feb 3 13:20:02 2013, Koji, Summary, General, Hypothesis mode_density_PRC.pdfmode_density_PRC.zip
    Reply  Mon Feb 4 10:45:51 2013, Jamie, Summary, General, rough analysis of aligned PRM-PR2 mode scan scan-labeled.pdf
       Reply  Mon Feb 4 11:10:59 2013, Koji, Summary, General, rough analysis of aligned PRM-PR2 mode scan 
          Reply  Mon Feb 4 19:33:19 2013, yuta, Summary, General, rough analysis of aligned PRM-PR2 mode scan 3peakdata.png
             Reply  Tue Feb 5 02:04:44 2013, yuta, Summary, General, rough analysis of aligned PRM-PR2 mode scan PRMPR2scan.png
                Reply  Tue Feb 5 03:16:51 2013, Koji, Summary, General, rough analysis of aligned PRM-PR2 mode scan 
                   Reply  Tue Feb 5 10:09:08 2013, yuta, Summary, General, rough analysis of aligned PRM-PR2 mode scan 
                      Reply  Tue Feb 5 11:30:19 2013, Koji, Summary, General, rough analysis of aligned PRM-PR2 mode scan 
                         Reply  Wed Feb 13 01:26:08 2013, yuta, Summary, General, rough analysis of aligned PRM-PR2 mode scan unbiased.png
       Reply  Wed Feb 6 15:20:55 2013, yuta, Summary, General, FWHM was wrong 
    Reply  Mon Feb 4 15:06:56 2013, Koji, Summary, General, Hypothesis 
    Reply  Mon Feb 4 19:48:32 2013, Jamie, Summary, General, arbcav recalc of PRC with correct ITM transmission mode_density_PRC_2.pdfmode_density_PRC_3.pdf
Message ID: 8012     Entry time: Wed Feb 6 15:20:55 2013     In reply to: 7990
Author: yuta 
Type: Summary 
Category: General 
Subject: FWHM was wrong 

I have to blame Jamie for putting extra 2 randomly.
Measured PRM-PR2 cavity finesse was actually 108 +/- 3 (even if you use digital system to get data).

Lorentzian fit:
  Lorentzian function is;

f(x;x0,gamma,A) = A * gamma**2/((x-x0)**2+gamma**2)

  where x0 is the location of the peak, gamma is HWHM, and A is the peak height.
  Lorentzian fitting function in my original code (/users/yuta/scripts/modescanresults/analyzemodescan.py) was

fitFunc = lambda p,x,m: (m-p[2])*p[0]**4/(4*(x-p[1])**2+p[0]**4)+p[2]

  In this function, p[0] is sqrt(FWHM), not sqrt(HWHM). I doubled gamma to make it FWHM and squared it because they should be positive.
  During Jamie's modification of my code, he doubled p[0]**2 to get FWHM, which is wrong (/users/jrollins/modescan/modescan.py).

  I should have commented that p[0] is sqrt(FWHM).

Redoing the analysis:
  1. I pulled 2 out, and modified Jamie's modescan.py so that you can name each peak with peakdistinguish=True option. I also modified fitpeak function so that it throws away "peaks" which don't look like a peak.

  2. If you run /users/yuta/PRCmodescan/run.py and name each peak, you will get peaks.csv which includes peak position, FWHM, and the type of the peak;

0.065017,0.001458,l
0.070446,0.001463,3
0.075940,0.001509,2
0.081552,0.001526,1
0.087273,0.001565,0
0.112027,0.001911,u
0.278660,0.002211,u
0.306486,0.001658,0
0.312480,0.001576,1
0.313626,2.507910,
0.318486,0.001626,2
0.319730,2.633097,
0.324801,0.001739,3
0.331848,0.001922,l
0.527509,0.001603,l
0.533231,0.001445,3
0.538648,0.001488,2
0.544081,0.001455,1
0.549517,0.001498,0
0.551725,2.422759,
0.570972,0.001346,u


  3. /users/yuta/PRCmodescan/calcmodescanresults.py reads peaks.csv and tells you the results;

Time between TEM00 and sideband  0.0239435  pm  0.00115999887452  sec
Calibration factor is  462.167602898  pm  22.3907907867  MHz/sec
FSR is  78.4797010471  MHz
FWHM is  0.729828720682  pm  0.0174145743828  MHz
TMS is  2.64718671684  pm  0.0538858477824  MHz
Finesse is  107.53166986  pm  2.5658325169
Cavity g-factor is  0.994390582331  pm  0.000228155661075
Cavity g-factor is  0.988812630228  pm  0.000453751681357   (Edited by YM; see elog #8056)
RoC of PR2 is  -187.384503001  pm  4.26100999578  m (assuming PRM RoC= 122.1  m)
RoC of PRM is  217.915890722  pm  5.65451518991  m (assuming PR2 RoC= -600  m)

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