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Entry  Fri Feb 8 23:59:42 2013, yuta, Update, Locking, PR2-flipped half-PRC mode scan halfPRCmodescan.png
    Reply  Sat Feb 9 11:25:35 2013, Koji, Update, Locking, PR2-flipped half-PRC mode scan 
       Reply  Sun Feb 10 17:30:39 2013, yuta, Update, Locking, PR2-flipped half-PRC mode scan modescan_pitmisalign.pngmodescan_yawmisalign.png
          Reply  Mon Feb 11 13:15:16 2013, yuta, Update, Locking, PR2-flipped half-PRC mode scan 
          Reply  Mon Feb 11 21:03:15 2013, yuta, Update, Locking, PR2-flipped half-PRC mode scan modespacing_pit.pngmodespacing_yaw.png
Message ID: 8064     Entry time: Mon Feb 11 21:03:15 2013     In reply to: 8052
Author: yuta 
Type: Update 
Category: Locking 
Subject: PR2-flipped half-PRC mode scan 

To estimate the systematic effects to the g-factor measurement, I changed how to analyze the data in multiple ways.
From the estimation, I get the following g-factors for half-PRC;
  tangential: 0.986 +/- 0.001(stat.) +/- 0.008(sys.)
    sagittal: 0.968 +/- 0.001(stat.) +/- 0.003(sys.)


The a la mode/arbcav calculation is not so far from the measurement(elog #8059). So, mirror curvatures and lengths are not far from what we expect.

Method:
  Method I used to analyze the mode scan data is as follows;

  1. Use the spacing between upper sideband and lower sideband to calibrate the data.
  2. Measure the position of 00, 1st, 2nd and 3rd mode.
  3. Used the following formula to get TMS

  nu_TMS = sum((n_i-n)*(nu_i-nu)) / sum((n_i-n)^2)

  where n_i is the order of transverse mode, n is average of n_i's, nu_i is the frequency if i-th order mode and nu is average of nu_i's. This is just a linear fitting.

  But since it is hard to resolve where the higher order mode is, it is maybe better to use only 00, 1st, and 2nd mode. Also, since cavity sweep is not linear enough, it is maybe better to use spacing between 00 and lower sideband (sideband closer to HOMs) to calibrate the data. Changing the analysis will give us information about the effect of peak choosing and linearity.

How the result differ:
  Below are the plots of order of tranverse mode vs measured relative frequency difference from 00 mode. 5 plots on left are when PRM is misaligned in pitch and right are same in yaw. From the plot, you can see using 3rd order mode tend to give larger TMS. Did I picked the wrong one??
left:modespacing_pit.png    right:modespacing_yaw.png

Results:
  Below table is the result when I changed the analyzing method;

PRM misaligned in pitch
  calibration    how many HOMs    measured g-factor
  upper-lower    up to 3rd    0.968
  upper-lower    up to 2nd    0.974
  upper-lower    up to 1st    0.975
  00-lower       up to 3rd    0.952
  00-lower       up to 2nd    0.962
  00-lower       up to 1st    0.963


PRM misaligned in yaw
  calibration    how many HOMs    measured g-factor
  upper-lower    up to 3rd    0.986
  upper-lower    up to 2nd    0.989
  upper-lower    up to 1st    0.991
  00-lower       up to 3rd    0.964
  00-lower       up to 2nd    0.988
  00-lower       up to 1st    0.991


  Using 00-lower calibration tend to give us smaller g-factor. Using less higer order-mode tend to give us higher g-factor.
  By taking standard deviation of these, I roughly estimated the systematic error as above.

Discussion:
  I think it is OK to move on to PRMI now.
  But I wonder how much astigmatism is needed to get this measurement data. If astigmatism is not so crazy, it's OK. But if it's not, I think it is better to do more measurement like PRM-PR2-TM cavity.

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