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 40m Log Not logged in 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: right: 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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