I analyzed mode scan data from last week.
Mode matching ratio for Y arm is 86.7 +/- 0.3 %. Assuming we can get rid of TEM01/10 by alignment, this can be improved up to ~ 90%.

Peak search, peak fitting and finnesse calculation:
  I made a python script for doing this. It currently lives in /users/yuta/scripts/modescanresults/analyzemodescan.py.
  What it does is as follows

  1. Read mode scan data(coarse5FSRscan.csv, fine1FSRscan.csv). Each column in the data file should be

[time] [some thing like C1:ALS-BEAT(Y|X)_(COARSE|FINE)_(I|Q)_IN1] [C1:LSC-POY11_I_ERR] [C1:LSC-TRY_OUT]

Each separated by comma. Currently, this script uses only TRY, but it reads all anyway

  2. Find peak in TRY data. For the peak search, it splits data in 1 sec and find local maximum. If the local maximum is higher than given threshold, it recognize it as a peak. If two peaks are very close, it uses higher one. This sometimes fails, because mode scan data we have is not so nice.

  3. Fit each peak with Lorentzian function,

TRY = a*b/(4*(t-c)^2+b^2) + d  (a>0, b>0)

  where a/b is a peak height, b is a linewidth (FWHM), c is a peak position in time, and d is a offset.
  I don't like this, but currently, a/b+c is fixed to the maximum value of TRY data used for fitting. This is because sometimes TRY data is so bad and I couldn't get the peak height correctly. Each points of TRY data doesn't have same error because cavity length is fluctuating and relation between cavity length and TRY is not linear. I think I should use some weighting for the fit, but currently, I just use least squares.

  4. Find TEM00 and calculate FSR in "seconds". I just used "seconds" assuming we did a linear sweep. This script recognize TEM00 from the given threshold.

  5. Calculate finesse using FSR and linewidth of the closest TEM00.

  Below are the result plots from this analysis. Calculated finesse looks quite high (~1000). I think this is from non-linearity in the sweep and error in "measured" line width.



Higher order modes and RF sidebands:
  Assuming the curvature of ITMY/ETMY are flat/57.5 m, Y arm length is 38.6 m(FSR 3.9 MHz), positions of HOMs and RF sidebands(11/55 MHz) in frequency domain should look like the plot below.
  The script for calculating this currently lives in /users/yuta/scripts/modescanresults/HOMRFSB.py, inspired by Yoichi's script for KAGRA


Mode-matching ratio:
  By comparing mode scan data and HOM/RF SB positions in a sophisticated way, you can tell which peak is which.



  From COARSE 5FSR measurement, peak heights are

TEM00 0.884, 0.896, 0.917, 0.905, 0.911
TEM01 0.040, 0.037, 0.051, 0.054, 0.062
TEM02 0.083, 0.078, 0.079, 0.071, 0.078
TEM03 0.018, 0.015, 0.013, 0.015, 0.014

  So the mode-matching ratio is

MMR = 86.2 %, 87.3 %, 86.5 %, 86.6 %, 85.5 %

  From FINE 1FSR measurement, peak heights and mode matching ratio is

TEM00 0.921
TEM01 0.031
TEM02 0.078
TEM03 0.014

MMR = 88.2 %

  Assuming each measurement had same error, mode-matching ratio from these 6 values is

MMR = 86.7 +/- 0.3 %  (error in 1 sigma)

  This can be improved by ~5% by alignment because we still see ~5% of TEM01/10. Study in systematic errors on going.