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Entry  Thu Jan 22 23:36:50 2009, pete, HowTo, oplevs, arm cavity oplev calibration ETMYpitpower.pngETMYpitcal.png
    Reply  Fri Jan 23 12:48:12 2009, Kakeru, Update, oplevs, arm cavity oplev calibration ITMX_pitch.png
       Reply  Thu Jan 29 17:24:41 2009, Kakeru, Update, oplevs, arm cavity oplev calibration 
          Reply  Sat Mar 14 22:53:12 2009, Kakeru, Update, oplevs, arm cavity oplev calibration oplev.pdf
             Reply  Fri Mar 20 15:37:58 2009, Kakeru, Update, oplevs, arm cavity oplev calibration 
                Reply  Thu Mar 26 09:08:18 2009, Kakeru, Update, oplevs, arm cavity oplev calibration 
Message ID: 1247     Entry time: Thu Jan 22 23:36:50 2009     Reply to this: 1249
Author: pete 
Type: HowTo 
Category: oplevs 
Subject: arm cavity oplev calibration 
calibrated the y-arm oplevs. the procedure is contained in a matlab script. the whereabouts of this script will be revealed in a future log entry.

ITMYpit 140 microrad/ct
ITMYyaw 98 microrad/ct
ETMYpit 400 microrad/ct
ETMYyaw 440 microrad/ct (previous measurement gave 420 microrad/ct)

procedure:

1) Start with a single arm aligned and locked. Dither the mirror tilt in a DOF. Measure arm cavity power and oplev error signal. See the first attached plot.

2) Fit the plot to a gaussian and determine mu and sigma.

3) For a spherical ETM optic, the power in the cavity P(a), as a function of translational beam axis displacement a=R*sin(theta), is proportional to exp[-a^2/(2*x^2)] where x is the waist size (D. Anderson APPLIED OPTICS, Vol. 23, No. 17, 1984). The power as a function of mirror tilt in cts, P(tilt) is proportional to exp[-(tilt-mu)^2 /(2*sigma^2)]. So if R is the mirror radius then theta = arcsin(a/R) = arcsin[(1/R)*(tilt-mu)*x/sigma)].

4) Fit theta versus mirror tilt to get the calibration. See the second attached plot.

5) For a flat ITM optic, mirror tilt causes an angular displacement of the beam. The math for this case is given in Anderson.
Attachment 1: ETMYpitpower.png  15 kB  | Show | Hide all | Show all
Attachment 2: ETMYpitcal.png  12 kB  | Hide | Hide all | Show all
ETMYpitcal.png
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