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Message ID: 1087     Entry time: Fri Oct 24 18:05:01 2008
Author: Alberto 
Type: Update 
Category: General 
Subject: Abs length: transverse mode spacing measured for the X arm 
The ETMX suffers of astigmatism. I measured the following frequencies for the higher order modes:
- f_01 = 6317500 +/- 500 Hz
- f_10 = 6305500 +/- 500 Hz

From

g2=1/g1*(cos(A*L*pi/c))^2

where A= (fsr-f_i), fsr=(3897654+/-15)Hz (see elog entry 956), L=(38.4580+/-0.0003)m, g1=0.9947 (from R1=7280m), I get the following values for the g-factor coefficients:

g2_x = 0.3164 +/- 0.0002
g2_y = 0.3209 +/- 0.0002

from which we have the radius of curvature of ETMX:

R_x = 56.26 +/- 0.01 m
R_y = 56.63 +/- 0.01 m


The specs for the mirror have R2= 57.57 m (unc).

So, they seem conditions similar of those of ETMY that Koji measured:

Rx = 56.1620 +/- 0.0013 [m]
Ry = 57.3395 +/- 0.0011 [m]

for which L_yarm: 38.6462 m +/- 0.0003 m
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