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Entry  Tue Apr 27 22:28:58 2010, Zach, Update, IOO, MC alignment MC_misaligned.png
    Reply  Wed Apr 28 12:05:44 2010, Zach, Update, IOO, MC alignment 
       Reply  Wed Apr 28 14:15:58 2010, Alberto, Update, IOO, MC alignment 
          Reply  Wed Apr 28 14:42:55 2010, Zach, Update, IOO, MC alignment 
Message ID: 2855     Entry time: Wed Apr 28 12:05:44 2010     In reply to: 2852     Reply to this: 2856
Author: Zach 
Type: Update 
Category: IOO 
Subject: MC alignment 

I have worked out the first set of adjustments to make on the MC mirrors (all angle figures are in units of the increments on the control screen)

Using the method described in the previous post, I obtained the following matrix relating the angle-to-length coupling and the angular deviations. In the following matrix, Mij corresponds to the contribution of the jth degree of freedom to the ith A-to-L coupling, with the state vector defined as xi = (MC1P, MC2P, MC3P, MC1Y, MC2Y, MC3Y), where each element is understood as the angular deviation of the specific mirror in the specific direction from the ideal position, such that x = 0 when the cavity eigenmode is the correct one and the beams are centered on the mirrors (thus giving no A-to-L coupling regardless of the components of M).

 

M =

   1.0e+03 *

   -0.2843   -0.4279   -0.1254         0         0         0

   -0.8903   -0.4820   -0.6623         0         0         0

    0.5024    0.0484   -0.0099         0         0         0

         0         0         0         0.1145   -0.1941   -0.3407

         0         0         0         0.0265    1.5601    0.2115

         0         0         0         0.1015    0.1805   -0.0103,

giving an inverse

M-1 =  

    0.0003   -0.0001    0.0020         0         0         0

   -0.0031    0.0006   -0.0007         0         0         0

    0.0018   -0.0018   -0.0022         0         0         0

         0         0         0        -0.0013   -0.0015    0.0117

         0         0         0         0.0005    0.0008   -0.0008

         0         0         0        -0.0037   -0.0010    0.0044

The initial coupling vector is then acted on with this inverse matrix to give an approximate state vector x containing the angular misalignments of each mirror in pitch and yaw. The results are below:

x

   1P:  0.0223

   2P: -0.0733

   3P:  0.3010

  1Y:  -0.1372

  2Y:   0.0194

  3Y:  -0.0681

 

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