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Entry  Sat Aug 20 00:42:22 2011, Keiko, Update, LSC, Tolerance of PRC, SRC, MICH length = 2 mm ? 
    Reply  Tue Aug 23 17:51:37 2011, Keiko, Update, LSC, Tolerance of PRC, SRC, MICH length = 2 mm ? 
    Reply  Fri Sep 2 04:41:35 2011, Keiko, Update, LSC, Tolerance of PRC, SRC, MICH length = 5 mm ? MATRIX.pngdphase.png
Message ID: 5334     Entry time: Fri Sep 2 04:41:35 2011     In reply to: 5273
Author: Keiko 
Type: Update 
Category: LSC 
Subject: Tolerance of PRC, SRC, MICH length = 5 mm ? 

 Keiko, Kiwamu

Length tolerance of the vertex part is about 5 mm.

Sorry for my procrastinating update on this topic. In my last post, I reported that the length tolerance of the vertex ifo would be 2mm, based on Kiwamu's code on CVS. Then we noticed that the MICH degrees of freedom was wrong in the code. I modified the code and ran again. You can find the modified codes on CVS (40m folder, analyzeDRMITolerance3f.m and DRMITolerance.m)

In this code, the arm lengths were kept to be ideal while some length offsets of random gaussian distribution were added on PRCL, SRCL and MICH lengths. The iteration was 1000 times for each sigma of the random gaussian distribution. The resulting sensing matrix is shown as histogram. Also, a histogram of the demodulation phase separation between MICH and SRCL is plotted by this code, as these two length degrees of freedom will be obtained by one channel separated by the demodulation phase. We check this separation because you want to make sure that the random length offsets does not make the separation of these two signals close.

The result is a bit different from the previous post, in the better way! The length tolerance is about 5 mm for the vertex ifo. Fig.1 shows the sensing matrix. Although signal levels are changed by the random offsets, only few orders of magnitude is changed in each degrees of freedom. Fig.2 shows that the signal separation between MICH and SRCL at  POP55 varies from  55 to 120 degrees, which may be OK. If you have 1cm sigma, it varies from 50 degrees to 150 degrees.

MATRIX.png

Fig. 1 Histgram of the sensing matrix including 3f channels, when sigma is 5mm. Please note that the x-axis is in long 10.

dphase.png

 Fig. 2 Histogram of the demodulation phase difference between MICH and SRCL, when sigma is 5 mm. To obtain the two signals independently, 90 is ideal. With the random offsets, the demodulation phase difference varies from 55 degrees to 120 degrees.

My next step is to run the similar code for LLO. 

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