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Diagonalization of Optical Lever signals for Type B suspensions

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Submitted by:
Tak Lun Terrence Tsang
Updated by:
Tak Lun Terrence Tsang
Document Created:
04 Sep 2018, 06:25
Contents Revised:
15 Oct 2018, 01:25
DB Info Revised:
03 May 2021, 23:45
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04 Sep 2018, 06:29
This document is OUTDATED.
Please check for JGW-T2112874 for a newer version https://gwdoc.icrr.u-tokyo.ac.jp/cgi-bin/private/DocDB/ShowDocument?docid=12874.

As a supplement to the student lecture (JGW-G1808874-v1), the diagonalization matrix of the Type-B suspensions optical lever signals is further discussed. In particular, we proposed two ways to decouple any two degrees of freedom, using DC offsets or power spectrum. And, the mathematical expression of the diagonalization matrix was also derived for length and tilt optical lever. One can simply plug parameters like beam path length, an angle of rotational transformation and calibration factor for QPD in order to obtain the numerical matrix that can be input to the MEDM OL2EUL matrix. However, the correction factor for compensating misplacement of the length OpLev hasn't been derived. But, this effect of misplacement should be minimal.
Related Documents:
  • JGW-T2112874: Sensing Matrices for Optical Levers (OpLev) of the KAGRA Main Optics
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