LIGO Document T0900647-v2

Ray optics calculations of alignment matrices

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Document type:
T - Technical notes
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The location of the mode of a resonant cavity can be completely
defined by the waist position and angle. In the case of a two mirror
cavity, its a simple matter to calculate how the waist shifts with
misalignment of the mirrors. For a ring cavity with three or more
mirrors, there are more mirror degrees of freedom than there are
cavity mode degrees of freedom and we must define a control matrix.
In this note, we show a general technique for calculating the waist
motion as a function of mirror alignment using ray optics.
Files in Document:
  • PDF file (AlignmentMatrix.pdf, 200.1 kB)
Other Files:
Notes and Changes:
Fixed typo in IMC matrix.

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