Ray optics calculations of alignment matrices

Document #:

LIGO-T0900647-v2

Document type:

T - Technical notes

Abstract:

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, file is not accessible)

Other Files:

• ZIP file of latex, figures (AlignmentMatrix.zip, file is not accessible)

Topics:

• Modelling
• Sensing and Control

Authors:

• Sam Waldman

Notes and Changes:

Fixed typo in IMC matrix.