Ray transfer matrix analysis: Difference between revisions

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== Eigenvalues of Ray Transfer Matrix ==

A ray transfer matrix can been ragarded as [[Linear canonical transformation]]. According to the eigenvalues of the optical system, the system can be classified into several classes<ref>{{Cite journal|last=Bastiaans|first=Martin J.|last2=Alieva|first2=Tatiana|date=2007-03-14|title=Classification of lossless first-order optical systems and the linear canonical transformation|url=http://dx.doi.org/10.1364/josaa.24.001053|journal=Journal of the Optical Society of America A|volume=24|issue=4|pages=1053|doi=10.1364/josaa.24.001053|issn=1084-7529}}</ref>. Assume the the ABCD matrix representing a system relates the output ray to the input according to

<math> \begin{bmatrix}x_2 \\ \theta_2\end{bmatrix} = \begin{bmatrix} A & B \\ C & D \end{bmatrix} \begin{bmatrix}x_1 \\ \theta_1\end{bmatrix}