Ray transfer matrix analysis: Difference between revisions

Revision as of 08:24, 15 December 2021

Revision as of 03:42, 30 December 2021

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== Eigenvalues of Ray Transfer Matrix ==

A ray transfer matrix can be regarded as a [[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 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}

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== Relation between geometrical ray optics and wave optics ==

The theory of [[Linear canonical transformation]] implies the relation between ray transfermatrix ([[geometrical optics]]) and wave optics.<ref>{{Cite journal|last=Nazarathy|first=Moshe|last2=Shamir|first2=Joseph|date=1982-03-01|title=First-order optics—a canonical operator representation: lossless systems|url=http://dx.doi.org/10.1364/josa.72.000356|journal=Journal of the Optical Society of America|volume=72|issue=3|pages=356|doi=10.1364/josa.72.000356|issn=0030-3941}}</ref>.

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