Classification of the linear canonical transformation and its associated real symplectic matrix

Abstract

Based on the eigenvalues of the real symplectic ABCD-matrix that characterizes the linear canonical integral transformation, a classification of this transformation and the associated ABCD-system is proposed and some nuclei (i.e. elementary members) in each class are described. In the one-dimensional case, possible optical nuclei are the magnifier, the lens, and the fractional Fourier transformer; in the two-dimensional case, we have - in addition to the obvious concatenations of one-dimensional nuclei - the four combinations of a magnifier or a lens with a rotator or a shearing operator, where the rotator and the shearer are obviously inherently two-dimensional. Any ABCD-system belongs to one of the classes described in this paper and is similar (in the sense of similarity of the respective symplectic matrices) to the corresponding nucleus.

DOI: 10.1109/ISSPA.2007.4555352

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Cite this paper

@article{Bastiaans2007ClassificationOT, title={Classification of the linear canonical transformation and its associated real symplectic matrix}, author={Martin J. Bastiaans and Tatiana Alieva}, journal={2007 9th International Symposium on Signal Processing and Its Applications}, year={2007}, pages={1-4} }