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

M.J. Bastiaans, T. Alieva

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1 Citaat (Scopus)

Samenvatting

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.
Originele taal-2Engels
TitelProc. ISSPA 2007, International Symposium on Signal Processing and its Applications, Sharjah, United Arab Emirates
Plaats van productiePiscataway, New Jersey, USA
UitgeverijInstitute of Electrical and Electronics Engineers
Pagina's1238.1-1238.4
ISBN van geprinte versie978-1-424-40778-1
DOI's
StatusGepubliceerd - 2007
Evenementconference; ISSPA 2007, Sharjah, United Arab Emirates; 2007-02-12; 2007-02-15 -
Duur: 12 feb 200715 feb 2007

Congres

Congresconference; ISSPA 2007, Sharjah, United Arab Emirates; 2007-02-12; 2007-02-15
Periode12/02/0715/02/07
AnderISSPA 2007, Sharjah, United Arab Emirates

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Citeer dit

Bastiaans, M. J., & Alieva, T. (2007). Classification of the linear canonical transformation and its associated real symplectic matrix. In Proc. ISSPA 2007, International Symposium on Signal Processing and its Applications, Sharjah, United Arab Emirates (blz. 1238.1-1238.4). Piscataway, New Jersey, USA: Institute of Electrical and Electronics Engineers. https://doi.org/10.1109/ISSPA.2007.4555352