Classification of lossless first-order optical systems and the linear canonical transformation

M.J. Bastiaans, T. Alieva

Onderzoeksoutput: Bijdrage aan tijdschriftTijdschriftartikelAcademicpeer review

29 Citaten (Scopus)


Based on the eigenvalues of the ray transformation matrix, a classification of ABCD systems is proposed and some nuclei (i.e., elementary members) in each class are described. In the one-dimensional case, possible 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 twodimensional. Any ABCD system belongs to one of the classes described in this paper and is similar (in the sense of matrix similarity of the ray transformation matrices) to the corresponding nucleus. Knowledge of a nucleus may be helpful in finding eigenfunctions of the corresponding class of first-order optical systems: one only has to find eigenfunctions of the nucleus and to determine how these functions propagate through a firstorder optical system. © 2007 Optical Society of America
Originele taal-2Engels
Pagina's (van-tot)1053-1062
Aantal pagina's9
TijdschriftJournal of the Optical Society of America A, Optics, Image Science and Vision
Nummer van het tijdschrift4
StatusGepubliceerd - 2007


Duik in de onderzoeksthema's van 'Classification of lossless first-order optical systems and the linear canonical transformation'. Samen vormen ze een unieke vingerafdruk.

Citeer dit