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

M.J. Bastiaans; T. Alieva

doi:10.1109/ISSPA.2007.4555352

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

M.J. Bastiaans
, T. Alieva

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

1 Citation (Scopus)

4 Downloads (Pure)

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.

Original language	English
Title of host publication	Proc. ISSPA 2007, International Symposium on Signal Processing and its Applications, Sharjah, United Arab Emirates
Place of Publication	Piscataway, New Jersey, USA
Publisher	Institute of Electrical and Electronics Engineers
Pages	1238.1-1238.4
ISBN (Print)	978-1-424-40778-1
DOIs	https://doi.org/10.1109/ISSPA.2007.4555352
Publication status	Published - 2007
Event	conference; ISSPA 2007, Sharjah, United Arab Emirates; 2007-02-12; 2007-02-15 - Duration: 12 Feb 2007 → 15 Feb 2007

Conference

Conference	conference; ISSPA 2007, Sharjah, United Arab Emirates; 2007-02-12; 2007-02-15
Period	12/02/07 → 15/02/07
Other	ISSPA 2007, Sharjah, United Arab Emirates

Access to Document

10.1109/ISSPA.2007.4555352

Cite this

@inproceedings{9e0d9cbe2fef4d8c80a406ad1a231b4f,

title = "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.",

author = "M.J. Bastiaans and T. Alieva",

year = "2007",

doi = "10.1109/ISSPA.2007.4555352",

language = "English",

isbn = "978-1-424-40778-1",

pages = "1238.1--1238.4",

booktitle = "Proc. ISSPA 2007, International Symposium on Signal Processing and its Applications, Sharjah, United Arab Emirates",

publisher = "Institute of Electrical and Electronics Engineers",

address = "United States",

note = "conference; ISSPA 2007, Sharjah, United Arab Emirates; 2007-02-12; 2007-02-15 ; Conference date: 12-02-2007 Through 15-02-2007",

}

Bastiaans, MJ & 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. Institute of Electrical and Electronics Engineers, Piscataway, New Jersey, USA, pp. 1238.1-1238.4, conference; ISSPA 2007, Sharjah, United Arab Emirates; 2007-02-12; 2007-02-15, 12/02/07. https://doi.org/10.1109/ISSPA.2007.4555352

Classification of the linear canonical transformation and its associated real symplectic matrix. / Bastiaans, M.J.; Alieva, T.
Proc. ISSPA 2007, International Symposium on Signal Processing and its Applications, Sharjah, United Arab Emirates. Piscataway, New Jersey, USA: Institute of Electrical and Electronics Engineers, 2007. p. 1238.1-1238.4.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

TY - GEN

T1 - Classification of the linear canonical transformation and its associated real symplectic matrix

AU - Bastiaans, M.J.

AU - Alieva, T.

PY - 2007

Y1 - 2007

N2 - 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.

AB - 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.

U2 - 10.1109/ISSPA.2007.4555352

DO - 10.1109/ISSPA.2007.4555352

M3 - Conference contribution

SN - 978-1-424-40778-1

SP - 1238.1-1238.4

BT - Proc. ISSPA 2007, International Symposium on Signal Processing and its Applications, Sharjah, United Arab Emirates

PB - Institute of Electrical and Electronics Engineers

CY - Piscataway, New Jersey, USA

T2 - conference; ISSPA 2007, Sharjah, United Arab Emirates; 2007-02-12; 2007-02-15

Y2 - 12 February 2007 through 15 February 2007

ER -

Bastiaans MJ, Alieva T. 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. Piscataway, New Jersey, USA: Institute of Electrical and Electronics Engineers. 2007. p. 1238.1-1238.4 doi: 10.1109/ISSPA.2007.4555352

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

Abstract

Conference

Access to Document

Fingerprint

Cite this