Expand this Topic clickable element to expand a topic
Skip to content
Optica Publishing Group

Two-dimensional nonseparable linear canonical transform: sampling theorem and unitary discretization

Not Accessible

Your library or personal account may give you access

Abstract

The two-dimensional (2D) nonseparable linear canonical transform (NS-LCT) is a unitary, linear integral transform that relates the input and output monochromatic, paraxial scalar wave fields of optical systems characterized by a 4×4 ray tracing matrix. In addition to the obvious generalizations of the 1D LCT (which are referred to as separable), the 2D-NS-LCT can represent a variety of nonaxially symmetric optical systems including the gyrator transform and image rotation. Unlike the 1D LCT, the numerical approximation of the 2D-NS-LCT has not yet received extensive attention in the literature. In this paper, (1) we develop a sampling theorem for the general 2D-NS-LCT which generalizes previously published sampling theorems for the 1D case and (2) we determine which sampling rates may be chosen to ensure that the obvious discrete transform is unitary.

© 2014 Optical Society of America

Full Article  |  PDF Article
More Like This
Unitary discrete linear canonical transform: analysis and application

Liang Zhao, John J. Healy, and John T. Sheridan
Appl. Opt. 52(7) C30-C36 (2013)

Two-dimensional nonseparable discrete linear canonical transform based on CM-CC-CM-CC decomposition

Soo-Chang Pei and Shih-Gu Huang
J. Opt. Soc. Am. A 33(2) 214-227 (2016)

Cited By

You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Figures (5)

You do not have subscription access to this journal. Figure files are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Tables (2)

You do not have subscription access to this journal. Article tables are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Equations (54)

You do not have subscription access to this journal. Equations are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Select as filters


Select Topics Cancel
© Copyright 2024 | Optica Publishing Group. All Rights Reserved