Unitary implementation of the discrete two-dimensional non-separable linear canonical transform

Liang Zhao; John J. Healy; John T. Sheridan

doi:10.1117/12.2060984

19 September 2014 Unitary implementation of the discrete two-dimensional non-separable linear canonical transform

Liang Zhao, John J. Healy, John T. Sheridan

Proceedings Volume 9216, Optics and Photonics for Information Processing VIII; 921610 (2014) https://doi.org/10.1117/12.2060984
Event: SPIE Optical Engineering + Applications, 2014, San Diego, California, United States

Abstract

The continuous linear canonical transforms is known to describes wave field propagation through paraxial (quadratic phase) optical systems. Digital algorithms to numerically calculate the LCT are therefore important in modelling field propagation through first order optical systems and are also of interest for many purely digital signal processing applications. Significantly the continuous LCTs are unitary, but discretization can destroy this property resulting in a loss of conservative properties. Previously we presented a sufficient condition on the sampling rates chosen during discretization to ensure that digital implementations of the 1D and 2D separable LCTs were unitary. In this paper we extend our analysis to discuss the cases of the 2D non-separable LCT which are used to describe non-orthogonal, nonaxially symmetric and anamorphic systems. We also examine the consequences of ours results.

Citation Download Citation

Liang Zhao, John J. Healy, and John T. Sheridan "Unitary implementation of the discrete two-dimensional non-separable linear canonical transform", Proc. SPIE 9216, Optics and Photonics for Information Processing VIII, 921610 (19 September 2014); https://doi.org/10.1117/12.2060984

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available