## Unitary discrete linear canonical transform: analysis and application |

Applied Optics, Vol. 52, Issue 7, pp. C30-C36 (2013)

http://dx.doi.org/10.1364/AO.52.000C30

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### Abstract

The numerical approximation of the linear canonical transforms (LCTs) is important in modeling coherent wave field propagation through first-order optical systems and in many digital signal processing applications. The continuous LCTs are unitary, but discretization can destroy this property. We present a sufficient condition on the sampling rates chosen in the discretization to ensure unitarity. We discuss the various subsets of the unitary matrices examined in this paper that have been proposed elsewhere. We offer a proof of the existence of all of the unitary matrices we discuss. We examine the consequences of these results, particularly in relation to the use of discrete transforms in iterative phase retrieval applications.

© 2013 Optical Society of America

**OCIS Codes**

(000.4430) General : Numerical approximation and analysis

(070.2590) Fourier optics and signal processing : ABCD transforms

(100.5070) Image processing : Phase retrieval

(100.6640) Image processing : Superresolution

(120.4120) Instrumentation, measurement, and metrology : Moire' techniques

(090.1995) Holography : Digital holography

**History**

Original Manuscript: October 2, 2012

Manuscript Accepted: November 11, 2012

Published: January 23, 2013

**Citation**

Liang Zhao, John J. Healy, and John T. Sheridan, "Unitary discrete linear canonical transform: analysis and application," Appl. Opt. **52**, C30-C36 (2013)

http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-52-7-C30

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