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Proceedings Paper

Linear canonical transform sampling: analysis
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Paper Abstract

A new sampling criterion for the linear canonical transform (LCT) was recently proposed by the authors. This criterion was based on an analysis of the consequences of sampling the LCT of a discrete signal. Previous LCT sampling work in the literature considered only sampling the LCT of continuous, band limited signals. This analysis has great significance for numerical simulations of first order optical systems using the LCT, as these simulations must necessarily consider a sampled input function, and evaluate only a sampled output function. It is also significant for the analysis of periodic structures such as gratings. We present a review of this new sampling criterion and the associated analysis. We clarifying its meaning and consider its applications. In particular, we consider the consequences of the analysis for fast LCT algorithms, and for the use of the discrete Fresnel transform in digital holography. We conclude that the spectral method of calculating Fresnel transforms may benefit greatly from recent advances to LCT sampling theory.

Paper Details

Date Published: 1 October 2009
PDF: 8 pages
Proc. SPIE 7427, Optical Modeling and Performance Predictions IV, 742703 (1 October 2009); doi: 10.1117/12.826886
Show Author Affiliations
John Healy, Univ. College Dublin (Ireland)
SFI Strategic Research Cluster in Solar Energy Conversion (Ireland)
John T. Sheridan, Univ. College Dublin (Ireland)
SFI Strategic Research Cluster in Solar Energy Conversion (Ireland)
James P. Ryle, Univ. College Dublin (Ireland)
SFI Strategic Research Cluster in Solar Energy Conversion (Ireland)


Published in SPIE Proceedings Vol. 7427:
Optical Modeling and Performance Predictions IV
Mark A. Kahan, Editor(s)

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