The linear canonical transform (LCT) is the name of a parameterized continuum of transforms that include, as particular cases, many widely used transforms in optics such as the Fourier transform, fractional Fourier transform, and Fresnel transform. It provides a generalized mathematical tool for representing the response of any first-order optical system in a simple and insightful way. In this work we present four uncertainty relations between LCT pairs and discuss their implications in some common optical systems.
© 2008 Optical Society of America
Diffraction and Gratings
Original Manuscript: November 11, 2007
Revised Manuscript: December 24, 2007
Manuscript Accepted: January 2, 2008
Published: February 12, 2008
Adrian Stern, "Uncertainty principles in linear canonical transform domains and some of their implications in optics," J. Opt. Soc. Am. A 25, 647-652 (2008)