Generalizing, optimizing, and inventing numerical algorithms for the fractional Fourier, Fresnel, and linear canonical transforms

On the Existence of Discrete Wigner Distributions

http://perso.ens-lyon.fr/patrick.flandrin/IEEE_SPL1999.pdf

• OPINION: Discussion on what happens when a discrete Wigner Distribution Function is used. Lists 6 properties, and show (via citation) that the WDF is the only Cohen class function that satisfies all of them. Then lists four types of signals, and there after show that the only discrete signal that satisfies the 6 properties is a periodic signal with odd length. The authors argue that the transforms for other types of discrete signals should not be called Wigner(-ville).

-Note: the last property is that the WDF should be real. This means that the complex wave field needs to be hermitian, which could be interesting to look at when trying to project LF to wave optics.

Ambiguity function and Wigner distribution function applied to partially coherent imagery

http://www.informaworld.com/index/DJQTY58T494W9PAD.pdf

• OPINION: Although the paper title indicate a focus on partially coherent light, also the simpler coherent light is discussed. Good recap on WDF/Ambiguity Function. Also relates to mutual intensity, and argue that the WDF/AF is more practical for some operations. I.e. hints at LCT. Shows what happens to WDF/AF in thin transparencies, transport, lenses, etc.