A review of the basic mathematical principles and properties of some phase space functions (Wigner and Ambiguity functions) is first presented in a more general mathematical context. Then, we deal in detail with three applications : image formation in optical systems (specifically cascading systems of lenses), image formation in Transmission Electron Microscopy, by taking advantage of some formal similarities with the previous examples and, finally, contrast transfer functions in Electron Microscopy in order to obtain 2-dimensional plots which provide information on the behavior of a transmission electron microscope. Also, the relations of these functions with other mathematical tools utilized in image processing and image formation theory are discussed.
Castaño, Victor; Vásquez-Polo, Gustavo; and Gutiérrez-Castrejón, Ramón
"Phase Space Methods in Image Formation Theory,"
Scanning Microscopy: Vol. 1992
, Article 37.
Available at: https://digitalcommons.usu.edu/microscopy/vol1992/iss6/37