WIGNER OPERATOR AND FUNCTION FOR VARIOUS OPTICAL-SYSTEMS

Recently, a Wigner operator was defined on Lie groups, and Wigner func tions for various physical models were introduced through correspondin g homogeneous Hilbert spaces. In this article, we summarize results ob tained so far within various optical models for signal analysis. The g roups we present here are the Heisenberg-Weyl group for polychromatic optical wave fields (color wave optics), the Euclidean group for the m odels of infinite discrete data sets (discrete optics) and two-dimensi onal monochromatic wave fields (Helmholtz optics), and the two-dimensi onal unitary group for finite data sets (finite optics).