Wigner distribution function for Euclidean systems

Euclidean systems include poly-and monochromatic wide-angle optics, acoustics, and also infinite discrete data sets. We use a recently defined Wigner operator and (quasiprobability) distribution function to set up and study the phase-space evolution of these models, subject to differential and difference equations, respectively. Infinite data sets and two-dimensional monochromatic (Helmholtz) fields are thus shown by their Wigner function on a cylinder of (2 pi) direction and location; the Wigner function for polychromatic wavefields has R(3) 'c-number' coordinates of (two-dimensional) wavenumber and position.