The Wigner function in paraxial optics II. Optical diffraction pattern representation

Abstract

The Wigner distribution function is a tool to visualize a signal in the space-frequency domain. Moreover, it can be produced by purely optical means. We describe the Brenner-Lohmann optical setup with monochromatic light, which produces the Wigner function. A signal composed of rectangle functions (optically produced by slits) has a Wigner function with a ``sand clock" form. We point out the strong oscillations of the Wigner function between two interfering components, which has been called the smile function\/ of a ``Schrödinger's cat" state. This bears interesting optical diffraction patterns in our figures.