The Wigner function in paraxial optics I. Matrix methods in Fourier optics

Abstract

The paraxial regime of scalar wave optics has the same structure as non-relativistic quantum mechanics, with wavelength taking the place of the Planck constant. The Wigner function is a central tool to explore the phase space of a system; in optics, moreover, it can be produced by purely optical means. In this first part, we present a matrix-based formalism for the study of paraxial optical systems, and apply it to the description of a setup that, as will be seen in the second part, produces the Wigner function.