Phase-space distributions for high-frequency fields

The Wigner distribution function and various windowed Fourier transforms are examples of phase-space distributions that are used, among other things, to formalize the link between ray and wave optics. It is well known that, in the limit of high frequencies, these distributions become localized for simple wave fields and therefore that the localization can be used to define the associated ray families. This localized form is characterized here for both the Wigner distribution function and a Gaussian windowed Fourier transform. Aside from the greater understanding of the distributions themselves, these results promise a clearer intuition of phase-space-based methods for optical modeling. In particular, regardless of the context, the geometric construction that is presented for estimating the Wigner distribution function gives a valuable appreciation of its highly structured and sometimes surprising form.