Phase-space projection identities for diffraction catastrophes

Abstract

For each standard 'diffraction catastrophe' wavefunction psi , describing the interference pattern near a stable caustic, the authors derive two nonlinear identities. These relate the intensity mod psi mod 2 to an integral over the wavefunction psi corresponding to the same catastrophe, or to a less singular one. The identities are interpreted in terms of projections of Wigner functions from phase space on to coordinate space.