A localized beam representation of high-frequency wave fields using a Wilson basis

A rigorous orthogonal basis is described for the representation of high-frequency wave fields using beam superpositions parameterized by both spatial position and spatial direction of each beam. This representation has many desirable features not found in conventional phase-space-based expansions such as the discrete or continuous Gabor schemes. The representation is highly efficient in the geometrical optics limit, that is, when it is strongly localized in the phase-space.