Caustics and Diffraction from a Line Source

Abstract

A combination of differential and ‘catastrophe’ geometry is used to make a comprehensive study of the caustics generated by a general line source in three dimensions. This also corresponds to the ‘initial wavefront’ model for edge-scattering by apertures and discontinuities. The local orientation, scaling, shear and curvature of the fold, cusp and swallowtail caustics that typically occur are described exactly, in terms of the curvature parameters of the line source. The diffraction patterns surrounding the caustics in the quasi-geometrical limit are discussed in terms of the mapping from the physical observation variables to the canonical parameters in the corresponding normal forms. Caustics from a line source are compared in detail with those generated by unconstrained waves, and the mathematical context and possible applications to remote sensing are discussed.