Caustics and caustic corrections to the field diffracted by a curved edge

The caustics for the singly diffracted rays from a circular disk are investigated when the rays emanate from a source which is placed off the axis of the disk. Either two or four singly diffracted rays appear dependent on the far-field direction. The caustics separate the region of space with two singly diffracted rays from the regions with four singly diffracted rays. Corrections are derived which allow the ray description to be continued across the caustics. These corrections depend on the local properties of the edge at the point of diffraction and may be used for edges with arbitrary curvature. Numerical examples are included to demonstrate how the caustic corrections improve calculations based on the geometrical theory of diffraction (GTD).