Scalar beam diffraction by a wide circular aperture

The complex-source-point technique and the geometrical theory of diffraction constitute a powerful combination for the rigorous solution of high-frequency diffraction problems. Here scalar diffraction by a beam normally incident upon a circular aperture is analyzed, a situation involving shadow boundaries, multiple diffraction, and an axial caustic. The result is a simple and accurate uniform solution that satisfies the boundary conditions in the aperture plane. Numerical results are shown for a circular aperture of radius 1.5λ and incident beams of varying directivity.