Theoretical and numerical treatment of diffraction through a circular aperture

The three-dimensional diffraction of a scalar plane wave through a circular aperture in an infinite plane screen is analyzed and numerically computed for the case of normal incidence. A modified Babinet's principle is formulated, and this is used to find the diffraction of sound by an acoustically soft circular disk. The spheroidal wave functions are described and applied to the diffraction theory. Numerical values of the rigorous diffraction functions are computed, and these are compared to the approximation obtained by the Huygen-Kirchhoff formulation.