Diffracted field by an arbitrary aperture

Diffraction patterns of apertures on screens uniformly illuminated are stan dard calculations in undergraduate optics and acoustics courses. These calc ulations imply two-dimensional (2-D) integrations which are often performed in the far zone, at moderate angles of diffraction, i.e., using Fresnel an d Fraunhofer approximations. In this note, the 2-D integration is reduced t o a I-D parametric integration over the perimeter of the aperture-resemblin g the Rubinowicz's representation of the Kirchhoff diffraction integral-whi ch allows numerical evaluation with few computational resources. The propos ed formula allows mathematically exact calculation of the near-field, in th e context of scalar wave theory. Explicit calculations for circular and ell iptical apertures are shown. (C) 1999 American Association of Physics Teach ers.