Diffracted wavefield by an arbitrary aperture from Maggi–Rubinowicz transformation: Fraunhofer approximation

Fraunhofer diffraction patterns through apertures in opaque screens are the cases of most interest in optics. The major purpose of this paper is to establish a general and explicit formula for calculating diffracted wavefield from Maggi–Rubinowicz transformation. The 2-D integration (Rayleigh–Sommerfeld or Helmholtz–Kirchhoff integral formulas) is reduced to a 1-D integration over the rim of the aperture. Some examples for elliptical and polygonal apertures are given.