Aberrations of diffracted wave fields

This paper is an attempt to provide new insight into the behavior of near-field scalar diffraction phenomena by showing that the Rayleigh-Sommerfeld diffraction integral is equivalent to the Fourier transform integral of a generalized pupil function which includes a term that represents phase errors in the aperture. This term can be interpreted as describing a conventional wavefront aberration function. The resulting aberration coefficients are calculated and expressed in terms of the aperture diameter, observation distance, and appropriate field parameter for several different geometrical configurations of incident beam and observation space. These aberrations, which are inherently associated with the diffraction process, are precisely the effects ignored when making the usual Fresnel and Fraunhofer approximations.