Diffraction limit for a circular mask with a periodic rectangular apertures array

A mask with periodic apertures imaging system is adopted very widely and plays a leading role in modern technology for uses such as pinhole cameras, coded imaging systems, optical information processing, etc. because of its high resolution, its infinite depth of focus, and its usefulness over a broad frequency spectra ranging from visible light to x rays and gamma rays. While the masks with periodic apertures investigated in the literature are limited only to far-field diffraction, they do not take the shift of apertures within the mask into consideration. Therefore the derivation of the far-field diffraction for a single aperture cannot be applied to a mask with periodic apertures. The far-field diffraction formula modified for a multiaperture mask has been proposed in the past, the analysis remains too complicated to offer some practical guidance for mask design. We study a circular mask with periodic rectangular apertures and develop an easier way to interpret it. First, the near-field diffraction intensity of a circular aperture is calculated by means of Lommel's function. Then the convolution of the circular mask diffraction with periodic rectangular apertures is put together, and we can present a simple mathematical tool to analyze the mask properties including the intensity distribution, blurring aberration, and the criterion of defining the far- or near-field diffraction. This concept can also be expanded to analyze different types of masks with the arbitrarly shaped apertures. (C) 2002 Society of Photo-Optical Instrumentation Engineers.