document: 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 can not 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 arbitrarily shaped apertures
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