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Because of high resolution, infinite depth of focus and the usefulness over a broadfrequency spectra which range from visible light to x-ray and (gamma) -ray, the mask with periodic apertures image system is adopted very widely and play the part of leading role in the modern technology, such as pinhole camera, coded image system and optical information processing et al. While masks with periodic apertures investigated in the literatures are only limited to far-field diffraction, it did not take the shift of apertures within the mask into consideration. Therefore the derivation of far-field diffraction for single aperture can not be applied to mask with periodic apertures. The modified formula of far-field diffraction for multi-aperture mask has been proposed in the past, the analysis is still too complex to offer some practical rules for mask design. In order to develop an easier interpretation, this paper studies the circular mask with periodic rectangular apertures. First, we calculate the near- field diffraction intensity of circular aperture by means of Lommel's function. After the convolution of circular mask diffraction with periodic rectangular apertures together, we present a simple mathematical tool to analyze the mask including the distribution of intensity, aberration of blurring and the criterion of defining the far- or near-field diffraction. This concept can also be expanded to analyze the different type of mask with the arbitrary shape apertures.
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