This paper theoretically analyzes the axial intensity distribution of an optical imaging system with a low-frequency binary phase mask. Based on the derivation, a novel but simple one-step phase mask is designed to extend the depth of field. A comparison is made between the novel phase mask and the one designed in previous research [Opt. Express 14, 2631 (2006)]. Both masks are numerically tested in an achromatic doublet system. The numerical results show that two phase masks have comparable performance in depth of field extension. However, the phase mask designed in this paper has a simpler structure because it has only one step while the previous one has two. Consequently, the easy fabrication of the novel phase mask leads to cost reduction. This novel low-frequency binary phase mask provides a new choice to design depth-of-field-extended optical systems without digital image processing.
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