Large depth of field (DOF) is a longstanding goal in optical imaging field. In this paper we presented a simple but efficient method to extend the DOF of a diffraction-limited imaging system using a thin scattering diffuser. The DOF characteristic of the imaging system with random phase modulation was analyzed based on the analytical model of ambiguity function as a polar display of the optical transfer function (OTF). The results of numerical simulation showed that more high-frequency components existed in the defocused OTF curve when the exit pupil of the imaging system exhibited a random phase modulation. It proved the important role of the scattering diffuser in extending the DOF of imaging systems. For the reconstruction, a stack of point spread functions (PSFs) corresponding to different axial locations within a measurement range were superimposed to construct the stacked PSF. Then the large DOF image was recovered from a speckle pattern by deconvolution. In this proof-of-concept, we experimentally demonstrated the single-shot imaging with larger DOF using a thin glass scattering diffuser in both a single-lens imaging system and a microscopic imaging system.
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