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• An accurate analyzing method for depth of field of the integral image 3D display is proposed. • An integral imaging 3D display with an enhanced depth of field is realized. • The 2D/3D convertible display is realized. Depth of field (DOF) enhancement and two-dimensional (2D)/three-dimensional (3D) convertible display are important research areas of integral imaging 3D display. However, there is no accurate definition of DOF in existing integral imaging 3D displays, and it is difficult to realize DOF enhancement and 2D/3D convertible display simultaneously. In this paper, we propose a DOF analysis method for integral imaging 3D display, and derive an accurate definition of DOF by analyzing the voxel formation mechanism and the minimum resolution angle of the human eyes. Then a 2D/3D convertible integral imaging display with an enhanced DOF is proposed based on the definition of the DOF. The DOF enhancement and different display modes of 2D and 3D are realized by using two sets of dual-state optical components, including polymer dispersed liquid crystal (PDLC) films and liquid crystal micro-lens arrays (LCMLAs). When PDLC film in one set is scattering and LCMLA has the optical properties of a micro-lens array, while PDLC film in the other set is transparent and LCMLA has the optical properties of a flat glass at the same time, the system operates in 3D display modes. Two sets of DOFs are formed in turns and spliced to enhance the whole DOF based on the persistence of vision. When only one PDLC film is scattering and two LCMLAs both have the optical properties of a flat glass, the system realizes 2D display. The experiments on the 2D/3D convertible integral imaging display prototype verify that the DOF is enhanced to 1.71 times and 2D/3D convertible display is realized simultaneously compared with the display based on a conventional micro-lens array. The proposed display has potential for applications in areas such as education and medical care. [ABSTRACT FROM AUTHOR]