Concave micro-mirror arrays fabricated as holographic optical elements are used in projector-based light field displays due to their see-through characteristics. The optical axes of each micro-mirror in the array are usually made parallel to each other, which simplifies the fabrication, integral image rendering, and calibration process. However, this demands that the beam from the projector be collimated and made parallel to the optical axis of each elemental micro-mirror. This requires additional collimation optics, which puts serious limitations on the size of the display. In this Letter, we propose a solution to the above issue by introducing a new method to fabricate holographic concave micro-mirror array sheets and explain how they work in detail. 3D light field reconstructions of the size 20 cm×10 cm and 6 cm in depth are achieved using a conventional projector without any collimation optics.