Synthetic holography takes advantage of multi-parallax images to realize stereo display, and it can produce large area image through partition exposure. We describe the theory and system of digital synthetic holography and discuss the principle of the image division and recombination for two sampling modes. After analyzing the overlapped projection of the recombination image during the unit holograms exposure, we design an overlapped projecting lens based on nonimaging optics theory. The lens is simulated through optical design software. Finally we perform synthetic holography experiments with the lens. The results show that using the overlapped projecting lens and an appropriate image processing method, a clear-cut holographic stereogram with a strong three-dimensional sense can be obtained.