Based on the recording and reconstruction theory of Fresnel incoherent digital holography, we analyze and calculate the imaging process of the synthetic aperture incoherent digital holography. The effect of mounting the double lens symmetry mode on a spatial light modulator on imaging characteristics of synthetic aperture incoherent digital holography is simulated, and the simulation results are analyzed. We compare two representation methods including different phase sub-holograms which are first spliced and reconstructed or first reconstructed and spliced. The simulation results are verified by experiments. The results show that the central aperture is the most important sub-aperture. The central aperture and four cross-bonding sub-apertures has better imaging performance, or the double lens symmetry mode can greatly reduce the number of sub-apertures and the holographic recording time. The applicability of synthetic aperture technique in incoherent digital holography is verified.