The resolution of digital holography as an optical imaging system is described by the point spread function of the system. Here the point spread function of double-aperture digital holography is determined. It promises the possibility of a resolution increase by the use of synthetic apertures, where we combine the digital holograms of two CCD arrays in one large hologram and reconstruct, or we superpose coherently the two reconstructed wave fields after a proper shift. An experimental method for the determination of this shift with subpixel accuracy is given. Furthermore, experimental results on numerically reconstructed wave fields from synthetic holograms stemming from two mutually shifted digital holograms of the same scene are presented.