A method for numerically removing the twin image in on-axis digital holography, based on multiple digital holograms, is discussed. The digital holograms under examination are captured experimentally using an in-line modified Mach-Zehnder interferometric setup and subsequently reconstructed numerically. The technique is suitable for both transmission and reflection geometry. Each individual hologram is recorded with a statistically independent diffuse illumination field. This is achieved by shifting a glass diffuser in the x-y plane of the object path. By recording the holograms in this manner the twin image, from a numerical reconstruction, appears as speckle. By reducing this speckle pattern the twin image can be effectively removed in the reconstruction plane. A theoretical model is developed and experimental results are presented that validate this model.