Analysis on image recovery for digital Fresnel hologram with aliased fringe generated from self-similarity of point spread function

We analyze the aliasing phenomenon for digital Fresnel hologram with an enhanced numerical aperture (NA). The enhanced-NA digital hologram acquired computationally or optically at a closer distance from the object has an aliased fringe generated by undersampling process of the Fresnel prefactor. The point spread function known as Fresnel factor reveals a self-similar envelope when being sampled, which becomes a crucial mechanism in making this type of aliasing fringe of hologram. We describe that as the enhanced-NA hologram involves already the complementary aliased fringe that might come up in the reconstruction process, the robust recovery of object image can be realized. These behaviors are confirmed through numerical simulation. Based on the analysis of aliased hologram fringe, we provide a method for reconstructing the object image from the enhanced-NA digital Fresnel hologram without the shrinkage of image size.