  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.
