Viewing-angle expansion in holographic displays implemented with a modulator having finite space-bandwidth

The expansion of viewing angle is a crucial factor in holographic displays implemented with a spatial light modulator having a finite space-bandwidth. A holographic image is reconstructed at a viewing angle dependent on the numerical aperture of digital hologram. However, an interference of high-order noises is inevitable at an angle larger than the diffraction angle by a hologram pixel. This study presents the theoretical foundation for optimizing the Fresnel hologram to recover the low space-bandwidth. The higher spectrum components of the digital hologram beyond the bandwidth exists in the form of their replications. The expansion of angular spectrum by its repetition during optimization procedure increases the image resolution, resulting in a viewing angle that is determined by the hologram numerical aperture. We numerically and experimentally verify our strategy to expand a viewing angle of holographic image.