Suppression of alias and replica noises in phase holograms using fractal topologies

Two-dimensional fractal topologies featuring (scaling) self-similarity, dense set of Bragg (diffraction) peaks, and inherent rotation symmetry, which are not achievable with regular grid-matrix geometries, exhibit optical robustness against structural damage and noise immunity of optical transmission paths. In this work, we numerically and experimentally demonstrate phase holograms using fractal plane-divisions. By taking advantage of the symmetries of the fractal topology, we propose numerical algorithms to design the fractal holograms. This algorithm solves the inapplicability of the conventional iterative Fourier transform algorithm (IFTA) method and enables efficient optimizations of millions of adjustable parameters in the optical element. Experimental samples show that the alias and replica noises in the image plane of fractal holograms are clearly suppressed, facilitating applications for high-accuracy and compact requirements.