Analysis of Chaotic Systems in the Generation of Random Phases for Amplitude Holograms

In recent decades, there has been great interest in the development of applications of chaotic systems in cryptographic systems and communication systems due to their non-periodic and long-term unpredictable nature. In this work, the properties of different chaotic systems, both continuous and discrete in time, are analyzed for the generation of pseudo-random phases practical for holography. The different types of dynamics generated by different systems are analyzed using bifurcation diagrams, transition from chaos to periodic orbits and equilibrium points, as well as two methodologies to construct the phase (Cartesian and polar). Our results shows a better performance in discrete-time systems by generating smooth transitions in the formed patterns and avoiding the generation of artifacts in the holograms, given the wider range of parameters in which the system is stable.