Multiscale Talbot effects in Fibonacci geometry

Abstract

This article investigates the Talbot effects in Fibonacci geometry by introducing the cut-and-projection construction, which allows for capturing the entire infinite Fibonacci structure in a single computational cell. Theoretical and numerical calculations demonstrate the Talbot foci of Fibonacci geometry at distances that are multiples or of the Talbot distance. Here (p, q) are coprime integers, μ is an integer, τ is the golden mean, and and are Fibonacci and Lucas numbers, respectively. The image of a single Talbot focus exhibits a multiscale-interval pattern due to the self-similarity of the scaling Fourier spectrum.