Some remarks on the visible points of a lattice
Michael Baake (Tuebingen), Uwe Grimm (Chemnitz), David Warrington, (Sheffield)
TL;DR
This paper investigates the properties of visible points in a lattice and their Fourier transforms, providing a new formula involving Dirichlet series and comparing theoretical results with optical Fourier transform experiments.
Contribution
It introduces a closed-form formula for the Fourier transform of visible lattice points using Dirichlet series, extending previous research.
Findings
Derived a closed formula for the Fourier transform of visible points
Compared theoretical Fourier transform with optical experiments
Extended previous work on lattice visible points
Abstract
We comment on the set of visible points of a lattice and its Fourier transform, thus continuing and generalizing previous work by Schroeder and Mosseri. A closed formula in terms of Dirichlet series is obtained for the Bragg part of the Fourier transform. We compare this calculation with the outcome of an optical Fourier transform of the visible points of the 2D square lattice.
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