Some comments on the inverse problem of pure point diffraction

TL;DR

This paper discusses the inverse problem of pure point diffraction, exploring solutions and examples of homometric structures using recent methods, with a focus on clarifying the concepts in a non-technical manner.

Contribution

It applies recent techniques to construct solutions for the inverse diffraction problem and provides illustrative examples of homometric structures, extending prior work.

Findings

Constructed families of solutions to the inverse diffraction problem.

Presented examples of homometric structures.

Discussed potential extensions of existing methods.

Abstract

In a recent paper, Lenz and Moody (arXiv:1111.3617) presented a method for constructing families of real solutions to the inverse problem for a given pure point diffraction measure. Applying their technique and discussing some possible extensions, we present, in a non-technical manner, some examples of homometric structures.