Surprises in aperiodic diffraction

TL;DR

This paper discusses recent advances in mathematical diffraction theory, highlighting new findings related to systems with continuous spectra and the surprising phenomenon of homometry, which complicates structure determination.

Contribution

It provides an informal overview of recent results in diffraction theory, emphasizing new insights into homometry and spectral properties of structures.

Findings

Improved understanding of systems with continuous and mixed spectra

Identification of unexpected facets of homometry

Recent results in diffraction image analysis

Abstract

Mathematical diffraction theory is concerned with the diffraction image of a given structure and the corresponding inverse problem of structure determination. In recent years, the understanding of systems with continuous and mixed spectra has improved considerably. Moreover, the phenomenon of homometry shows various unexpected new facets. Here, we report on some of the recent results in an exemplary and informal fashion.