Homometry in the light of coherent beams

TL;DR

This paper explores how coherent diffraction can distinguish homometric systems, specifically analyzing the Rudin-Shapiro sequence to understand the impact of correlation functions on speckle patterns and material analysis.

Contribution

It introduces a method to differentiate homometric systems using coherent diffraction and studies the Rudin-Shapiro sequence's unique properties.

Findings

Coherent diffraction can distinguish certain homometric systems.

Rudin-Shapiro sequence allows independent manipulation of correlation functions.

Correlation functions significantly influence speckle pattern statistics.

Abstract

Two systems are homometric if they are indistinguishable by diffraction. We first make a distinction between Bragg and diffuse scattering homometry, and show that in the last case, coherent diffraction can allow the diffraction diagrams to be differentiated. The study of the Rudin-Shapiro sequence, homometric to random sequences, allows one to manipulate independently two-point and four-point correlation functions, and to show their effect on the statistics of speckle patterns. Consequences for the study of real materials is discussed.