Cross-spectral purity: a generalization of spatiotemporal separability

TL;DR

This paper explores the relationship between cross-spectral purity and spatiotemporal separability in nonstationary scalar fields, revealing their equivalence under complete coherence and extending the concept to partial coherence.

Contribution

It establishes a two-way relation between cross-spectral purity and spatiotemporal separability and introduces a generalization to partially coherent fields.

Findings

Complete coherence links cross-spectral purity with spatiotemporal separability.

Cross-spectral purity extends to partial coherence via correlation function separability.

Simple measurement methods can detect cross-spectral purity.

Abstract

We study the connection between cross-spectral purity and spatiotemporal separability of nonstationary (pulsed) scalar fields. It is found that in the case of complete coherence, there is a two-way relation between global cross-spectral purity and spatiotemporal separability of the field. Moreover, we show that cross-spectral purity generalizes the notion of spatiotemporal separability to partially coherent fields, due to the separability of the correlation functions. We also briefly discuss simple self-referencing linear measurement methods that can reveal cross-spectral purity.