Fisher Information as an Operational Metric for Structured Optical Beams

TL;DR

This paper introduces Fisher information as a practical metric to evaluate the sensing capabilities of structured optical beams, revealing how different modes influence measurement sensitivity beyond traditional entropy measures.

Contribution

It proposes using Fisher information to quantify the metrological usefulness of structured optical fields, providing a new operational criterion for sensing applications.

Findings

Fisher information varies significantly among modes with similar entropy.

Higher modal orders systematically increase Fisher information.

Fisher information effectively compares structured light fields for sensing purposes.

Abstract

Structured optical beams possess rich spatial features that are commonly characterized using entropic measures of field complexity. However, such measures do not directly quantify the operational usefulness of optical structure for parameter estimation and sensing. Here we introduce Fisher information as an operational metric to assess the metrological content of structured optical fields. By treating the measured intensity distribution as a statistical object, we define Fisher information with respect to physically relevant parameters, such as transverse displacement. We demonstrate that optical modes with comparable Shannon entropy can exhibit markedly different Fisher information, revealing sensitivity features associated with nodal structure and local curvature. Using Hermite--Gaussian modes as minimal test cases, we show that increasing modal order systematically enhances Fisher information. We then extend the analysis to two widely used families in structured light: Laguerre--Gaussian vortex beams and finite-energy Bessel--Gauss beams. Across these representative families, Fisher information provides a unified and experimentally accessible criterion for comparing structured optical fields in sensing applications.