Controlling the Flow of Information in Optical Metrology

Optical metrology has progressed beyond the Abbe-Rayleigh limit, unlocking (sub)atomic precision by leveraging nonlinear phenomena, statistical accumulation, and AI estimators trained on measurand variations. Here, we show that Fisher information, which defines the fundamental precision limit, can be viewed as a physical entity that propagates through space, and we derive a wave equation for sensitivity fields describing its flow, which can resonate, diffract, and interfere. We reveal how material composition, geometry, and environmental design dictate where information is generated and how it travels, analogous to antennas and metasurfaces sculpting electromagnetic energy. Plasmonic and dielectric resonances enhance information flow, while gratings and near-field structures reshape radiation patterns. This perspective reframes metrology as a discipline in which resolution can be engineered by tailoring information sources and flow for applications in atomic-scale diagnostics and beyond, including optimisation of Light Detection and Ranging (LiDAR), remote sensing, and radar technologies.

💡 Research Summary

The paper introduces a fundamentally new perspective on optical metrology by treating Fisher information (FI)—the quantity that sets the Cramér‑Rao bound for any estimator—as a physical field that propagates through space much like an electromagnetic wave. Starting from the standard definition of FI as the second derivative of the log‑likelihood with respect to a parameter θ, the authors derive a continuity equation for FI that mirrors the energy‑continuity equation of classical electrodynamics. By identifying “effective currents” that arise wherever material parameters (permittivity ε or permeability μ) depend on θ, they show that the associated sensitivity fields (the derivatives of the electric and magnetic fields with respect to θ) satisfy a wave equation of the form

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