Temporal shaping of wave fields for optimally precise measurements in scattering environments

TL;DR

This paper introduces a method to shape wave fields in scattering media to maximize Fisher information, enabling optimal precision in measurements for applications like ultrasound imaging and structural health monitoring.

Contribution

It presents a theoretical and experimental framework for maximizing Fisher information in wave fields, setting a benchmark for precision in complex media.

Findings

Maximized Fisher information transmission in scattering environments.

Achieved optimal measurement precision in ultrasound experiments.

Provided a general benchmark for time-resolved measurements in complex media.

Abstract

A wave propagating through a scattering medium typically yields a complex temporal field distribution. Over the years, a number of procedures have emerged to shape the temporal profile of the field in order to temporally focus its energy on a receiver. By analogy, we theoretically and experimentally demonstrate here how to maximize the total Fisher information transmitted to a receiver, and how to focus the Fisher information at any given time. This enables one to estimate the value of any physical observable with optimal precision from noisy measurements, as experimentally illustrated using acoustic waves in the ultrasound regime. By yielding the ultimate precision limit achievable from time-resolved measurements performed in arbitrarily complex media, our approach sets a general benchmark for many applications such as structural health monitoring and biomedical imaging.