Fundamental bounds on the precision of iSCAT, COBRI and dark-field microscopy for 3D localization and mass photometry

TL;DR

This paper derives fundamental precision bounds for interferometric microscopy techniques like iSCAT, COBRI, and dark-field microscopy, providing a rigorous comparison and revealing the potential and limitations for 3D localization and mass photometry.

Contribution

It introduces a quantum and classical Cramér-Rao bound framework for assessing the measurement limits of interferometric imaging techniques.

Findings

iSCAT's geometry enhances axial position sensitivity

Quantum bounds set a minimum relative error of 1/(2√N) for mass estimation

Comparison of techniques highlights fundamental precision limits

Abstract

Interferometric imaging is an emerging technique for particle tracking and mass photometry. Mass or position are estimated from weak signals, coherently scattered from nanoparticles or single molecules, and interfered with a co-propagating reference. In this work, we perform a statistical analysis and derive lower bounds on the measurement precision of the parameters of interest from shot-noise limited images. This is done by computing the classical Cram\'er-Rao bound for localization and mass estimation, using a precise vectorial model of interferometric imaging techniques. We then derive fundamental bounds valid for any imaging system, based on the quantum Cram\'er-Rao formalism. This approach enables a rigorous and quantitative comparison of common techniques such as interferometric scattering microscopy (iSCAT), Coherent Brightfield microscopy (COBRI), and dark-field microscopy. In particular, we demonstrate that the light collection geometry in iSCAT greatly increases the axial position sensitivity, and that the Quantum Cram\'er-Rao bound for mass estimation yields a minimum relative estimation error of $\sigma_m/m=1/(2\sqrt{N})$, where $N$ is the number of collected scattered photons.