Fundamental bounds on the precision of iSCAT, COBRI and dark-field microscopy for 3D localization and mass photometry
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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 Cramér-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 Cramér-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 Cramér-Rao bound for mass estimation yields a minimum relative estimation error of σ_m/m=1/(2√(N)), where N is the number of collected scattered photons.
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