Fundamental Bounds on the Precision of iSCAT, COBRI and Dark-Field Microscopy for 3D Localization and Mass Photometry

J. Dong, D. Maestre, C. Conrad-Billroth, T. Juffmann

Journal of Physics D: Applied Physics, vol. 54, no. 39, paper no. 394002, pp. 1-12, September 30, 2021.

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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 (CRB) 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, 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 CRB 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.

@ARTICLE(http://bigwww.epfl.ch/publications/dong2101.html,
AUTHOR="Dong, J. and Maestre, D. and Conrad-Billroth, C. and Juffmann,
	T.",
TITLE="Fundamental Bounds on the Precision of {iSCAT}, {COBRI} and
	Dark-Field Microscopy for {3D} Localization and Mass Photometry",
JOURNAL="Journal of Physics {D}: Applied Physics",
YEAR="2021",
volume="54",
number="39",
pages="1--12",
month="September 30,",
note="paper no.\ 394002")

DOI: 10.1109/OJSP.2021.3116482