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

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