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Interferometric scattering (iSCAT) microscopy is an emerging label-freetechnique optimized for the sensitive detection of nano-matter. Previous iSCATstudies have approximated the point spread function in iSCAT by a Gaussianintensity distribution. However, recent efforts to track the mobility ofnanoparticles in challenging speckle environments and over extended axialranges has necessitated a quantitative description of the interferometric pointspread function (iPSF). We present a robust vectorial diffraction model for theiPSF in tandem with experimental measurements and rigorous FDTD simulations. Weexamine the iPSF under various imaging scenarios to understand how aberrationsdue to the experimental configuration encode information about thenanoparticle. We show that the lateral shape of the iPSF can be used to achievenanometric three-dimensional localization over an extended axial range on theorder of 10$\,\mu$m either by means of a fit to an analytical model orcalibration-free unsupervised machine learning. Our results have immediateimplications for three-dimensional single particle tracking in complexscattering media.

The point spread function in interferometric scattering microscopy (iSCAT). I. Aberrations in defocusing and axial localization