Motion-Based Beamshape Recovery Enables Precision Nanoparticle Sizing
Label-free all-optical nanosizing approaches based on interferometric or darkfield-imaging infer size, composition, or shape from single-particle scattering signals, but these signals are inseparably coupled to the spatially non-uniform illumination profile of the imaging system. Existing normalisation strategies require directly measuring this illumination field, an approach that fails for background-free geometries, such as lightsheet-type illumination, where the field cannot be detected. Here we introduce a self-normalisation method that reconstructs the illumination profile directly from the scattering signals of many freely diffusing nanoparticles, requiring no additional hardware, calibration samples, or direct field measurement. Critically, our approach eliminates the particle-heterogeneity bias that otherwise corrupts such reconstructions, by normalising single-particle trajectories against each other in regions of spatial overlap, where distinct particles necessarily sample identical illumination and detection conditions. We validate this method for gold nanoparticles of various size in two- and three-dimensional geometries, including a 90{\deg} side-illumination configuration in which the illumination field is entirely undetectable by conventional means, and show that reconstructed profiles closely match ground-truth measurements, thus drastically reducing signal variability. Relying solely on the scattering signal already acquired for sizing, our approach is immediately compatible with existing interferometric and darkfield nanoscopy platforms and broadly extendable to other scattering or fluorescent modalities, including light-sheet microscopy.