Super-Resolution without Imaging: Library-Based Approaches Using Near-to-Far-Field Transduction by a Nanophotonic Structure

Super-resolution imaging is often viewed in terms of engineering narrow point spread functions, but nanoscale optical metrology can be performed without real-space imaging altogether. In this paper, we investigate how partial knowledge of scattering nanostructures enables extraction of nanoscale spatial information from far-field radiation patterns. We use principal component analysis to find patterns in calibration data and use these patterns to retrieve the position of a point source of light. In an experimental realization using angle-resolved cathodoluminescence, we retrieve the light source position with an average error below lambda/100. The patterns found by principal component analysis reflect the underlying scattering physics and reveal the role the scattering nanostructure plays in localization success. The technique described here is highly general and can be applied to gain insight into and perform subdiffractive parameter retrieval in various applications.