Fundamental limit of bandwidth-extrapolation-based superresolution

Here we relate two methods of subdiffraction imaging: bandwidth extrapolation for spatially bounded sources and quantum-metrology-inspired methods under assumptions about source structure. We present a quantum estimation theoretical approach in which the source is modeled in terms of unknown parameters corresponding to the Fourier components, whose impact on resolution is very intuitive. Using this method, we find that imaging spatially bounded sources faces an unavoidable fundamental resolution limit, but that in the small-source limit, certain measurement approaches can significantly improve the sensitivity over conventional methods.