Thomas A. Grant

It has been seen recently that when probing a nanoscale object to determine, for example, size or position via light scattering, a significant advantage in measurement precision can be gained from exploiting phase singularities in a topologically structured incident light field. Here, we demonstrate that this advantage, derived from the dependence of scattered intensity profiles on strong local (subwavelength-scale) intensity and phase variations in the incident field, can be extended towards imaging applications: analysis of scattering patterns from arbitrary binary gratings under superoscillatory illumination successfully resolves feature sizes down to ∼λ/6.6 in single-shot measurements (a factor of 1.3× smaller than is achieved with plane wave illumination), and ∼λ/10.5 in positionally-displaced few-shot measurements (which yields no improvement in the plane wave case). Interestingly, there are circumstances in which more complex objects are better resolved than simple structures, because interference effects increase the information content of their scattering patterns.

Unprecedented atomic‐scale measurement resolution has recently been demonstrated in single‐shot optical localization measurements based on deep‐learning analyses of diffraction patterns of topologically structured light scattered from objects. Here, we show that variations in the diffraction patterns caused by positional changes of an object depend upon the spatial derivatives of the amplitude and phase of the incident field, most strongly around phase singularities. Despite lower intensity near the singularity, an orders‐of‐magnitude increase in Fisher information contained in the diffraction patterns can be achieved when a nano‐object is illuminated by light containing phase singularities, rather than a plane wave. Our work provides a fundamental explanation and motivation for singularity‐based metrology with deeply subwavelength precision.