Localization of nanoscale objects with light singularities

TL;DR

This paper demonstrates that using light with phase singularities significantly enhances the precision of nanoscale object localization, surpassing traditional methods by leveraging increased Fisher information.

Contribution

It provides a fundamental explanation for singularity-based metrology and shows how phase singularities improve localization precision at the nanoscale.

Findings

Orders-of-magnitude increase in Fisher information with phase singularities

Enhanced localization precision near phase singularities

Fundamental link between diffraction pattern variations and phase derivatives

Abstract

Unprecedented atomic-scale measurement resolution has recently been demonstrated in single-shot optical localization metrology 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 magnitude and phase of the incident field, with the latter strongly enhanced at 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.