Quantum limit to subdiffraction incoherent optical imaging

TL;DR

This paper establishes a quantum limit on the precision of imaging subdiffraction incoherent sources, showing that SPADE measurements approach this fundamental bound and are nearly optimal.

Contribution

It derives a general quantum bound on Fisher information for subdiffraction imaging, extending previous two-source results to more complex objects.

Findings

SPADE measurement approaches the quantum limit in scaling

Quantum bound applies to diffusion parameter estimation

Results demonstrate near-optimality of SPADE measurements

Abstract

The application of quantum estimation theory to the problem of imaging two incoherent point sources has recently led to new insights and better measurements for incoherent imaging and spectroscopy. To establish a more general limit beyond the case of two sources, here I evaluate a quantum bound on the Fisher information that can be extracted by any far-field optical measurement about the moments of a subdiffraction object. The bound matches the performance of a spatial-mode-demultiplexing (SPADE) measurement scheme in terms of its scaling with the object size, indicating that SPADE is close to quantum-optimal. Coincidentally, the result is also applicable to the estimation of diffusion parameters with a quantum probe subject to random displacements.