Precision Estimation of Source Dimensions from Higher-Order Intensity Correlations

TL;DR

This paper demonstrates that higher-order intensity correlations in far-field imaging can significantly improve the precision of source dimension estimation beyond traditional methods, approaching the theoretical Cramér-Rao bound.

Contribution

It introduces a method using third and fourth order correlations for superresolution imaging, validated through simulations and maximum likelihood estimation.

Findings

Higher-order correlations improve estimation precision.

Third and fourth order correlations approach the Cramér-Rao bound.

Method is applicable to various incoherent sources and noise conditions.

Abstract

An important topic of interest in imaging is the construction of protocols that are not diffraction limited. This can be achieved in a variety of ways, including classical superresolution techniques or quantum entanglement-based protocols. Here, we consider superresolving imaging in the far field using higher-order intensity correlations. We show that third and fourth order correlations can improve upon the first and second order correlations that are traditionally used in classical optics and Hanbury Brown and Twiss type experiments. The improvement is achieved entirely by post-processing of the data. As a demonstrator, we simulate the far field intensity distribution of a circular aperture that emits thermal light and use maximum likelihood estimation to determine the radius of the aperture. We compare the achieved precision to the Cram\'er-Rao lower bound and find that the variance of measurements for the third and fourth order correlation functions are indeed closer to the Cram\'er-Rao bound than that of the second order correlation function. The method presented here is general, and can be used for all kinds of incoherent emitters, geometries, and types of noise.