Spatial sub-Rayleigh imaging analysis via speckle laser illumination

TL;DR

This paper demonstrates that confining the divergence and source size in speckle laser illumination enables sub-Rayleigh imaging beyond traditional limits, with insights into high-order correlation algorithms and their limitations.

Contribution

It reveals the physics behind high-order correlation imaging and identifies the specific conditions where sub-Rayleigh features can be achieved.

Findings

First-order intensity measurement surpasses Rayleigh limit with speckle illumination.

High-order algorithms are limited to binary objects, causing distortion with gray objects.

Cross-correlation functions identify optimal conditions for sub-Rayleigh imaging.

Abstract

It is commonly accepted that optical sub-Rayleigh imaging has potential application in many fields. In this Letter, by confining the divergence of the optical field, as well as the size of the illumination source, we show that the first-order averaged intensity measurement via speckle laser illumina- tion can make an actual breakthrough on the Rayleigh limit. For a high-order algorithm, it has been reported that the autocorrelation function can be utilized to achieve the sub-Rayleigh feature. However, we find that this sub- Rayleigh feature for the high-order algorithm is limited only to binary objects, and the image will be distorted when a gray object is placed. This property encourages us to find the physics behind the high-order correlation imaging algo- rithm. We address these explanations in this Letter and find that for different types of high-order algorithm, there is always a seat in the right place from the cross-correlation function.