# Theory of coherent active convolved illumination for superresolution enhancement

## TL;DR

This paper presents a comprehensive mathematical theory of active convolved illumination, a technique that enhances superresolution imaging by coherently amplifying specific spectral components, with potential applications across various optical and quantum systems.

## Contribution

It provides the first detailed mathematical analysis of active convolved illumination, revealing its spectral amplification and correlation features for loss compensation in coherent imaging.

## Key findings

- Significant improvement in spectral signal-to-noise ratio.
- Enhanced resolution limits in superresolution imaging.
- Potential generalization to other linear systems and quantum technologies.

## Abstract

Recently an optical amplification process called the plasmon injection scheme was introduced as an effective solution to overcoming losses in metamaterials. Implementations with near-field imaging applications have indicated substantial performance enhancements even in the presence of noise. This powerful and versatile compensation technique, which has since been renamed to a more generalized active convolved illumination, offers new possibilities of improving the performance of many previously conceived metamaterial-based devices and conventional imaging systems. In this work, we present the first comprehensive mathematical breakdown of active convolved illumination for coherent imaging. Our analysis highlights the distinctive features of active convolved illumination, such as selective spectral amplification and correlations, and provides a rigorous understanding of the loss compensation process. These features are achieved by an auxiliary source coherently superimposed with the object field. The auxiliary source is designed to have three important properties. First, it is correlated with the object field. Second, it is defined over a finite spectral bandwidth. Third, it is amplified over that selected bandwidth. We derive the variance for the image spectrum and show that utilizing the auxiliary source with the above properties can significantly improve the spectral signal-to-noise ratio and resolution limit. Besides enhanced superresolution imaging, the theory can be potentially generalized to the compensation of information or photon loss in a wide variety of coherent and incoherent linear systems including those, for example, in atmospheric imaging, time-domain spectroscopy, ${\cal PT}$ symmetric non-Hermitian photonics, and even quantum computing.