Theorem on subwavelength imaging with arrays of discrete sources

TL;DR

This paper presents a theorem for subwavelength imaging using discrete source arrays, analogous to the Nyquist-Shannon sampling theorem, defining the limits of imaging accuracy and proposing a physical system at the resolution limit.

Contribution

It introduces a novel theorem linking subwavelength imaging to sampling theory and outlines a physical system achieving the resolution limit.

Findings

The theorem establishes fundamental limits on subwavelength imaging accuracy.

A physical realization of an imaging system at the resolution limit is proposed.

The theorem parallels the Nyquist-Shannon sampling theorem in spatial imaging.

Abstract

A theorem on subwavelength imaging with arrays of discrete sources is formulated. This theorem is analogous to the Kotelnikov (also named Nyquist-Shannon) sampling theorem as it represents the field at an arbitrary point of space in terms of the same field taken at discrete points and imposes similar limitations on the accuracy of the image. A physical realization of an imaging system operating exactly on the resolution limit enforced by the theorem is outlined.