A statistical analysis of diffraction-limited imaging

The Rayleigh criterion is generally regarded as a fundamental limit and due to its practical accuracy in predicting the performance of optical imaging systems, it has unfortunately become Accepted as a de-facto physical law. In this work, we will show that this limit is simply a very good rule of thumb, which under proper conditions typically related to the signal-to-noise (SNR) of the sensor, can be overcome. While we will not be discussing specific methodology (e.g. [1]) for improving resolution in this paper, it is the aim of this work to explore how far beyond the Rayleigh limit one can go, and to identify the theoretical limits to such resolution enhancement.