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. We 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 do not discuss specific methodology for improving resolution, 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.