Rayleigh's criterion is widely in optical microscopy to determine the resolution of microscopes. Despite its widespread use, it is well known that this criterion is heuristic and does not consider the actual measurement process. For instance, it has been pointed out that the resolution of a fluorescence microscope can, in principle, exceed Rayleigh's criterion when distance determination between two point sources is postulated as a parameter estimation problem. In fact, recent results from single molecule fluorescence experiments show that the location of two closely spaced point sources with distance of separation well below Rayleigh's criterion can be accurately estimated. These results suggest that Rayleigh's criterion is inadequate for current microscope techniques. Here, by adopting an information-theoretic stochastic framework, we re-visit the resolution problem and derive a new stochastic resolution criterion that provides a limit to the accuracy with which the distance between two point sources can be determined. Our results predict that the distance between two point sources can be determined to an arbitrary accuracy provided a sufficient number of photons are detected. The new criterion is given in terms of quantities such as the expected number of detected photons, the numerical aperture of the objective lens and the wavelength of the detected photons. We also investigate how the new resolution measure is influenced by deteriorating experimental factors such as pixelation of the detector and additive noise sources.
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