Breaking resolution limits: advances and challenges in single molecule microscopy

The resolution of an optical system is a measure of its ability to distinguish two closely spaced point sources. In optical microscopy, Rayleigh's criterion has been extensively used to determine the resolution of microscopes. Despite its widespread use, it is well known that this criterion is based on heuristic notions that are not suited to modern imaging approaches. Formulated within a deterministic framework, this criterion neglects the stochastic nature of photon emission and therefore does not take into account the total number of detected photons. In fact, single molecule experiments have shown that this criterion can be surpassed in a regular optical microscope thereby illustrating that Rayleigh's criterion is inadequate for current microscopy techniques. This inadequacy of Rayleigh's criterion has, in turn, necessitated a reassessment of the resolution limits of optical microscopes. By adopting an information-theoretic framework and using the theory concerning the Fisher information matrix, we proposed a new resolution measure that overcomes the limitations of Rayleigh's criterion. Here, we provide a review of this and other related results. The new resolution measure predicts that distances well below Rayleigh's limit can be resolved in an optical microscope. The effect of deteriorating experimental factors on the new resolution measure is also investigated. Further, it is experimentally verified that distances well below Rayleigh's limit can be measured from images of closely spaced fluorescent single molecules with an accuracy as predicted by the new resolution measure. We have also addressed an important problem in single molecule microscopy that concerns the accuracy with which the location of a single molecule can be determined. In particular, by using the theory concerning the Fisher information matrix we have derived analytical expressions for the limit to the 2D/3D localization accuracy of a single molecule.