Resolution beyond Rayleigh´s criterion: a modern resolution measure with applications to single molecule imaging

Rayleigh´s criterion, although extensively used, is well known to be based on heuristic notions that are inadequate for modern optical microscopy applications. This inadequacy has necessitated a reassessment of the resolution limits of optical microscopes. By adopting a stochastic framework and using the statistical theory concerning the Fisher information matrix, we have derived a new resolution measure that overcomes the limitations of Rayleigh´s criterion. Here, we provide a brief overview of this and other related results published by our group. The new resolution measure predicts that there is no resolution limit, but that the resolvability depends on the number of detected photons. It has been experimentally verified that distances well below Rayleigh´s limit can be measured from images of closely spaced single molecules with an accuracy as predicted by the new resolution measure. The stochastic framework used to obtain the new resolution measure is applicable to a wide variety of estimation problems encountered in optical microscopy. As an application, we have investigated the localization accuracy problem, which is concerned with how accurately the 2D/3D location of a microscopic object can determined from its image. One of the shortcomings of current microscopy techniques is that they suffer from poor depth discrimination and as a result they are not well adapted for 3D tracking of single molecules/particles. We have recently developed a novel imaging modality called multifocal plane microscopy (MUM) to overcome this limitation. Using the stochastic framework, we have shown that MUM has significantly improved depth discrimination, which in turn enables 3D single particle tracking at high axial localization accuracy.