Resolution Limit of Label-free Far-field Microscopy

We derive the fundamental limit to the resolution of far-field optical imaging, and demonstrate that, while a bound to the resolution of a fundamental nature does exit, contrary to the conventional wisdom it is neither exactly equal to nor necessarily close to Abbe's estimate. Our approach to imaging resolution that combines the tools from the physics of wave phenomena and the methods of information theory, is general, and can be extended beyond optical microscopy, to e.g. geophysical and ultrasound imaging.