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In 1873, Ernst Abbe discovered what was to become a well-known paradigm: the inability of a lens-based optical microscope to discern details that are closer together than half of the wavelength of light. However, for its most popular imaging mode, fluorescence microscopy, the diffraction barrier is crumbling. Here, I discuss the physical concepts that have pushed fluorescence microscopy to the nanoscale, once the prerogative of electron and scanning probe microscopes. Initial applications indicate that emergent far-field optical nanoscopy will have a strong impact in the life sciences and in other areas benefiting from nanoscale visualization.