The advent of single molecule microscopy has generated significant interest in imaging single biomolecular interactions
within a cellular environment in three dimensions. It is widely believed that the classical 2D (3D)
resolution limit of optical microscopes precludes the study of single molecular interactions at distances of less
than 200 nm (1 micron). However, it is well known that the classical resolution limit is based on heuristic notions.
In fact, recent single molecule experiments have shown that the 2D resolution limit, i.e. Rayleigh's criterion, can
be surpassed in an optical microscope setup. This illustrates that Rayleigh's criterion is inadequate for modern
imaging approaches, thereby necessitating a re-assessment of the resolution limits of optical microscopes.
Recently, we proposed a new modern resolution measure that overcomes the limitations of Rayleigh's criterion.
Known as the fundamental resolution measure FREM, the new result predicts that distances well below the classical
2D resolution limit can be resolved in an optical microscope. By imaging closely spaced single molecules,
it was experimentally verified that the new resolution measure can be attained in an optical microscope setup.
In the present work, we extend this result to the 3D case and propose a 3D fundamental resolution measure 3D
FREM that overcomes the limitations of the classical 3D resolution limit. We obtain an analytical expression for
the 3D FREM. We show how the photon count of the single molecules affects the 3D FREM. We also investigate
the effect of deteriorating experimental factors such as pixelation of the detector and extraneous noise sources
on the new resolution measure. In contrast to the classical 3D resolution criteria, our new result predicts that
distances well below the classical limit can be resolved. We expect that our results would provide novel tools for
the design and analysis of 3D single molecule imaging experiments.