Abstract
Superresolution fluorescence microscopy techniques such as PALM, STORM, STED, and Structured Illumination
Microscopy (SIM) enable imaging of live cells at nanometer resolution. The common theme in all of these
techniques is that the diffraction limit is circumvented by controlling the states of fluorescent molecules. Although
the samples are labeled very densely (i.e. with spacing much smaller than the Airy distance), not all of the
molecules are emitting at the same time. Consequently, one does not encounter overlapping blurs. In the
deterministic techniques (STED, SIM) the achievable resolution scales as the wavelength of light divided by the
square root of the intensity of a beam used to control the fluorescent state. In the stochastic techniques (PALM,
STORM), the achievable resolution scales as the wavelength of light divided by the square root of the number of
photons collected. Although these limits arise from very different mechanisms (parabolic beam profiles for STED
and SIM, statistics for PALM and STORM), in all cases the resolution scales inversely with the square root of
a measure of the number of photons used in the experiment. We have developed a proof that this relationship
between resolution and photon count is universal to techniques that control the states of fluorophores using
classical light. Our proof encompasses linear and nonlinear optics, as well as computational post-processing
techniques for extracting information beyond the diffraction limit. If there are techniques that can achieve a
more efficient relationship between resolution and photon count, those techniques will require light exhibiting
non-classical correlations.
