  Superresolution fluorescence microscopy techniques beat the diffraction
limit, enabling ultra-high resolution imaging in biological physics and
nanoscience. In all cases that have been studied experimentally, the resolution
scales inversely with the square root of some parameter that measures the
number of photons used. However, this ubiquitous limit arises from very
distinct mechanisms in different approaches, raising the question of whether it
is a fundamental limit that cannot be exceeded, or merely a coincidence of the
techniques studied thus far. We demonstrate that, under very general
assumptions that encompass essentially all fluorescence microscopy situations,
the known resolution limit is indeed universal. Our model considers experiments
that build up an image via any arbitrary sequence of steps compatible with our
assumptions of (1) light that exhibits shot noise and (2) molecules that can be
modeled with rate equations. A detailed examination of our assumptions shows
that exceeding this resolution limit will require the use of quantum optical
effects, pointing to an avenue for future innovation.
