  First discovered by Ernest Abbe in 1873, the resolution limit of a far-field
microscope is considered determined by the numerical aperture and wavelength of
light, approximately $\lambda$/2NA. With the advent of modern fluorescence
microscopy and nanoscopy methods over the last century, it is recognized that
Abbe's resolution definition alone could not solely characterize the resolving
power of the microscope system. To determine the practical resolution of a
fluorescence microscope, photon noise remains one essential factor yet to be
incorporated in a statistics-based theoretical framework. Techniques such as
confocal allow trading photon noise in gaining its resolution limit, which may
increase or worsen the resolvability towards fluorescently tagged targets.
Proposed as a theoretical measure of fluorescence microscopes' resolving power
with finite photons, we quantify the resolvability of periodic structures in
fluorescence microscopy systems considering both the diffraction limit and
photon statistics. Using the Cramer-Rao Lower Bound of a parametric target, the
resulting precision lower bound establishes a practical measure of the
theoretical resolving power for various modern fluorescence microscopy methods
in the presence of noise.
